Merge pull request #365 from Abdullah-Shah-26/feature/floyd_warshall_pr

Feature/floyd warshall pr

Author: Pradeepsingh61

CPP/algorithms/graph_algorithms/floyd_warshall.cpp

@@ -0,0 +1,134 @@
+// Floyd–Warshall Algorithm — All-Pairs Shortest Path
+// Problem
+//   Compute shortest distances between every pair of vertices in a weighted graph.
+//
+// Approach
+//   1. Initialize dist[i][j]:
+//        - 0 if i==j
+//        - weight(u,v) if edge exists
+//        - INF otherwise
+//   2. For k in [0..V-1] (intermediate vertex):
+//        for i in [0..V-1] (source):
+//          for j in [0..V-1] (destination):
+//             dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])
+//   3. After all iterations, dist[i][j] is the shortest distance.
+//
+// Complexity
+//   Time  : O(V^3)
+//   Space : O(V^2)
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+
+int main()
+{
+  ios::sync_with_stdio(false);
+  cin.tie(nullptr);
+
+  int V, E;
+  cin >> V >> E;
+  const int INF = 1e9;
+
+  vector<vector<int>> dist(V, vector<int>(V, INF));
+  for (int i = 0; i < V; i++)
+    dist[i][i] = 0;
+
+  for (int i = 0; i < E; i++)
+  {
+    int u, v, w;
+    cin >> u >> v >> w;
+    dist[u][v] = min(dist[u][v], w);
+    dist[v][u] = min(dist[v][u], w); // remove if directed
+  }
+
+  cout << "Initial distance matrix:\n";
+  for (auto &row : dist)
+  {
+    for (auto x : row)
+      cout << (x == INF ? -1 : x) << " ";
+    cout << "\n";
+  }
+  cout << "\n";
+
+  // Floyd–Warshall dry run
+  for (int k = 0; k < V; k++)
+  {
+    cout << "Considering intermediate vertex k=" << k << ":\n";
+    for (int i = 0; i < V; i++)
+      for (int j = 0; j < V; j++)
+        if (dist[i][k] < INF && dist[k][j] < INF)
+          dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
+
+    // print matrix after this k
+    for (auto &row : dist)
+    {
+      for (auto x : row)
+        cout << (x == INF ? -1 : x) << " ";
+      cout << "\n";
+    }
+    cout << "\n";
+  }
+
+  cout << "Final All-Pairs Shortest Distances:\n";
+  for (auto &row : dist)
+  {
+    for (auto x : row)
+      cout << (x == INF ? -1 : x) << " ";
+    cout << "\n";
+  }
+
+  return 0;
+}
+
+/*
+Example Input:
+4 5
+0 1 5
+0 3 10
+1 2 3
+2 3 1
+0 2 100
+
+Visualization:
+Graph:
+   (5)        (3)       (1)
+0 ----- 1 -------- 2 -------- 3
+ \                               ^
+  \____________ (10) ___________/
+
+Dry Run Steps:
+
+Initial dist:
+0   5 100 10
+5   0   3 -1
+100 3   0  1
+10  -1  1  0
+
+k = 0 (using vertex 0 as intermediate):
+- dist[2][3] = min(1, dist[2][0]+dist[0][3]) = min(1,100+10)=1 (no change)
+- dist[2][0] = min(100, dist[2][0]+dist[0][0]) = 100 (no change)
+... print matrix
+
+k = 1 (vertex 1 intermediate):
+- dist[0][2] = min(100, dist[0][1]+dist[1][2]) = min(100,5+3)=8
+- dist[3][0] = min(10, dist[3][1]+dist[1][0]) = min(10, INF+5)=10 (no change)
+... print matrix
+
+k = 2 (vertex 2 intermediate):
+- dist[0][3] = min(10, dist[0][2]+dist[2][3]) = min(10,8+1)=9
+- dist[1][3] = min(INF, 3+1)=4
+... print matrix
+
+k = 3 (vertex 3 intermediate):
+- no further updates
+
+Final dist:
+0 5 8 9
+5 0 3 4
+8 3 0 1
+9 4 1 0
+*/
+
+// prepare PR