Open chore(CPlusPlus): add Floyd Warshall algorithm (#791)

algorithms/CPlusPlus/Graphs/floyd-warshall.cpp

@@ -0,0 +1,106 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+const int N = 500, OO = 1e9;
+
+int dist[N][N];
+
+//Initialize the distance matrix with infinities to indicate that there is no edge between nodes
+void initialize_dist(int n) {
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++) {
+            dist[i][j] = OO;
+            if (i == j) {
+                dist[i][j] = 0;
+            }
+        }
+    }
+}
+
+//Take Edge input and update the distance matrix
+void input(int m) {
+    for (int i = 0; i < m; i++) {
+        int a, b, c;
+        cin >> a >> b >> c;
+        dist[a][b] = c;
+        dist[b][a] = c;
+    }
+}
+
+//Perform Floyd-Warshall algorithm to calculate all shortest paths
+int floyd(int n) {
+    for (int k = 0; k < n; k++) {
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                if (dist[i][j] > dist[i][k] + dist[k][j]) {
+                    dist[i][j] = dist[i][k] + dist[k][j];
+                }
+            }
+        }
+    }
+}
+
+//Take queries and output the shortest distance for each query
+void output(int q) {
+    for (int i = 0; i < q; i++) {
+        int x, y;
+        cin >> x >> y;
+        cout << dist[x][y] << endl;
+    }
+}
+
+int main() {
+    int n, m, q;
+    cin >> n; // Number of nodes
+    initialize_dist(n);
+    cin >> m; // Number of edges
+    input(m);
+    floyd(n);
+    cin >> q; // Number of queries
+    output(q);
+    return 0;
+}
+
+/*
+Time Complexity: O(n^3)
+Memory Complexity: O(n^2)
+*/
+
+/*
+Example:
+    5 // Number of nodes
+    10 // Number of edges
+    0 1 5 // Edge from Node 0 to Node 1 with Weight 5
+    0 2 3
+    0 3 4
+    0 4 1
+    1 2 4
+    1 3 1
+    1 4 1
+    2 3 1
+    2 4 2
+    3 4 4
+    10 // Number of Queries
+    0 1 // Print Minimum Path between Nodes 0 and 1
+    0 2
+    0 3
+    0 4
+    1 2
+    1 3
+    1 4
+    2 3
+    2 4
+    3 4
+
+Output:
+    2 //Minimum path from 0 to 1
+    3 //Minimum path from 0 to 2
+    3 //Minimum path from 0 to 3
+    1 //Minimum path from 0 to 4
+    2 //Minimum path from 1 to 2
+    1 //Minimum path from 1 to 3
+    1 //Minimum path from 1 to 4
+    1 //Minimum path from 2 to 3
+    2 //Minimum path from 2 to 4
+    2 //Minimum path from 3 to 4
+ */

algorithms/CPlusPlus/README.md

@@ -51,6 +51,7 @@
 - [Connected Components](Graphs/total-connected-components.cpp)
 - [Dijkstra's Algorithm](Graphs/dijkstra.cpp)
 - [Cycle Detection](Graphs/cycle-detection.cpp)
+- [Floyd Warshall](Graphs/floyd-warshall.cpp)
 
 ## Multiplication