Added Ford Fulkerson algorithm for Hacktoberfest contribution

Graphs/FordFulkerson.js

@@ -0,0 +1,52 @@
+// https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm
+function fordFulkerson(capacity, source, sink) {
+  const V = capacity.length;
+  const residualCapacity = capacity.map((arr) => arr.slice());
+  const parent = Array(V).fill(-1);
+  let maxFlow = 0;
+
+  function bfs(source, sink) {
+    const visited = Array(V).fill(false);
+    const queue = [source];
+    visited[source] = true;
+    parent[source] = -1;
+
+    while (queue.length > 0) {
+      const u = queue.shift();
+
+      for (let v = 0; v < V; v++) {
+        if (!visited[v] && residualCapacity[u][v] > 0) {
+          if (v === sink) {
+            parent[v] = u;
+            return true;
+          }
+          queue.push(v);
+          parent[v] = u;
+          visited[v] = true;
+        }
+      }
+    }
+    return false;
+  }
+
+  while (bfs(source, sink)) {
+    let pathFlow = Infinity;
+    for (let v = sink; v !== source; v = parent[v]) {
+      const u = parent[v];
+      pathFlow = Math.min(pathFlow, residualCapacity[u][v]);
+    }
+
+    for (let v = sink; v !== source; v = parent[v]) {
+      const u = parent[v];
+      residualCapacity[u][v] -= pathFlow;
+      residualCapacity[v][u] += pathFlow;
+    }
+
+    maxFlow += pathFlow;
+  }
+
+  return maxFlow;
+}
+
+export { fordFulkerson };
+

Graphs/test/FordFulkerson.test.js

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+import { fordFulkerson } from '../FordFulkerson.js'
+
+test('Test Case 1', () => {
+  const capacity = [
+    [0, 16, 13, 0, 0, 0],
+    [0, 0, 10, 12, 0, 0],
+    [0, 4, 0, 0, 14, 0],
+    [0, 0, 9, 0, 0, 20],
+    [0, 0, 0, 7, 0, 4],
+    [0, 0, 0, 0, 0, 0],
+  ]
+  const source = 0
+  const sink = 5
+  const maxFlow = fordFulkerson(capacity, source, sink)
+  expect(maxFlow).toBe(23)
+})
+
+test('Test Case 2', () => {
+  const capacity = [
+    [0, 10, 0, 10, 0, 0],
+    [0, 0, 5, 0, 15, 0],
+    [0, 0, 0, 0, 10, 10],
+    [0, 0, 10, 0, 0, 10],
+    [0, 0, 0, 0, 0, 10],
+    [0, 0, 0, 0, 0, 0],
+  ]
+  const source = 0
+  const sink = 5
+  const maxFlow = fordFulkerson(capacity, source, sink)
+  expect(maxFlow).toBe(20)
+})
+
+test('Test Case 3', () => {
+  const capacity = [
+    [0, 7, 0, 0, 3, 0],
+    [0, 0, 5, 0, 2, 0],
+    [0, 0, 0, 8, 0, 7],
+    [0, 0, 0, 0, 0, 5],
+    [0, 0, 0, 5, 0, 0],
+    [0, 0, 0, 0, 0, 0],
+  ]
+  const source = 0
+  const sink = 5
+  const maxFlow = fordFulkerson(capacity, source, sink)
+  expect(maxFlow).toBe(10)
+})