Coin Change solution

Author: kim-young

coin-change/kimyoung.js

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+var coinChange = function (coins, amount) {
+    // create a dp array that stores the minimum amount of coins used for each amount leading up to the target amount
+    // fill with array with amount + 1 as a default 
+    const dp = [0, ...new Array(amount).fill(amount + 1)];
+
+    // loop through the coins 
+    for (const coin of coins) {
+        // for each amount, assess how the current coin can modify the existing value within the dp array by comparing the min value
+        for (let i = 1; i <= amount; i++) {
+            // only works if coin is less than or equal to the assessing amount
+            if (coin <= i) {
+                // min comparison 
+                dp[i] = Math.min(dp[i], dp[i - coin] + 1);
+            }
+        }
+    }
+    // check target amount in dp array to see if it's the default value
+    // if it's default value, it means coin combination cannot lead up to target amount
+    // if it's not default value, that is the minimum required coin change to lead up to target amount
+    return dp[amount] === amount + 1 ? -1 : dp[amount];
+};
+
+// time - O(a * c) loops through amount * loops through coin
+// space - O(a) depends on the size of amount