Added Ford Fulkerson algorithm for Hacktoberfest contribution

Author: Sameeksha-12

Graphs/FordFulkerson.js

@@ -0,0 +1,51 @@
+// 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

@@ -0,0 +1,46 @@
+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)
+})