Added the implementation of the Edmond Karp algorithm along with test cases

graph/edmondkarp.ts

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+/**
+ * @function edmondkarp
+ * @description Compute the maximum flow from a source node to a sink node. The input graph is in adjacency list form. It is a multidimensional array of edges. graph[i] holds the edges for the i'th node. Each edge is a 3-tuple where the 0'th item is the destination node, the 1'th item is the edge weight, and the 2'nd item is the edge capacity.
+ * @Complexity_Analysis
+ * Time complexity: O(V*E^2) where V is the number of vertices and E is the number of edges
+ * Space Complexity: O(V) where V is the number of vertices
+ * @param {[number, number, number][][]} graph - The graph in adjacency list form
+ * @param {number} source - The source node
+ * @param {number} sink - The sink node
+ * @return {number} - The maximum flow from the source node to the sink node
+ * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm
+ */
+
+function edmondkarp(graph: [number, number, number][][], source: number, sink: number): number {
+    // Initialize capacity and flow matrices with zeros and build capacity matrix from graph 
+    const n = graph.length;
+    const capacity = Array.from({ length: n }, () => Array(n).fill(0));
+    const flow = Array.from({ length: n }, () => Array(n).fill(0));
+
+    // Build capacity matrix 
+    for (let u = 0; u < n; u++) {
+        for (const [v, , cap] of graph[u]) {
+            capacity[u][v] = cap;
+        }
+    }
+
+    // Breadth-first search
+    const bfs = (parent: number[]): boolean => {
+        const visited = Array(n).fill(false);
+        const queue: number[] = [];
+        queue.push(source);
+        visited[source] = true;
+
+        // Find an augmenting path from source to sink by doing a BFS traversal
+        while (queue.length > 0) {
+            // Dequeue
+            const u = queue.shift()!;
+            // Enqueue all adjacent unvisited vertices with available capacity
+            for (let v = 0; v < n; v++) {
+                // If there is available capacity and the vertex has not been visited
+                if (!visited[v] && capacity[u][v] - flow[u][v] > 0) {
+                    queue.push(v);
+                    visited[v] = true;
+                    parent[v] = u;
+                    // If we reach the sink, we have found the augmenting path
+                    if (v === sink) {
+                        return true;
+                    }
+                }
+            }
+        }
+        return false;
+    };
+
+    let maxFlow = 0;
+    const parent = Array(n).fill(-1);
+
+    while (bfs(parent)) {
+        let pathFlow = Infinity;
+        // Find the maximum flow through the path found
+        for (let v = sink; v !== source; v = parent[v]) {
+            const u = parent[v];
+            pathFlow = Math.min(pathFlow, capacity[u][v] - flow[u][v]);
+        }
+        // Update the flow matrix
+        for (let v = sink; v !== source; v = parent[v]) {
+            const u = parent[v];
+            flow[u][v] += pathFlow;
+            flow[v][u] -= pathFlow;
+        }
+
+        maxFlow += pathFlow;
+    }
+
+    return maxFlow;
+}

graph/test/edmondkarp_test.ts

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+import { edmondsKarp } from '../edmondsKarp'
+
+describe('edmondsKarp', () => {
+  const init_flow_network = (N: number): number[][] => {
+    const graph = Array.from({ length: N }, () => Array(N).fill(0));
+    return graph;
+  }
+
+  const add_capacity = (
+    graph: number[][],
+    u: number,
+    v: number,
+    capacity: number
+  ) => {
+    graph[u][v] = capacity;
+  }
+
+  it('should return the correct maximum flow value for basic graph', () => {
+    const graph = init_flow_network(6);
+    add_capacity(graph, 0, 1, 16);
+    add_capacity(graph, 0, 2, 13);
+    add_capacity(graph, 1, 2, 10);
+    add_capacity(graph, 1, 3, 12);
+    add_capacity(graph, 2, 1, 4);
+    add_capacity(graph, 2, 4, 14);
+    add_capacity(graph, 3, 2, 9);
+    add_capacity(graph, 3, 5, 20);
+    add_capacity(graph, 4, 3, 7);
+    add_capacity(graph, 4, 5, 4);
+    expect(edmondsKarp(graph, 0, 5)).toBe(23);
+  });
+
+  it('should return the correct maximum flow value for single element graph', () => {
+    const graph = init_flow_network(1);
+    expect(edmondsKarp(graph, 0, 0)).toBe(0);
+  });
+
+  const linear_flow_network = init_flow_network(4);
+  add_capacity(linear_flow_network, 0, 1, 10);
+  add_capacity(linear_flow_network, 1, 2, 5);
+  add_capacity(linear_flow_network, 2, 3, 15);
+  test.each([
+    [0, 3, 5],  
+    [0, 2, 5],  
+    [1, 3, 5],  
+    [1, 2, 5],  
+  ])(
+    'correct result for linear flow network with source node %i and sink node %i',
+    (source, sink, maxFlow) => {
+      expect(edmondsKarp(linear_flow_network, source, sink)).toBe(maxFlow);
+    }
+  );
+
+  const disconnected_flow_network = init_flow_network(4);
+  add_capacity(disconnected_flow_network, 0, 1, 10);
+  add_capacity(disconnected_flow_network, 2, 3, 5);
+  test.each([
+    [0, 3, 0],  
+    [1, 2, 0],  
+    [2, 3, 5],  
+  ])(
+    'correct result for disconnected flow network with source node %i and sink node %i',
+    (source, sink, maxFlow) => {
+      expect(edmondsKarp(disconnected_flow_network, source, sink)).toBe(maxFlow);
+    }
+  );
+
+  const cyclic_flow_network = init_flow_network(5);
+  add_capacity(cyclic_flow_network, 0, 1, 10);
+  add_capacity(cyclic_flow_network, 1, 2, 5);
+  add_capacity(cyclic_flow_network, 2, 0, 7);  
+  add_capacity(cyclic_flow_network, 2, 3, 10);
+  add_capacity(cyclic_flow_network, 3, 4, 10);
+  test.each([
+    [0, 4, 10], 
+    [1, 4, 10], 
+    [2, 4, 10], 
+  ])(
+    'correct result for cyclic flow network with source node %i and sink node %i',
+    (source, sink, maxFlow) => {
+      expect(edmondsKarp(cyclic_flow_network, source, sink)).toBe(maxFlow);
+    }
+  );
+});

maths/bisection_method.ts

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+/**
+ * @function bisectionMethod 
+ * @description Bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs.
+ * @param  {number} a - The first value
+ * @param  {number} b - The second value
+ * @param  {number} e - The error value
+ * @param  {Function} f - The function
+ * @return {number} - The root of the function
+ * @see [BisectionMethod](https://en.wikipedia.org/wiki/Bisection_method)
+ * @example bisectionMethod(1, 2, 0.01, (x) => x**2 - 2) = 1.4140625
+ * @example bisectionMethod(1, 2, 0.01, (x) => x**2 - 3) = 1.732421875
+ */
+
+export const bisectionMethod = (a: number, b: number, e: number, f: Function): number => {
+    let c = a
+    while ((b - a) >= e) {
+        c = (a + b) / 2
+        if (f(c) === 0.0) {
+            break
+        } else if (f(c) * f(a) < 0) {
+            b = c
+        } else {
+            a = c
+        }
+    }
+    return c
+}

maths/decimal_convert.ts

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+/**
+ * @function decimalConvert
+ * @description Convert the binary to decimal.
+ * @param {string} binary - The input binary
+ * @return {number} - Decimal of binary.
+ * @see [DecimalConvert](https://www.programiz.com/javascript/examples/binary-decimal)
+ * @example decimalConvert(1100) = 12
+ * @example decimalConvert(1110) = 14
+ */
+
+export const decimalConvert = (binary: string): number => {
+    let decimal = 0
+    let binaryArr = binary.split('').reverse()
+
+    for (let i = 0; i < binaryArr.length; i++) {
+        decimal += parseInt(binaryArr[i]) * Math.pow(2, i)
+    }
+
+    return decimal
+}

maths/euler_method.ts

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+/**
+ * @function eulerMethod
+ * @description Euler's method is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
+ * @param {number} x0 - The initial value of x
+ * @param {number} y0 - The initial value of y
+ * @param {number} h - The step size
+ * @param {number} n - The number of iterations
+ * @param {Function} f - The function
+ * @return {number} - The value of y at x
+ * @see [EulerMethod](https://en.wikipedia.org/wiki/Euler_method)
+ * @example eulerMethod(0, 1, 0.1, 10, (x, y) => x + y) = 2.5937424601
+ * @example eulerMethod(0, 1, 0.1, 10, (x, y) => x * y) = 1.7715614317
+ */
+
+export const eulerMethod = (x0: number, y0: number, h: number, n: number, f: Function): number => {
+    let x = x0
+    let y = y0
+
+    for (let i = 1; i <= n; i++) {
+        y = y + h * f(x, y)
+        x = x + h
+    }
+
+    return y
+}