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| author | Jérémy Zurcher <jeremy@asynk.ch> | 2016-11-14 07:05:58 +0100 |
|---|---|---|
| committer | Jérémy Zurcher <jeremy@asynk.ch> | 2016-11-14 07:05:58 +0100 |
| commit | a3cf12ef675023fc864c364bf3c78dcbf0400891 (patch) | |
| tree | edcd79ef9401ec8f28c344414f8b75301d7e17bb | |
| parent | 52041be8af3d321f07feb27fbba70b364d72c10a (diff) | |
| download | coursera-a3cf12ef675023fc864c364bf3c78dcbf0400891.zip coursera-a3cf12ef675023fc864c364bf3c78dcbf0400891.tar.gz | |
Algorithms : add 05-advanced_algorithms_and_complexity 01-flows_in_networks
211 files changed, 45498 insertions, 0 deletions
diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/00_flows_In_Networks.pdf b/05-advanced_algorithms_and_complexity/01-flows_in_networks/00_flows_In_Networks.pdf Binary files differnew file mode 100644 index 0000000..a742745 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/00_flows_In_Networks.pdf diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/evacuation.cpp b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/evacuation.cpp new file mode 100644 index 0000000..db0dfe8 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/evacuation.cpp @@ -0,0 +1,83 @@ +#include <iostream> +#include <vector> + +using std::vector; + +/* This class implements a bit unusual scheme for storing edges of the graph, + * in order to retrieve the backward edge for a given edge quickly. */ +class FlowGraph { +public: + struct Edge { + int from, to, capacity, flow; + }; + +private: + /* List of all - forward and backward - edges */ + vector<Edge> edges; + + /* These adjacency lists store only indices of edges in the edges list */ + vector<vector<size_t> > graph; + +public: + explicit FlowGraph(size_t n): graph(n) {} + + void add_edge(int from, int to, int capacity) { + /* Note that we first append a forward edge and then a backward edge, + * so all forward edges are stored at even indices (starting from 0), + * whereas backward edges are stored at odd indices in the list edges */ + Edge forward_edge = {from, to, capacity, 0}; + Edge backward_edge = {to, from, 0, 0}; + graph[from].push_back(edges.size()); + edges.push_back(forward_edge); + graph[to].push_back(edges.size()); + edges.push_back(backward_edge); + } + + size_t size() const { + return graph.size(); + } + + const vector<size_t>& get_ids(int from) const { + return graph[from]; + } + + const Edge& get_edge(size_t id) const { + return edges[id]; + } + + void add_flow(size_t id, int flow) { + /* To get a backward edge for a true forward edge (i.e id is even), we should get id + 1 + * due to the described above scheme. On the other hand, when we have to get a "backward" + * edge for a backward edge (i.e. get a forward edge for backward - id is odd), id - 1 + * should be taken. + * + * It turns out that id ^ 1 works for both cases. Think this through! */ + edges[id].flow += flow; + edges[id ^ 1].flow -= flow; + } +}; + +FlowGraph read_data() { + int vertex_count, edge_count; + std::cin >> vertex_count >> edge_count; + FlowGraph graph(vertex_count); + for (int i = 0; i < edge_count; ++i) { + int u, v, capacity; + std::cin >> u >> v >> capacity; + graph.add_edge(u - 1, v - 1, capacity); + } + return graph; +} + +int max_flow(FlowGraph& graph, int from, int to) { + int flow = 0; + return flow; +} + +int main() { + std::ios_base::sync_with_stdio(false); + FlowGraph graph = read_data(); + + std::cout << max_flow(graph, 0, graph.size() - 1) << "\n"; + return 0; +} diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/01 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/01 new file mode 100644 index 0000000..ecd4e79 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/01 @@ -0,0 +1,8 @@ +5 7 +1 2 2 +2 5 5 +1 3 6 +3 4 2 +4 5 1 +3 2 3 +2 4 1 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/01.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/01.a new file mode 100644 index 0000000..1e8b314 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/01.a @@ -0,0 +1 @@ +6 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/02 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/02 new file mode 100644 index 0000000..9f9263c --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/02 @@ -0,0 +1,6 @@ +4 5 +1 2 10000 +1 3 10000 +2 3 1 +3 4 10000 +2 4 10000 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/02.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/02.a new file mode 100644 index 0000000..b92677e --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/02.a @@ -0,0 +1 @@ +20000 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/03 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/03 new file mode 100644 index 0000000..a74b3c2 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/03 @@ -0,0 +1 @@ +2 0 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/03.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/03.a new file mode 100644 index 0000000..573541a --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/03.a @@ -0,0 +1 @@ +0 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/04 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/04 new file mode 100644 index 0000000..1128d51 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/04 @@ -0,0 +1,6 @@ +2 5 +1 1 10000 +1 2 1 +1 2 4 +1 2 100 +2 1 900 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/04.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/04.a new file mode 100644 index 0000000..f96ac06 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/04.a @@ -0,0 +1 @@ +105 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/05 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/05 new file mode 100644 index 0000000..3461ded --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/05 @@ -0,0 +1,2 @@ +2 1 +1 2 10000 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/05.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/05.a new file mode 100644 index 0000000..5caff40 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/05.a @@ -0,0 +1 @@ +10000 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/06 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/06 new file mode 100644 index 0000000..6bb8fcc --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/06 @@ -0,0 +1,2 @@ +2 1 +1 2 5 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/06.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/06.a new file mode 100644 index 0000000..7ed6ff8 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/06.a @@ -0,0 +1 @@ +5 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/07 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/07 new file mode 100644 index 0000000..3401e51 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/07 @@ -0,0 +1,7 @@ +5 6 +1 2 10000 +2 3 1 +2 4 10000 +4 3 10000 +2 5 10000 +3 5 10000 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/07.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/07.a new file mode 100644 index 0000000..5caff40 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/07.a @@ -0,0 +1 @@ +10000 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/01-evacuation/tests/08 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-0,0 +1 @@ +411960 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/airline_crews.cpp b/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/airline_crews.cpp new file mode 100644 index 0000000..46765ea --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/airline_crews.cpp @@ -0,0 +1,66 @@ +#include <iostream> +#include <vector> +#include <algorithm> +#include <memory> + +using std::vector; +using std::cin; +using std::cout; + +class MaxMatching { + public: + void Solve() { + vector<vector<bool>> adj_matrix = ReadData(); + vector<int> matching = FindMatching(adj_matrix); + WriteResponse(matching); + } + + private: + vector<vector<bool>> ReadData() { + int num_left, num_right; + cin >> num_left >> num_right; + vector<vector<bool>> adj_matrix(num_left, vector<bool>(num_right)); + for (int i = 0; i < num_left; ++i) + for (int j = 0; j < num_right; ++j) { + int bit; + cin >> bit; + adj_matrix[i][j] = (bit == 1); + } + return adj_matrix; + } + + void WriteResponse(const vector<int>& matching) { + for (int i = 0; i < matching.size(); ++i) { + if (i > 0) + cout << " "; + if (matching[i] == -1) + cout << "-1"; + else + cout << (matching[i] + 1); + } + cout << "\n"; + } + + vector<int> FindMatching(const vector<vector<bool>>& adj_matrix) { + // Replace this code with an algorithm that finds the maximum + // matching correctly in all cases. + int num_left = adj_matrix.size(); + int num_right = adj_matrix[0].size(); + vector<int> matching(num_left, -1); + vector<bool> busy_right(num_right, false); + for (int i = 0; i < num_left; ++i) + for (int j = 0; j < num_right; ++j) + if (matching[i] == -1 && !busy_right[j] && adj_matrix[i][j]) { + matching[i] = j; + busy_right[j] = true; + } + return matching; + } +}; + +int main() { + std::ios_base::sync_with_stdio(false); + MaxMatching max_matching; + max_matching.Solve(); + return 0; +} diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/tests/01 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/tests/01 new file mode 100644 index 0000000..18b85db --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/tests/01 @@ -0,0 +1,4 @@ +3 4 +1 1 0 1 +0 1 0 0 +0 0 0 0 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/tests/01.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/tests/01.a new file mode 100644 index 0000000..050078c --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/tests/01.a @@ -0,0 +1 @@ +1 2 -1 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/tests/02 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/02-airline_crews/tests/02 new file mode 100644 index 0000000..0cf0a76 --- /dev/null +++ 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-1 55 17 8 -1 43 -1 3 -1 15 -1 33 39 -1 36 29 45 -1 19 -1 23 -1 -1 -1 4 47 -1 41 -1 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/stock_charts.cpp b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/stock_charts.cpp new file mode 100644 index 0000000..2a70c87 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/stock_charts.cpp @@ -0,0 +1,79 @@ +#include <iostream> +#include <vector> +#include <algorithm> +#include <memory> + +using std::vector; +using std::cin; +using std::cout; + +class StockCharts { + public: + void Solve() { + vector<vector<int>> stock_data = ReadData(); + int result = MinCharts(stock_data); + WriteResponse(result); + } + + private: + vector<vector<int>> ReadData() { + int num_stocks, num_points; + cin >> num_stocks >> num_points; + vector<vector<int>> stock_data(num_stocks, vector<int>(num_points)); + for (int i = 0; i < num_stocks; ++i) + for (int j = 0; j < num_points; ++j) { + cin >> stock_data[i][j]; + } + return stock_data; + } + + void WriteResponse(int result) { + cout << result << "\n"; + } + + int MinCharts(const vector<vector<int>>& stock_data) { + // Replace this incorrect greedy algorithm with an + // algorithm that correctly finds the minimum number + // of charts on which we can put all the stock data + // without intersections of graphs on one chart. + + int num_stocks = stock_data.size(); + // Vector of charts; each chart is a vector of indices of individual stocks. + vector<vector<int>> charts; + for (int i = 0; i < stock_data.size(); ++i) { + bool added = false; + for (auto& chart : charts) { + bool can_add = true; + for (int index : chart) + if (!compare(stock_data[i], stock_data[index]) && + !compare(stock_data[index], stock_data[i])) { + can_add = false; + break; + } + if (can_add) { + chart.push_back(i); + added = true; + break; + } + } + if (!added) { + charts.emplace_back(vector<int>{i}); + } + } + return charts.size(); + } + + bool compare(const vector<int>& stock1, const vector<int>& stock2) { + for (int i = 0; i < stock1.size(); ++i) + if (stock1[i] >= stock2[i]) + return false; + return true; + } +}; + +int main() { + std::ios_base::sync_with_stdio(false); + StockCharts stock_charts; + stock_charts.Solve(); + return 0; +} diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/01 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/01 new file mode 100644 index 0000000..aa54092 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/01 @@ -0,0 +1,4 @@ +3 4 +1 2 3 4 +2 3 4 6 +6 5 4 3 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/01.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/01.a new file mode 100644 index 0000000..0cfbf08 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/01.a @@ -0,0 +1 @@ +2 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/02 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/02 new file mode 100644 index 0000000..8dc039a --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/02 @@ -0,0 +1,4 @@ +3 3 +5 5 5 +4 4 6 +4 5 4 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/02.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/02.a new file mode 100644 index 0000000..00750ed --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/02.a @@ -0,0 +1 @@ +3 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/03 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/03 new file mode 100644 index 0000000..e4c3c6c --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/03 @@ -0,0 +1,6 @@ +5 2 +1 1 +2 2 +5 4 +4 4 +4 1 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/03.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/03.a new file mode 100644 index 0000000..0cfbf08 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/03.a @@ -0,0 +1 @@ +2 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/04 b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/04 new file mode 100644 index 0000000..69a8684 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/04 @@ -0,0 +1,3 @@ +2 1 +0 +1001 diff 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63 55 14 72 49 100 16 53 66 16 10 69 34 76 84 100 10 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/36.a b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/36.a new file mode 100644 index 0000000..29d6383 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/03-stock_charts/tests/36.a @@ -0,0 +1 @@ +100 diff --git a/05-advanced_algorithms_and_complexity/01-flows_in_networks/check b/05-advanced_algorithms_and_complexity/01-flows_in_networks/check new file mode 100755 index 0000000..b73ff99 --- /dev/null +++ b/05-advanced_algorithms_and_complexity/01-flows_in_networks/check @@ -0,0 +1,38 @@ +#! /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 -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 + echo -e " ${RED}compile $GREEN$src$RESET" && g++ $GPP_OPTS $src -o $BIN || exit 1 + if [ -d tests ]; then + 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 > $OUTA + cat $t.a > $OUTB + cmp $OUTA $OUTB >/dev/null + if [ $? -ne 0 ]; then + echo -e " $BROWN$t$RESET is ${RED}KO$RESET" + else + echo -e " $BROWN$t$RESET is ${GREEN}ok$RESET" + fi + fi + done + else + echo -e " ${RED}no tests$RESET" + fi + popd > /dev/null +done + |