chore: Merge pull request #650 from mandy8055/coinChangeCombMem

Added the recursive-memoized approach for coin change combination pro…

Dynamic-Programming/CoinChange.js

@@ -1,45 +1,33 @@
-function change (coins, amount) {
+/**
+ * @params {Array} coins
+ * @params {Number} amount
+ */
+export const change = (coins, amount) => {
+  // Create and initialize the storage
   const combinations = new Array(amount + 1).fill(0)
   combinations[0] = 1
-
+  // Determine the direction of smallest sub-problem
   for (let i = 0; i < coins.length; i++) {
-    const coin = coins[i]
-
-    for (let j = coin; j < amount + 1; j++) {
-      combinations[j] += combinations[j - coin]
+    // Travel and fill the combinations array
+    for (let j = coins[i]; j < combinations.length; j++) {
+      combinations[j] += combinations[j - coins[i]]
     }
   }
   return combinations[amount]
 }
-
-function minimumCoins (coins, amount) {
-  // minimumCoins[i] will store the minimum coins needed for amount i
-  const minimumCoins = new Array(amount + 1).fill(0)
-
-  minimumCoins[0] = 0
-
-  for (let i = 1; i < amount + 1; i++) {
-    minimumCoins[i] = Number.MAX_SAFE_INTEGER
+/**
+ * @params {Array} coins
+ * @params {Number} amount
+ */
+export const coinChangeMin = (coins, amount) => {
+  const map = { 0: 1 }
+  for (let i = 1; i <= amount; i++) {
+    let min = Infinity
+    for (const coin of coins) {
+      if (i < coin) continue
+      min = Math.min(min, 1 + map[i - coin])
     }
-  for (let i = 1; i < amount + 1; i++) {
-    for (let j = 0; j < coins.length; j++) {
-      const coin = coins[j]
-      if (coin <= i) {
-        const subRes = minimumCoins[i - coin]
-        if (subRes !== Number.MAX_SAFE_INTEGER && subRes + 1 < minimumCoins[i]) {
-          minimumCoins[i] = subRes + 1
+    map[i] = min
   }
-      }
-    }
-  }
-  return minimumCoins[amount]
+  return map[amount] === Infinity ? -1 : map[amount] - 1
 }
-
-function main () {
-  const amount = 12
-  const coins = [2, 4, 5]
-  console.log('Number of combinations of getting change for ' + amount + ' is: ' + change(coins, amount))
-  console.log('Minimum number of coins required for amount :' + amount + ' is: ' + minimumCoins(coins, amount))
-}
-
-main()

Dynamic-Programming/tests/CoinChange.test.js

@@ -0,0 +1,44 @@
+import { change, coinChangeMin } from '../CoinChange'
+
+test('Base Case 1', () => {
+  const coins = [2, 3, 5]
+  const amount = 0
+  expect(change(coins, amount)).toBe(1)
+  expect(coinChangeMin(coins, amount)).toBe(0)
+})
+test('Base Case 2', () => {
+  const coins = []
+  const amount = 100
+  expect(change(coins, amount)).toBe(0)
+  expect(coinChangeMin(coins, amount)).toBe(-1)
+})
+test('Test Case 1', () => {
+  const coins = [2, 4, 5]
+  const amount = 12
+  expect(change(coins, amount)).toBe(5)
+  expect(coinChangeMin(coins, amount)).toBe(3)
+})
+test('Test Case 2', () => {
+  const coins = [5, 2, 3, 7, 6, 1, 12, 11, 9, 15]
+  const amount = 45
+  expect(change(coins, amount)).toBe(12372)
+  expect(coinChangeMin(coins, amount)).toBe(3)
+})
+test('Test Case 3', () => {
+  const coins = [2]
+  const amount = 3
+  expect(change(coins, amount)).toBe(0)
+  expect(coinChangeMin(coins, amount)).toBe(-1)
+})
+test('Test Case 4', () => {
+  const coins = [3, 5, 7, 8, 9, 10, 11]
+  const amount = 500
+  expect(change(coins, amount)).toBe(35502874)
+  expect(coinChangeMin(coins, amount)).toBe(46)
+})
+test('Test Case 5', () => {
+  const coins = [10]
+  const amount = 10
+  expect(change(coins, amount)).toBe(1)
+  expect(coinChangeMin(coins, amount)).toBe(1)
+})