Feat: add coin change algorithm (#212)

* Feat: add coin change algorithm

* Use Infinity rather than just a large number

---------

Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>

Author: ayoubc

dynamic_programming/coin_change.ts

@@ -0,0 +1,46 @@
+
+export interface CoinChange {
+    minCoins: number,
+    coins: number[]
+}
+
+/**
+ * Given a set of categories of coins C and an amount of money S, the goal is:
+ * to give change for S but to use a minimum number of coins. Suppose each category of coin has an infinite number of pieces.
+ * @param money - amon of money.
+ * @param coins - The coins that are available.
+ * @returns CoinChange, the minimum number of coins, and which coins are selected
+ */
+export const coinChange = (money: number, coins: number[]): CoinChange => {
+
+    const minCoins: number[] = Array(money + 1).fill(Infinity);
+    const lastCoin: number[] = Array(money + 1).fill(-1);
+
+    minCoins[0] = 0;
+
+    // Fill in the DP table
+    for (let i = 0; i < coins.length; i++) {
+        for (let j = 0; j <= money; j++) {
+            if (j >= coins[i]) {
+                if (minCoins[j] > 1 + minCoins[j - coins[i]]) {
+                    minCoins[j] = 1 + minCoins[j - coins[i]];
+                    lastCoin[j] = coins[i];
+                }
+            }
+        }
+    }
+
+    const res: CoinChange = {
+        minCoins: minCoins[money],
+        coins: []
+    }
+
+    let total: number = money;
+    while (total > 0) {
+        res.coins.push(lastCoin[total]);
+        total -= lastCoin[total];
+    }
+
+    return res;
+}
+

dynamic_programming/test/coin_change.test.ts

@@ -0,0 +1,37 @@
+import { CoinChange, coinChange } from "../coin_change";
+
+
+interface TestCase {
+    money: number,
+    coins: number[],
+    expected: CoinChange
+}
+
+const cases: TestCase[] = [
+    {
+        money: 13,
+        coins: [7, 2, 3, 6],
+        expected: {
+            minCoins: 2,
+            coins: [6, 7]
+        }
+    },
+    {
+        money: 10,
+        coins: [1, 5],
+        expected: {
+            minCoins: 2,
+            coins: [5, 5]
+        }
+    }
+];
+
+describe("Coin Change Algorithm Test", () => {
+    test.each(cases)(
+        "given money: $money, and coins: $coins the minimum coin change should return $expected",
+        ({money, coins, expected}) => {
+            const result = coinChange(money, coins);
+            expect(result).toEqual(expected);
+        }
+    );
+});