Added CoinChange Algorithm (TheAlgorithms#260)

* Added CoinChange Algorithm * Minor Changes * Minor Changes * Minor Changes

Author: nttzamos

Dynamic-Programming/CoinChange.js

@@ -0,0 +1,45 @@
+function change (coins, amount) {
+ const combinations = new Array(amount + 1).fill(0)
+ combinations[0] = 1
+
+ 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]
+ }
+ }
+ 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
+ }
+ 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
+ }
+ }
+ }
+ }
+ return minimumCoins[amount]
+}
+
+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()