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-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/reschedule_exams.cpp161
-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/017
-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/01.a1
-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/027
-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/02.a1
-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/0310
-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/03.a1
-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/134286
-rw-r--r--05-advanced_algorithms_and_complexity/04-np-completeness/04-reschedule_exams/tests/13.a1
9 files changed, 4471 insertions, 4 deletions
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
+RGRGGBGRGBBRBGBGGGBRGGGGGBRRGRBBRRGRRBBRGRRBRRGRGRRBBRBRBBRGBBRRBBBRRBRRBBGBRRGRGGBRRGGGRGRGRRBRRRGGRGRGBBGRRRGGBRGRGGGGGRGRGRRRBGGGBBRRBGBRRRGBBBRBGBRGBBBBRBRRBGGRGGRRGGGBBRBGGBRBGRBBGGBRGBBBBRBBBGGGGBGGRBRGGRGBRRGGBGGBRBBGRGRGRRRRGGGRGRRBRBRBRRBGGRRGGRBRRBRBBBBGBRBRBRGGRRBRGGGBGRGRGBRBBBGGBRRBGBRBBGRGGGGBGRGBBBGBRRGBGRRRBGBGGGRRBRGBBRGBRRRBRRBGGGBBRRRGRGGRRGGBBRBGBRGGBBGRRGGBGGGGGGBRGBRGBBBBGBBGBBGGGGRGGGGBRRRRRRRBRRBGBRRGGGRRBBBGRRBGBBRGRRRRRGRBBGGGRRRRBBGGGRGGBGBGRBRRRGBRBBGRRRBBGGRGBRGBRGRGRRBGRGBGBBRRBGGGBGRRRBGBRRRRRBBGBBGGGGGBGGGRGBGGGGGGGGGGRRRGGGBBGBGBGBBBBBBGRGGBBBGGBRBBGBGBRGBGRRGGRBRRRRRRRRBRRGBBGGGGGRGRRRBRRBRRBBBGGBBGBGBRBBBGRBGRBGBBRRBGRBGBRBBGRBGBGGRBBBRRBRBGGGGRGRRBRBGRGBRRGGGRGBRBBGBGGRGBBBRBBRRRBGRRBRRBBBBRBBRGRBRBRGRGGBGRGGBRGGBGRRBGGRRRRBRRGGBGGGGBBRRBRBGGRGGBRRGRRBRBRRRBRGGRGBGBBBRRBBBBRBBBGGRGGGBGBGRRRGBBGGRGBRRBBRGBRGGBGRBGBRGGBBGRRGBGBRRBGRGRBRGRBRBGBRBBBGRBRRRBRRGBGBBBGGRBRGRGGBBBRGGRRBBRRGGRRGRRGRRBGGBBBGBBBGGGBRGGRRGGBBGRGBBBRRGGBBRRRRRGGRRGGGGGRRGBBBBBR
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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 @@
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