add: MinCoinCombinationTopDown, use target + 1 to replace float('inf') in python, since Integer.MAX_VALUE will lead to overflow in the question. Alternative is to check topDownDp return value before add 1 in 1 + topDownDp(coins, target - coin, memo)

Author: Jer3myYu

java/Dynamic Programming/MinCoinCombinationTopDown.java

@@ -0,0 +1,35 @@
+import java.util.HashMap;
+import java.util.Map;
+
+public class MinCoinCombinationTopDown {
+    int max;
+
+    public int minCoinCombinationTopDown(int[] coins, int target) {
+        max = target + 1;
+        int res = topDownDp(coins, target, new HashMap<>());
+        return res == max ? -1 : res;
+    }
+
+    private int topDownDp(int[] coins, int target, Map<Integer, Integer> memo) {
+        // Base case: if the target is 0, then 0 coins are needed to reach
+        // it.
+        if (target == 0) {
+            return 0;
+        }
+        if (memo.containsKey(target)) {
+            return memo.get(target);
+        }
+        // Initialize 'minCoins' to a large number.
+        int minCoins = max;
+        for (int coin : coins) {
+            // Avoid negative targets.
+            if (coin <= target) {
+                // Calculate the minimum number of coins needed if we use
+                // the current coin.
+                minCoins = Math.min(minCoins, 1 + topDownDp(coins, target - coin, memo));
+            }
+        }
+        memo.put(target, minCoins);
+        return memo.get(target);
+    }
+}