feat: add Fenwick Tree implementation with tests

Author: tanjumul

Data-Structures/Tree/FenwickTree.js

@@ -0,0 +1,56 @@
+/**
+ * Time Complexity:
+ * Update: O(log n)
+ * Query: O(log n)
+ * Range Query: O(log n)
+ *
+ * Space Complexity: O(n)
+ *
+ */
+
+export default class FenwickTree {
+  constructor(size) {
+    this.size = size
+    this.tree = new Array(size + 1).fill(0)
+  }
+
+  static fromArray(arr) {
+    const ft = new FenwickTree(arr.length)
+    for (let i = 0; i < arr.length; i++) {
+      ft.update(i, arr[i])
+    }
+    return ft
+  }
+
+  update(index, delta) {
+    let i = index + 1
+    while (i <= this.size) {
+      this.tree[i] += delta
+      i += i & -i // Adding the lowest set bit
+    }
+  }
+
+  query(index) {
+    let i = index + 1
+    let sum = 0
+    while (i > 0) {
+      sum += this.tree[i]
+      i -= i & -i // Removing the lowest set bit
+    }
+    return sum
+  }
+
+  rangeQuery(left, right) {
+    if (left === 0) return this.query(right)
+    return this.query(right) - this.query(left - 1)
+  }
+
+  get(index) {
+    return this.rangeQuery(index, index)
+  }
+
+  set(index, value) {
+    const current = this.get(index)
+    this.update(index, value - current)
+  }
+}

Data-Structures/Tree/test/FenwickTree.test.js

@@ -0,0 +1,93 @@
+import FenwickTree from '../FenwickTree'
+
+describe('Fenwick Tree', () => {
+  describe('Basic Operations', () => {
+    test('should handle point updates and prefix queries', () => {
+      const ft = new FenwickTree(5)
+      ft.update(0, 1)
+      ft.update(1, 2)
+      ft.update(2, 3)
+      ft.update(3, 4)
+      ft.update(4, 5)
+
+      expect(ft.query(0)).toBe(1)
+      expect(ft.query(1)).toBe(3)
+      expect(ft.query(2)).toBe(6)
+      expect(ft.query(3)).toBe(10)
+      expect(ft.query(4)).toBe(15)
+    })
+
+    test('should handle range queries', () => {
+      const ft = new FenwickTree(5)
+      ft.update(0, 10)
+      ft.update(1, 20)
+      ft.update(2, 30)
+      ft.update(3, 40)
+      ft.update(4, 50)
+
+      expect(ft.rangeQuery(1, 3)).toBe(90)
+      expect(ft.rangeQuery(0, 2)).toBe(60)
+      expect(ft.rangeQuery(2, 4)).toBe(120)
+    })
+  })
+
+  describe('Edge Cases', () => {
+    test('should handle empty tree', () => {
+      const ft = new FenwickTree(3)
+      expect(ft.query(0)).toBe(0)
+      expect(ft.query(1)).toBe(0)
+      expect(ft.query(2)).toBe(0)
+    })
+
+    test('should handle single element', () => {
+      const ft = new FenwickTree(1)
+      ft.update(0, 42)
+      expect(ft.query(0)).toBe(42)
+      expect(ft.rangeQuery(0, 0)).toBe(42)
+    })
+
+    test('should handle negative values', () => {
+      const ft = new FenwickTree(3)
+      ft.update(0, 5)
+      ft.update(1, -2)
+      ft.update(2, 3)
+
+      expect(ft.rangeQuery(0, 2)).toBe(6)
+      expect(ft.rangeQuery(0, 1)).toBe(3)
+    })
+  })
+
+  describe('Get and Set', () => {
+    test('should get value at specific index', () => {
+      const ft = new FenwickTree(3)
+      ft.update(0, 5)
+      ft.update(1, 10)
+      ft.update(2, 15)
+
+      expect(ft.get(0)).toBe(5)
+      expect(ft.get(1)).toBe(10)
+      expect(ft.get(2)).toBe(15)
+    })
+
+    test('should set value at specific index', () => {
+      const ft = new FenwickTree(3)
+      ft.update(0, 5)
+      ft.update(1, 10)
+      ft.update(2, 15)
+
+      ft.set(1, 20)
+      expect(ft.get(1)).toBe(20)
+      expect(ft.rangeQuery(0, 2)).toBe(40)
+    })
+  })
+
+  describe('Static Methods', () => {
+    test('should build from array', () => {
+      const arr = [1, 2, 3, 4, 5]
+      const ft = FenwickTree.fromArray(arr)
+
+      expect(ft.query(4)).toBe(15)
+      expect(ft.rangeQuery(1, 3)).toBe(9)
+    })
+  })
+})