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)
+})