From 9d34d783c6dc1bda8f0aedfaf19485bbda67938a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=A9r=C3=A9my=20Zurcher?= <jeremy@asynk.ch>
Date: Tue, 29 Mar 2022 10:29:56 +0200
Subject: Algorithms : complete 05-advanced_algorithms_and_complexity
 04-np-completeness

---
 .../01-circuit_design/circuit_design.cpp           |     99 +-
 .../04-np-completeness/01-circuit_design/tests/00  |      6 +
 .../01-circuit_design/tests/00.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/01  |      5 +
 .../01-circuit_design/tests/01.a                   |      1 +
 .../04-np-completeness/01-circuit_design/tests/02  |      5 +
 .../01-circuit_design/tests/02.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/03  |     13 +
 .../01-circuit_design/tests/03.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/04  |      4 +
 .../01-circuit_design/tests/04.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/08  |      4 +
 .../01-circuit_design/tests/08.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/09  |     22 +
 .../01-circuit_design/tests/09.a                   |      1 +
 .../04-np-completeness/01-circuit_design/tests/10  |     11 +
 .../01-circuit_design/tests/10.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/11  |      3 +
 .../01-circuit_design/tests/11.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/12  |      5 +
 .../01-circuit_design/tests/12.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/13  |      3 +
 .../01-circuit_design/tests/13.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/14  |      2 +
 .../01-circuit_design/tests/14.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/15  |      3 +
 .../01-circuit_design/tests/15.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/16  |      2 +
 .../01-circuit_design/tests/16.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/17  |      2 +
 .../01-circuit_design/tests/17.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/18  |     13 +
 .../01-circuit_design/tests/18.a                   |      2 +
 .../04-np-completeness/01-circuit_design/tests/23  | 100001 ++++++++++++++++++
 .../01-circuit_design/tests/23.a                   |      1 +
 .../04-np-completeness/01-circuit_design/tests/66  | 100001 ++++++++++++++++++
 .../01-circuit_design/tests/66.a                   |      2 +
 .../02-plan_party/plan_party.cpp                   |     39 +-
 .../04-np-completeness/02-plan_party/tests/01      |      2 +
 .../04-np-completeness/02-plan_party/tests/01.a    |      1 +
 .../04-np-completeness/02-plan_party/tests/02      |      3 +
 .../04-np-completeness/02-plan_party/tests/02.a    |      1 +
 .../04-np-completeness/02-plan_party/tests/03      |      6 +
 .../04-np-completeness/02-plan_party/tests/03.a    |      1 +
 .../03-school_bus/school_bus.cpp                   |    103 +-
 .../04-np-completeness/03-school_bus/tests/01      |      7 +
 .../04-np-completeness/03-school_bus/tests/01.a    |      2 +
 .../04-np-completeness/03-school_bus/tests/02      |      5 +
 .../04-np-completeness/03-school_bus/tests/02.a    |      1 +
 .../04-np-completeness/03-school_bus/tests/03      |      5 +
 .../04-np-completeness/03-school_bus/tests/03.a    |      2 +
 .../04-np-completeness/03-school_bus/tests/04      |      5 +
 .../04-np-completeness/03-school_bus/tests/04.a    |      2 +
 .../04-np-completeness/03-school_bus/tests/05      |      7 +
 .../04-np-completeness/03-school_bus/tests/05.a    |      2 +
 .../04-np-completeness/03-school_bus/tests/06      |      8 +
 .../04-np-completeness/03-school_bus/tests/06.a    |      2 +
 .../04-np-completeness/03-school_bus/tests/07      |      4 +
 .../04-np-completeness/03-school_bus/tests/08      |      7 +
 .../04-np-completeness/03-school_bus/tests/08.a    |      2 +
 .../04-reschedule_exams/reschedule_exams.cpp       |    161 +-
 .../04-reschedule_exams/tests/01                   |      7 +
 .../04-reschedule_exams/tests/01.a                 |      1 +
 .../04-reschedule_exams/tests/02                   |      7 +
 .../04-reschedule_exams/tests/02.a                 |      1 +
 .../04-reschedule_exams/tests/03                   |     10 +
 .../04-reschedule_exams/tests/03.a                 |      1 +
 .../04-reschedule_exams/tests/13                   |   4286 +
 .../04-reschedule_exams/tests/13.a                 |      1 +
 .../04-np-completeness/URL                         |      5 +
 .../04-np-completeness/check                       |     45 +
 71 files changed, 204936 insertions(+), 43 deletions(-)
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/00
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/00.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/01
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/01.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/02
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/02.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/03
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/03.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/04
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/04.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/08
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/08.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/09
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/09.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/10
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/10.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/11
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/11.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/12
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/12.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/13
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/13.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/14
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/14.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/15
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/15.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/16
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/16.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/17
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/17.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/18
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/18.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/23
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/23.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/66
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/66.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/01
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/01.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/02
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/02.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/03
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/03.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/01
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/01.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/02
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/02.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/03
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/03.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/04
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/04.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/05
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/05.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/06
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/06.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/07
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/08
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/08.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13.a
 create mode 100644 05-advanced_algorithms_and_complexity/04-np-completeness/URL
 create mode 100755 05-advanced_algorithms_and_complexity/04-np-completeness/check

diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/circuit_design.cpp b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/circuit_design.cpp
index afc1a9f..2768e93 100644
--- a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/circuit_design.cpp
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/circuit_design.cpp
@@ -6,45 +6,90 @@ struct Clause {
     int secondVar;
 };
 
+struct Vertex {
+    int index;
+    int lowLink;
+    bool onStack;
+};
+
 struct TwoSatisfiability {
     int numVars;
+    int x;
     vector<Clause> clauses;
+    stack<int> st;
+    vector<Vertex> vertices;
+    vector<vector<int> > adj;
 
     TwoSatisfiability(int n, int m) :
         numVars(n),
-        clauses(m)
-    {  }
+        clauses(m),
+        x(0),
+        vertices(n * 2, {-1, -1, false}),
+        adj(n * 2, vector<int>())
+    {
+    }
 
-    bool isSatisfiable(vector<int>& result) {
-        // This solution tries all possible 2^n variable assignments.
-        // It is too slow to pass the problem.
-        // Implement a more efficient algorithm here.
-        for (int mask = 0; mask < (1 << numVars); ++mask) {
-            for (int i = 0; i < numVars; ++i) {
-                result[i] = (mask >> i) & 1;
+    // bool tarjan(int &x, int i, vector<int> &result) {
+    bool tarjan(int i, vector<int> &result) {
+        Vertex &v = vertices[i];
+        v.index = x;
+        v.lowLink = x;
+        v.onStack = true;
+        st.push(i);
+        x++;
+        for (int a : adj[i]) {
+            Vertex &w = vertices[a];
+            if (w.index == -1) {
+                if (!tarjan(a, result)) return false;
+                v.lowLink = min(v.lowLink, w.lowLink);
+            } else if (w.onStack) {
+                v.lowLink = min(v.lowLink, w.index);
             }
-
-            bool formulaIsSatisfied = true;
-
-            for (const Clause& clause: clauses) {
-                bool clauseIsSatisfied = false;
-                if (result[abs(clause.firstVar) - 1] == (clause.firstVar < 0)) {
-                    clauseIsSatisfied = true;
-                }
-                if (result[abs(clause.secondVar) - 1] == (clause.secondVar < 0)) {
-                    clauseIsSatisfied = true;
+        }
+        // is a SCC root node
+        if (v.lowLink == v.index) {
+            for (;;) {
+                int i = st.top();
+                int iv = inv(i);
+                if (vertices[iv].index == v.index) return false;
+                st.pop();
+                if (i < numVars) {
+                    if (result[i] == -1)
+                        result[i] = 1;
+                } else {
+                    if (result[iv] == -1)
+                        result[iv] = 0;
                 }
-                if (!clauseIsSatisfied) {
-                    formulaIsSatisfied = false;
+                vertices[i].onStack = false;
+                if (vertices[i].index == v.index) {
                     break;
                 }
             }
+        }
+        return true;
+    }
 
-            if (formulaIsSatisfied) {
-                return true;
+    inline int idx(int v) { return (v > 0 ? (v - 1) : (numVars - v - 1)); }
+    inline int inv(int i) { return i + ((i < numVars) ? numVars : -numVars); }
+
+    bool isSatisfiable(vector<int>& result) {
+
+        // construct the implication graph        (l1 l2) -> !l1 ->l2 !l2->l1
+        for(Clause clause : clauses) {
+            adj[idx(-clause.firstVar)].push_back(idx(clause.secondVar));
+            adj[idx(-clause.secondVar)].push_back(idx(clause.firstVar));
+        }
+
+        // find SCC's of graph
+        // int x = 0;
+        for (int i = 0; i < vertices.size(); i++) {
+            Vertex &v = vertices[i];
+            if (v.index == -1)  {
+                if (!tarjan(i, result)) return false;
             }
         }
-        return false;
+
+        return true;
     }
 };
 
@@ -58,14 +103,14 @@ int main() {
         cin >> twoSat.clauses[i].firstVar >> twoSat.clauses[i].secondVar;
     }
 
-    vector<int> result(n);
+    vector<int> result(n, -1);
     if (twoSat.isSatisfiable(result)) {
         cout << "SATISFIABLE" << endl;
         for (int i = 1; i <= n; ++i) {
             if (result[i-1]) {
-                cout << -i;
-            } else {
                 cout << i;
+            } else {
+                cout << -i;
             }
             if (i < n) {
                 cout << " ";
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/00 b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/00
new file mode 100644
index 0000000..48012ce
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/00
@@ -0,0 +1,6 @@
+4 5
+1 2
+2 3
+3 4
+-1 -3
+-2 -4
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/00.a b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/00.a
new file mode 100644
index 0000000..c46e332
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/00.a
@@ -0,0 +1,2 @@
+SATISFIABLE
+-1 2 3 -4
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/01 b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/01
new file mode 100644
index 0000000..ad5974a
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/01
@@ -0,0 +1,5 @@
+2 4
+1 2
+-1 2
+-2 1
+-1 -2
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/01.a b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/01.a
new file mode 100644
index 0000000..bb10104
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/01.a
@@ -0,0 +1 @@
+UNSATISFIABLE
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/02 b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/02
new file mode 100644
index 0000000..5336e74
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/02
@@ -0,0 +1,5 @@
+2 4
+1 2
+-1 2
+2 -1
+-1 -2
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/02.a b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/02.a
new file mode 100644
index 0000000..5c4ced5
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/02.a
@@ -0,0 +1,2 @@
+SATISFIABLE
+-1 2
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/03 b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/03
new file mode 100644
index 0000000..b72bba2
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/03
@@ -0,0 +1,13 @@
+8 12
+1 4
+-2 5
+3 7
+2 -5
+-8 -2
+3 -1
+4 -3
+5 -4
+-3 -7
+6 7
+1 7
+-7 -1
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/03.a b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/03.a
new file mode 100644
index 0000000..61e7cb1
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/03.a
@@ -0,0 +1,2 @@
+SATISFIABLE
+1 2 3 4 5 6 -7 -8
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/04 b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/04
new file mode 100644
index 0000000..cfb1c7d
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/04
@@ -0,0 +1,4 @@
+3 3
+1 -3
+-1 2
+-2 -3
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/04.a b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/04.a
new file mode 100644
index 0000000..4369989
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/04.a
@@ -0,0 +1,2 @@
+SATISFIABLE
+1 2 -3
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/08 b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/08
new file mode 100644
index 0000000..cfb1c7d
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/08
@@ -0,0 +1,4 @@
+3 3
+1 -3
+-1 2
+-2 -3
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/08.a b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/08.a
new file mode 100644
index 0000000..4369989
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/08.a
@@ -0,0 +1,2 @@
+SATISFIABLE
+1 2 -3
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/09 b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/09
new file mode 100644
index 0000000..d8e5420
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/09
@@ -0,0 +1,22 @@
+21 9
+1 4 0
+-1 -4 0
+-1 -7 0
+-4 -7 0
+2 8 0
+-2 -5 0
+-2 -8 0
+-5 -8 0
+3 9 0
+-3 -6 0
+-3 -9 0
+-6 -9 0
+-1 -2 0
+-4 -5 0
+-7 -8 0
+-2 -3 0
+-5 -6 0
+-8 -9 0
+-3 -1 0
+-6 -4 0
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diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/23.a b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/23.a
new file mode 100644
index 0000000..bb10104
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/23.a
@@ -0,0 +1 @@
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diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/66 b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/66
new file mode 100644
index 0000000..05584c2
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/66
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diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/66.a b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/66.a
new file mode 100644
index 0000000..7571f81
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/01-circuit_design/tests/66.a
@@ -0,0 +1,2 @@
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diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/plan_party.cpp b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/plan_party.cpp
index 70249aa..f612252 100644
--- a/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/plan_party.cpp
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/plan_party.cpp
@@ -1,5 +1,6 @@
 #include <iostream>
 #include <vector>
+#include <sys/resource.h>
 
 struct Vertex {
     int weight;
@@ -27,23 +28,39 @@ Graph ReadTree() {
     return tree;
 }
 
-void dfs(const Graph &tree, int vertex, int parent) {
-    for (int child : tree[vertex].children)
-        if (child != parent)
-            dfs(tree, child, vertex);
-
-    // This is a template function for processing a tree using depth-first search.
-    // Write your code here.
-    // You may need to add more parameters to this function for child processing.
+int dfs(const Graph &tree, int vertex, int parent, std::vector<int> &w) {
+    if ( w[vertex] == -1) {
+        if (tree[vertex].children.size() == 0) {
+            w[vertex] = tree[vertex].weight;
+        } else {
+            int m0 = tree[vertex].weight;
+            for (int child : tree[vertex].children) {
+                if (child != parent) {
+                    for (int gchild : tree[child].children) {
+                        if (gchild != child && gchild != vertex) {
+                            m0 += dfs(tree, gchild, child, w);
+                        }
+                    }
+                }
+            }
+            int m1 = 0;
+            for (int child : tree[vertex].children) {
+                if (child != parent) {
+                    m1 += dfs(tree, child, vertex, w);
+                }
+            }
+            w[vertex] = std::max(m0, m1);
+        }
+    }
+    return w[vertex];
 }
 
 int MaxWeightIndependentTreeSubset(const Graph &tree) {
     size_t size = tree.size();
     if (size == 0)
         return 0;
-    dfs(tree, 0, -1);
-    // You must decide what to return.
-    return 0;
+    std::vector<int> w(size, -1);
+    return dfs(tree, 0, -1, w);
 }
 
 int main() {
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/01 b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/01
new file mode 100644
index 0000000..4f88743
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/01
@@ -0,0 +1,2 @@
+1
+1000
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/01.a b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/01.a
new file mode 100644
index 0000000..83b33d2
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/01.a
@@ -0,0 +1 @@
+1000
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/02 b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/02
new file mode 100644
index 0000000..0777210
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/02
@@ -0,0 +1,3 @@
+2
+1 2
+1 2
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/02.a b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/02.a
new file mode 100644
index 0000000..0cfbf08
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/02.a
@@ -0,0 +1 @@
+2
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/03 b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/03
new file mode 100644
index 0000000..4867a3e
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/03
@@ -0,0 +1,6 @@
+5
+1 5 3 7 5
+5 4
+2 3
+4 2
+1 2
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/03.a b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/03.a
new file mode 100644
index 0000000..b4de394
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/02-plan_party/tests/03.a
@@ -0,0 +1 @@
+11
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/school_bus.cpp b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/school_bus.cpp
index 26bd942..14848e0 100644
--- a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/school_bus.cpp
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/school_bus.cpp
@@ -20,7 +20,7 @@ Matrix read_data() {
     return graph;
 }
 
-std::pair<int, vector<int> > optimal_path(const Matrix& graph) {
+std::pair<int, vector<int> > optimal_path_(const Matrix& graph) {
     // This solution tries all the possible sequences of stops.
     // It is too slow to pass the problem.
     // Implement a more efficient algorithm here.
@@ -60,6 +60,107 @@ std::pair<int, vector<int> > optimal_path(const Matrix& graph) {
     return std::make_pair(best_ans, best_path);
 }
 
+struct Memory {
+    int w; int c; int r;
+};
+
+std::pair<int, vector<int> > optimal_path(const Matrix& graph) {
+
+    int n = graph.size();   // edges
+    int m = (1 << n);       // max combinations
+    vector<vector<Memory>> cost(m, vector<Memory>(n, {INF, 0, 0}));
+    cost[0][0] = {0, -1, -1};
+
+    // C(S, i) be the cost of the minimum cost path visiting each vertex in set S exactly once, starting at 1 and ending at i.
+    // If size of S is 2, then S must be {1, i},
+    //    C(S, i) = dist(1, i)
+    for (int i = 1; i < n; i++) {
+        int sid = (1 << i) + 1;
+        int v = graph[0][i];
+        if (v != INF) {
+            cost[sid][i] = {v, 0, 0};
+            // std::cout << "   set : ["<< sid << "][" << i << "] = " << cost[sid][i].w << std::endl;
+        }
+    }
+
+    // Else if size of S is greater than 2.
+    //    C(S, i) = min { C(S-{i}, j) + dis(j, i)} where j belongs to S, j != i and j != 1.
+    // Note that 1 must be present in every subset S, so 1 less bit:
+    m = (1 << (n - 1));
+    for (int s = 2; s <= n; s++) {
+        // std::cout << " size : " << s << std::endl;
+        // loop from 0 ..m, with n=5, s=2 => 110, 101, 011
+        for (int b = 0; b < m; b++) {
+            int nb = 0;
+            int v = b;
+            while(v) {
+                nb += (v & 1);  // check last bit
+                v >>= 1;        // shift
+            }
+            if (nb != s) {
+                continue;
+            }
+            // shift them and add 1 -> 1100, 1010, 0110
+            int bits = (b << 1);
+            // std::cout << "   bits : " << bits << std::endl;
+            for (int i = 1; i < n; i++) { // not 0 it's our start
+                if (bits & (1 << i)) {
+                    for (int j = 0; j < n; j++) {
+                        if (j != i && (bits & (1 << j))) {  // do not stay on the same vertex
+                            int k = bits + 1;
+                            int nk = (bits ^ (1 << i)) + 1;
+                            // std::cout << "       try : " << nk << "->" << j << "->" << i <<std::endl;
+                            int c = cost[nk][j].w + graph[j][i];
+                            if (c < cost[k][i].w) {
+                                cost[k][i] = {c, nk, j};
+                                // std::cout << "   set : ["<< k << "][" << i << "] = " << c << std::endl;
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+    // std::cout << std::endl;
+    // for (auto &row : cost) {
+    //     for(auto &m : row) {
+    //         std::cout << "   " << (m.w == INF ? 0 : m.w) << " (" << m.c << ";" << m.r << ") ";
+    //     }
+    //     std::cout << std::endl;
+    // }
+    // std::cout << std::endl;
+
+    int best = INF;
+    vector<int> path;
+
+    auto &last_row = cost[(1 << n) - 1];
+    Memory& last_m = cost[0][0];
+    int j;
+    for (int i = 0; i < cost[0].size(); i++) {
+        auto &cell = last_row[i];
+        int c = cell.w + graph[i][0];
+        if (c < best) {
+            j = i;
+            best = c;
+            last_m = cell;
+        }
+    }
+    if (best == INF) {
+        best = -1;
+    } else {
+        path.push_back(j + 1);
+        while(last_m.r > 0) {
+            // std::cout << last_m.w << " " << last_m.c << " " << last_m.r << std::endl;
+            path.push_back(last_m.r + 1);
+            last_m = cost[last_m.c][last_m.r];
+        }
+        path.push_back(1);
+    }
+    std::reverse(std::begin(path), std::end(path));
+
+    return std::make_pair(best, path);
+}
+
 void print_answer(const std::pair<int, vector<int> >& answer) {
     std::cout << answer.first << "\n";
     if (answer.first == -1)
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/01 b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/01
new file mode 100644
index 0000000..0c9a76d
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/01
@@ -0,0 +1,7 @@
+4 6
+1 2 20
+1 3 42
+1 4 35
+2 3 30
+2 4 34
+3 4 12
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/01.a b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/01.a
new file mode 100644
index 0000000..27d0ecd
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/01.a
@@ -0,0 +1,2 @@
+97
+1 4 3 2 
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/02 b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/02
new file mode 100644
index 0000000..68e1c9f
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/02
@@ -0,0 +1,5 @@
+4 4
+1 2 1
+2 3 4
+3 4 5
+4 2 1
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/02.a b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/02.a
new file mode 100644
index 0000000..3a2e3f4
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/02.a
@@ -0,0 +1 @@
+-1
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/03 b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/03
new file mode 100644
index 0000000..51dbfa3
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/03
@@ -0,0 +1,5 @@
+4 4
+1 3 6
+1 4 2
+2 3 6
+2 4 2
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/03.a b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/03.a
new file mode 100644
index 0000000..a18caef
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/03.a
@@ -0,0 +1,2 @@
+16
+1 4 2 3 
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/04 b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/04
new file mode 100644
index 0000000..0e84957
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/04
@@ -0,0 +1,5 @@
+4 4
+1 2 1
+1 4 2
+2 3 2
+3 4 6
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/04.a b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/04.a
new file mode 100644
index 0000000..57181c1
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/04.a
@@ -0,0 +1,2 @@
+11
+1 4 3 2 
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/05 b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/05
new file mode 100644
index 0000000..bec5ee5
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/05
@@ -0,0 +1,7 @@
+5 6
+1 2 3
+1 3 1
+1 5 5
+2 5 9
+3 4 8
+4 5 5
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/05.a b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/05.a
new file mode 100644
index 0000000..8229c1a
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/05.a
@@ -0,0 +1,2 @@
+26
+1 3 4 5 2 
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/06 b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/06
new file mode 100644
index 0000000..c37302e
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/06
@@ -0,0 +1,8 @@
+5 7
+1 2 1
+1 4 9
+2 4 1
+2 5 9
+3 4 6
+3 5 8
+4 5 1
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/06.a b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/06.a
new file mode 100644
index 0000000..c426ac6
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/06.a
@@ -0,0 +1,2 @@
+33
+1 4 3 5 2 
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/07 b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/07
new file mode 100644
index 0000000..f6b5137
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/07
@@ -0,0 +1,4 @@
+3 3
+1 2 2
+2 3 3
+3 1 1
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/08 b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/08
new file mode 100644
index 0000000..4307f22
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/08
@@ -0,0 +1,7 @@
+4 6
+1 2 12
+1 3 30
+1 4 42
+2 3 34
+2 4 35
+3 4 20
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/08.a b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/08.a
new file mode 100644
index 0000000..ea1553b
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/03-school_bus/tests/08.a
@@ -0,0 +1,2 @@
+97
+1 3 4 2 
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/reschedule_exams.cpp b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/reschedule_exams.cpp
index b3ff8eb..5a3a875 100644
--- a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/reschedule_exams.cpp
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/reschedule_exams.cpp
@@ -1,8 +1,104 @@
 #include <iostream>
 #include <vector>
 #include <string>
+#include <bits/stdc++.h>
 using namespace std;
 
+struct Clause {
+    int firstVar;
+    int secondVar;
+};
+
+struct Vertex {
+    int index;
+    int lowLink;
+    bool onStack;
+};
+
+struct TwoSatisfiability {
+    int numVars;
+    int x;
+    vector<Clause> &clauses;
+    stack<int> st;
+    vector<Vertex> vertices;
+    vector<vector<int> > adj;
+
+    TwoSatisfiability(int n, vector<Clause> &clauses) :
+        numVars(n),
+        clauses(clauses),
+        x(0),
+        vertices(n * 2, {-1, -1, false}),
+        adj(n * 2, vector<int>())
+    {
+    }
+
+    bool tarjan(int i, vector<int> &result) {
+        Vertex &v = vertices[i];
+        v.index = x;
+        v.lowLink = x;
+        v.onStack = true;
+        st.push(i);
+        x++;
+        for (int a : adj[i]) {
+            Vertex &w = vertices[a];
+            if (w.index == -1) {
+                if (!tarjan(a, result)) return false;
+                v.lowLink = min(v.lowLink, w.lowLink);
+            } else if (w.onStack) {
+                v.lowLink = min(v.lowLink, w.index);
+            }
+        }
+        // is a SCC root node
+        if (v.lowLink == v.index) {
+            for (;;) {
+                int i = st.top();
+                int iv = inv(i);
+                if (vertices[iv].index == v.index) return false;
+                st.pop();
+                if (i < numVars) {
+                    if (result[i] == -1)
+                        result[i] = 1;
+                } else {
+                    if (result[iv] == -1)
+                        result[iv] = 0;
+                }
+                vertices[i].onStack = false;
+                if (vertices[i].index == v.index) {
+                    break;
+                }
+            }
+        }
+        return true;
+    }
+
+    inline int idx(int v) { return (v > 0 ? (v - 1) : (numVars - v - 1)); }
+    inline int inv(int i) { return i + ((i < numVars) ? numVars : -numVars); }
+
+    bool isSatisfiable(vector<int>& result) {
+
+        // construct the implication graph        (l1 l2) -> !l1 ->l2 !l2->l1
+        for(Clause clause : clauses) {
+            adj[idx(-clause.firstVar)].push_back(idx(clause.secondVar));
+            adj[idx(-clause.secondVar)].push_back(idx(clause.firstVar));
+        }
+
+        // find SCC's of graph
+        // int x = 0;
+        for (int i = 0; i < vertices.size(); i++) {
+            Vertex &v = vertices[i];
+            if (v.index == -1)  {
+                if (!tarjan(i, result)) return false;
+            }
+        }
+
+        return true;
+    }
+};
+
+enum Color { R=1, G, B };
+
+static inline int var(int vertex, int color) { return vertex * 3 + color; }
+
 /*
   Arguments:
     * `n` - the number of vertices.
@@ -13,11 +109,68 @@ using namespace std;
     * Otherwise, return value is an empty string.
 */
 string assign_new_colors(int n, vector<pair<int, int>> edges, string colors) {
-    // Insert your code here.
-    if (n % 3 == 0) {
+
+    // cout << " N      : " << n << endl;
+    // cout << " edges  : " << edges.size() << endl;
+    // cout << " colors : " << colors << endl;
+
+    int vars = 3 * n;
+    vector<Clause> clauses;
+
+    // for each vertex
+    for (int i = 0; i < n; i++) {
+        //  each node must be of a different color than its initial state
+        int v1, v2, v3;
+        if (colors[i] == 'R') {
+            v1 = var(i, R);
+            v2 = var(i, G);
+            v3 = var(i, B);
+        } else if (colors[i] == 'G') {
+            v1 = var(i, G);
+            v2 = var(i, B);
+            v3 = var(i, R);
+        } else {
+            v1 = var(i, B);
+            v2 = var(i, R);
+            v3 = var(i, G);
+        }
+        clauses.push_back({-v1, -v1}); // !1 || !1 => different from initial color
+        clauses.push_back({ v2,  v3}); //  2 ||  3 => one of the other
+        clauses.push_back({-v2, -v3}); // !2 || !3 => not both
+    }
+    //  both node of an edge cannot be of the same color
+    for (auto &p : edges) {
+        int i = p.first - 1;
+        int j = p.second - 1;
+        clauses.push_back({-var(i, R), -var(j, R)});
+        clauses.push_back({-var(i, G), -var(j, G)});
+        clauses.push_back({-var(i, B), -var(j, B)});
+    }
+
+    // cout << "clauses : " << clauses.size() << endl;
+    // cout << "vars    : " << vars << endl;
+    TwoSatisfiability twoSat(vars, clauses);
+
+    vector<int> result(vars, -1);
+    if (twoSat.isSatisfiable(result)) {
+        // cout << "SATISFIABLE" << endl;
+        // for (int i = 1; i <= vars; ++i) {
+        //     if (result[i-1]) {
+        //         cout << i;
+        //     } else {
+        //         cout << -i;
+        //     }
+        //     if (i < vars) {
+        //         cout << " ";
+        //     } else {
+        //         cout << endl;
+        //     }
+        // }
         string new_colors;
-        for (int i = 0; i < n; i++) {
-            new_colors.push_back("RGB"[i % 3]);
+        for (int i = 0; i < vars; ++i) {
+            if (result[i]) {
+                new_colors.push_back("RGB"[i % 3]);
+            }
         }
         return new_colors;
     } else {
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01 b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01
new file mode 100644
index 0000000..5580d77
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01
@@ -0,0 +1,7 @@
+4 5
+RRRG
+1 3
+1 4
+3 4
+2 4
+2 3
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01.a b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01.a
new file mode 100644
index 0000000..cc16375
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01.a
@@ -0,0 +1 @@
+GGBR
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02 b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02
new file mode 100644
index 0000000..121c83a
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02
@@ -0,0 +1,7 @@
+4 5
+RGRR
+1 3
+1 4
+3 4
+2 4
+2 3
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02.a b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02.a
new file mode 100644
index 0000000..21454ad
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02.a
@@ -0,0 +1 @@
+Impossible
\ No newline at end of file
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03 b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03
new file mode 100644
index 0000000..f58eeb9
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03
@@ -0,0 +1,10 @@
+7 8
+GBGBRBR
+1 3
+3 2
+3 4
+4 6
+2 6
+4 5
+5 6
+1 2
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03.a b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03.a
new file mode 100644
index 0000000..c6ddcd6
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03.a
@@ -0,0 +1 @@
+RGBGBRG
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13 b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13
new file mode 100644
index 0000000..d4d7e91
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13
@@ -0,0 +1,4286 @@
+997 4284
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diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13.a b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13.a
new file mode 100644
index 0000000..30fd83d
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13.a
@@ -0,0 +1 @@
+BRGRBGRBRRGBRBGRBRGBRBBRBRGGBBRRGBRGBRGGRBGRGGBGRBBGGBGGRRGBRRGBRGRBBGGBRGBGGBRGRBGGBRBRGBGRBGRGBBRBGRGBRRBGGBRBGGRGBRRBBGRGRBBGRRBBRGBGRRRBGBRGGGBGRRGBRRGRBGBGGRBGRRGBRBBGRGRBRGBRBBRGRRGGBRGRGBRRGRBBRGRBBRGRBGRRGBRBGRBRBGRRGBGRGBGBRBRGBBGRBRBRGGRRBGGBRBGGBRBGRGRBRGRGRBRBGBGGRBRGBGBGBRBRGGBRRGBRRGBRGRGBRRBGRGBRGGBRGBRRBGGBRBGBRRBGGGBRGGRRBGBRBGRBRBRGBBBRGRBGBRBGGBRBRGRBRGBGBRBGRBRBRBGBRGGBGRRGBRGBGRRBRRGBBRBGGBGBGBGRGBRBGGBRRBGBRGRBGGRBRRGRGBGGBRBRGBRBGBGBRGBRRGBRRBGRGRBGGBRBRGBGBBGRRRGBGBBRGRGRBBRBGBRBRGGGRBRRGBGGGRBRGBGGBRGBRGBRBRRGBRBGRGBBRRBRBRRBGGBBBRRGRGBRBGRGRRRBGRBRGGBRGBGRBGRRGBRRGBRRBGGBBGGBGBRBGBRGBRBRBGRBBGRGBRBBGRGRBRGBRBGGGRGBBGRBGRRGBGGRGRBRBGRBBGRGRBGRGRBBGGRBRBRGRBGRBRBBRGGBRBBGBGBGRRGBRBRGGRBRGBGGGRBGRGBRGRGBGRGBGRBRGBGBRGBGBRGGBRGRBGRRBGBBGRGBRBGRBRBGRBGGBRBBGRBRGBRBGRBRGGBRGBRBBGRGRGGBRGRGBRRGBRGBBRGBRBGBBRGGRRGBRBBGRGBRGRBRBBGRGBRRGGBGBRGBGGGRRBBGRGRBGGRBRBGRRBGRGGBGGBRRBRRGRBGGBRBRBRGGGRBGBRGGBRBGBBGBRGBGBRGRGBGRGRBBGGRBGBRBRGRBRGRGGBRBGRBGGBGRBGBRRBRRBGBGRRRGB
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/URL b/05-advanced_algorithms_and_complexity/04-np-completeness/URL
new file mode 100644
index 0000000..e3d5188
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/URL
@@ -0,0 +1,5 @@
+https://github.com/BessieChen/Coursera-Advanced-Algorithms-and-Complexity/tree/master/week4-Assignment-4
+
+https://courses.engr.illinois.edu/cs473/sp2011/Lectures/09_handout.pdf
+
+https://www.youtube.com/watch?v=-JjA4BLQyqE
diff --git a/05-advanced_algorithms_and_complexity/04-np-completeness/check b/05-advanced_algorithms_and_complexity/04-np-completeness/check
new file mode 100755
index 0000000..796234d
--- /dev/null
+++ b/05-advanced_algorithms_and_complexity/04-np-completeness/check
@@ -0,0 +1,45 @@
+#! /bin/bash
+
+RESET="\033[0m"
+RED="\033[0;31m"
+GREEN="\033[0;32m"
+BROWN="\033[0;33m"
+
+BIN=/tmp/bin
+OUTA=/tmp/_outa
+OUTB=/tmp/_outb
+# GPP_OPTS="-std=c++11 -O0 -ggdb"
+GPP_OPTS="-std=c++11 -O2"
+
+for path in $(find . -name \*.cpp | sort); do
+    src=${path##*/}
+    dir=${path%/*}
+    echo -e "${RED}validate $BROWN$dir$RESET/$GREEN$src$RESET"
+    pushd $dir >/dev/null || exit 1
+    # sed -i 's/^#define DEBUG 1/\/\/ #define DEBUG 1/' $src
+    echo -e "   ${RED}compile $GREEN$src$RESET" && g++ $GPP_OPTS $src -o $BIN || exit 1
+    if [ -d tests ]; then
+        start=`date +%s.%N`
+        echo -e "   ${RED}check $GREEN$src$RESET"
+        for t in $(find ./tests -name "*[^a~]"|sort); do
+            if [ -f $t -a -f "$t.a" ]; then
+                cat $t | $BIN 2>/dev/null > $OUTA || echo "segfault"
+                cat $t.a > $OUTB
+                cmp $OUTA $OUTB >/dev/null
+                if [ $? -ne 0 ]; then
+                    echo -e "     $BROWN$t$RESET is ${RED}KO$RESET"
+                    cat $OUTA
+                    cat $OUTB
+                else
+                    echo -e "     $BROWN$t$RESET is ${GREEN}ok$RESET"
+                fi
+            fi
+        done
+        end=`date +%s.%N`
+        echo "runtime : $(echo "$end - $start" | bc -l)"
+    else
+        echo -e "   ${RED}no tests$RESET"
+    fi
+    popd > /dev/null
+done
+
-- 
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