Added the recursive-memoized approach for coin change combination problem

Dynamic-Programming/CoinChange.js

@@ -1,4 +1,4 @@
-function change (coins, amount) {
+function change(coins, amount) {
   const combinations = new Array(amount + 1).fill(0)
   combinations[0] = 1
 
@@ -12,7 +12,47 @@ function change (coins, amount) {
   return combinations[amount]
 }
 
-function minimumCoins (coins, amount) {
+/** Coin-change combination using recursive approach along with Memoization
+ * @param {number} amount
+ * @param {number[]} coins
+ */
+const changeRecursive = (amount, coins) => {
+  const mem = new Map()
+  return coinChangeComb(amount, coins, 0, mem)
+}
+/** Coin-change combination using recursive approach along with Memoization
+ * @param {number} amount
+ * @param {number[]} coins
+ * @param {number} idx
+ * @param {Map} mem
+ */
+
+const coinChangeComb = (amount, coins, idx, mem) => {
+  // Negative Base Case
+  if (amount < 0 || idx === coins.length) {
+    return 0
+  }
+  // Positive Base Case
+  if (amount === 0) {
+    return 1
+  }
+
+  // Main Case
+  // Check if the recursive function call results is already memoized
+  if (mem.has(`${amount} - ${idx}`)) {
+    return mem.get(`${amount} - ${idx}`)
+  }
+  let res = 0
+  // Consider the coin at index idx
+  res += coinChangeComb(amount - coins[idx], coins, idx, mem)
+  // Leave the coin at index idx
+  res += coinChangeComb(amount, coins, idx + 1, mem)
+  // Cache the intermediate result in mem
+  mem.set(`${amount} - ${idx}`, res)
+  return res
+}
+
+function minimumCoins(coins, amount) {
   // minimumCoins[i] will store the minimum coins needed for amount i
   const minimumCoins = new Array(amount + 1).fill(0)
 
@@ -26,7 +66,10 @@ function minimumCoins (coins, amount) {
       const coin = coins[j]
       if (coin <= i) {
         const subRes = minimumCoins[i - coin]
-        if (subRes !== Number.MAX_SAFE_INTEGER && subRes + 1 < minimumCoins[i]) {
+        if (
+          subRes !== Number.MAX_SAFE_INTEGER &&
+          subRes + 1 < minimumCoins[i]
+        ) {
           minimumCoins[i] = subRes + 1
         }
       }
@@ -35,11 +78,27 @@ function minimumCoins (coins, amount) {
   return minimumCoins[amount]
 }
 
-function main () {
+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))
+  console.log(
+    'Number of combinations of getting change for ' +
+      amount +
+      ' is: ' +
+      change(coins, amount)
+  )
+  console.log(
+    'Number of combinations of getting change for ' +
+      amount +
+      ' is: ' +
+      changeRecursive(coins, amount)
+  )
+  console.log(
+    'Minimum number of coins required for amount :' +
+      amount +
+      ' is: ' +
+      minimumCoins(coins, amount)
+  )
 }
 
 main()