From 9c9a0bf0bed7ac89d069286a36d774804afe2b34 Mon Sep 17 00:00:00 2001 From: Visrutha Date: Fri, 22 Oct 2021 15:53:55 +0530 Subject: [PATCH 1/2] Add Bipartite checking algorithm --- .../graphtheory/BipartiteChecking.cpp | 56 +++++++++++++++++++ 1 file changed, 56 insertions(+) create mode 100644 src/main/cpp/algorithms/graphtheory/BipartiteChecking.cpp diff --git a/src/main/cpp/algorithms/graphtheory/BipartiteChecking.cpp b/src/main/cpp/algorithms/graphtheory/BipartiteChecking.cpp new file mode 100644 index 0000000..b6a181d --- /dev/null +++ b/src/main/cpp/algorithms/graphtheory/BipartiteChecking.cpp @@ -0,0 +1,56 @@ +#include +#include + +using namespace std; + +int bipartite(int g[][10], int s, int n) +{ + int *col = new int [n]; + + for (int i = 0; i < n; i++) + col[i] = -1; + + queue q; + + col[s] = 1; + q.push(s); + + while (!q.empty()) + { + int u = q.front(); + q.pop(); + + if (g[u][u] == 1) + return 0; + + for (int v = 0; v < n; v++) + { + if (g[u][v] && col[v] == -1) + { + col[v] = 1 - col[u]; + q.push(v); + } + else if (g[u][v] == 1 && col[u] == col[v]) + return 0; + } + } + + return 1; +} + + +int main() +{ + int g[10][10], n; + + cin >> n; + + for (int i = 0; i < n; i++) + for (int j = 0; j < n; j++) + cin >> g[i][j]; + + int x = bipartite(g, 0, n); + + cout << x << endl; + return 0; +} \ No newline at end of file From 05373eccaab23c6dda9f346ad2ada0ea4a52ada4 Mon Sep 17 00:00:00 2001 From: Visrutha Date: Tue, 23 Nov 2021 11:47:58 +0530 Subject: [PATCH 2/2] Added Boruvka Minimum spanning tree --- .../graphtheory/BipartiteChecking.cpp | 94 +++++++++------ .../graphtheory/BipartiteChecking.exe | Bin 0 -> 931665 bytes .../graphtheory/BipartiteChecking.o | Bin 0 -> 34908 bytes .../other/boruvka_minimum_spanning_tree.cpp | 112 ++++++++++++++++++ 4 files changed, 170 insertions(+), 36 deletions(-) create mode 100644 src/main/cpp/algorithms/graphtheory/BipartiteChecking.exe create mode 100644 src/main/cpp/algorithms/graphtheory/BipartiteChecking.o create mode 100644 src/main/cpp/algorithms/other/boruvka_minimum_spanning_tree.cpp diff --git a/src/main/cpp/algorithms/graphtheory/BipartiteChecking.cpp b/src/main/cpp/algorithms/graphtheory/BipartiteChecking.cpp index b6a181d..589b0c6 100644 --- a/src/main/cpp/algorithms/graphtheory/BipartiteChecking.cpp +++ b/src/main/cpp/algorithms/graphtheory/BipartiteChecking.cpp @@ -1,56 +1,78 @@ + #include #include +#define V 4 using namespace std; -int bipartite(int g[][10], int s, int n) +bool isBipartite(int G[][V], int src) { - int *col = new int [n]; + int colorArr[V]; + for (int i = 0; i < V; ++i) + colorArr[i] = -1; - for (int i = 0; i < n; i++) - col[i] = -1; + // Assign first color to source + colorArr[src] = 1; - queue q; + // Create a queue (FIFO) of vertex + // numbers and enqueue source vertex + // for BFS traversal + queue q; + q.push(src); - col[s] = 1; - q.push(s); + // Run while there are vertices + // in queue (Similar to BFS) + while (!q.empty()) + { + // Dequeue a vertex from queue ( Refer http://goo.gl/35oz8 ) + int u = q.front(); + q.pop(); - while (!q.empty()) - { - int u = q.front(); - q.pop(); + // Return false if there is a self-loop + if (G[u][u] == 1) + return false; - if (g[u][u] == 1) - return 0; + // Find all non-colored adjacent vertices + for (int v = 0; v < V; ++v) + { + // An edge from u to v exists and + // destination v is not colored + if (G[u][v] && colorArr[v] == -1) + { + // Assign alternate color to this adjacent v of u + colorArr[v] = 1 - colorArr[u]; + q.push(v); + } - for (int v = 0; v < n; v++) - { - if (g[u][v] && col[v] == -1) - { - col[v] = 1 - col[u]; - q.push(v); - } - else if (g[u][v] == 1 && col[u] == col[v]) - return 0; - } - } + // An edge from u to v exists and destination + // v is colored with same color as u + else if (G[u][v] && colorArr[v] == colorArr[u]) + return false; + } + } - return 1; + // If we reach here, then all adjacent + // vertices can be colored with alternate color + return true; } - +// Driver program to test above function int main() { - int g[10][10], n; + int G[][V] = {{0, 1, 0, 1}, + {1, 0, 1, 0}, + {0, 1, 0, 1}, + {1, 0, 1, 0} + }; - cin >> n; + isBipartite(G, 0) ? cout << "Yes\n" : cout << "No\n"; - for (int i = 0; i < n; i++) - for (int j = 0; j < n; j++) - cin >> g[i][j]; + int GN[][V] = {{1, 1, 0, 1}, + {1, 0, 1, 1}, + {0, 1, 0, 1}, + {1, 0, 1, 0} + }; - int x = bipartite(g, 0, n); - - cout << x << endl; - return 0; -} \ No newline at end of file + isBipartite(GN, 0) ? cout << "Yes\n" : cout << "No\n"; + return 0; +} diff --git a/src/main/cpp/algorithms/graphtheory/BipartiteChecking.exe b/src/main/cpp/algorithms/graphtheory/BipartiteChecking.exe new file mode 100644 index 0000000000000000000000000000000000000000..4dbbca056234f1b3cc81dec9079a03513e0a00ac GIT binary patch literal 931665 zcmeFa4R}*k)-Qh2CJ-Q)phc@wv}#pQRH~>{KttO|MXKc^f=U$?D=MQX3E)Vfm{fZ> z7V8W+jDt>5bgI*tsft(>HHF#~#jye^3OZG*o*2}sh{dnm-&*^elan?ny#DX&o&S3; z&qK4${#;*s@3q(dD!#l%N|z+bivO{gBsJof{<-;Y?|&)~eaJD-9U`sk_u8?ImWi(& 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+ return parent[x] = getSR(parent[x]); +} + +int areUnited(int x, int y) +{ + return getSR(x) == getSR(y); +} + +void unite(int x, int y) +{ + x = getSR(x); + y = getSR(y); + if (rank[x] > rank[y]) + parent[y] = x; + else + { + parent[x] = y; + if (rank[x] == rank[y]) + rank[y]++; + } +} + +std::pair cheapEdge[MAXN]; +int solve() +{ + int numberOfTrees = nodeCount; + int weightSum = 0; + initDisjoint(); + + while (numberOfTrees > 1) + { + // initializing cheapest edge to "none" + for (int i = 0; i < nodeCount; i++) + cheapEdge[i].first = -1; + for (int i = 0; i < nodeCount; i++) + for (size_t j = 0; j < graf[i].size(); j++) + { + std::pair edge = graf[i][j]; + int xsr = getSR(i); + int ysr = getSR(edge.first); + int w = edge.second; + if (xsr == ysr) + continue; + if (cheapEdge[xsr].first == -1 || + w < graf[cheapEdge[xsr].first][cheapEdge[xsr].second].second) + cheapEdge[xsr] = {i, j}; + if (cheapEdge[ysr].first == -1 || + w < graf[cheapEdge[ysr].first][cheapEdge[ysr].second].second) + cheapEdge[ysr] = {i, j}; + } + for (int i = 0; i < nodeCount; i++) + { + int xsr = getSR(i); + if (cheapEdge[xsr].first == -1) + continue; + std::pair edge = graf[cheapEdge[xsr].first][cheapEdge[xsr].second]; + int ysr = getSR(edge.first); + if (xsr == ysr) + continue; + weightSum += edge.second; + unite(xsr, ysr); + numberOfTrees--; + } + } + + return weightSum; +} + +int main() +{ + readGraph(); + int weight = solve(); + std::cout << "The weight of the minimum spanning tree is " << weight; + return 0; +} \ No newline at end of file