Create 518-Coin-Change-2.cpp

cpp/518-Coin-Change-2.cpp

@@ -0,0 +1,23 @@
+class Solution {
+public:
+    int change(int amount, vector<int>& coins) {
+        vector<vector<int>> dp(coins.size() + 1, vector<int>(amount + 1));
+
+        // loop with c(number of selected coin types) and a(amount) and the coin value is coins[c-1]
+        for (int c = 0; c <= coins.size(); ++c) {
+            int coinVal = c > 0 ? coins[c - 1] : 0;
+            for (int a = 0; a <= amount; ++a) {
+                if (a == 0) // amount is 0: only 1 way, which is selecting 0 coin
+                    dp[c][a] = 1;
+                else if (c == 0) // select 0 coin but amount is not 0: 0 way
+                    dp[c][a] = 0;
+                else if (coinVal > a) // selected coin(coins[c-1]) is bigger than amount: only can exclude
+                    dp[c][a] = dp[c - 1][a];
+                else // include + exclude
+                    dp[c][a] = dp[c][a - coinVal] + dp[c - 1][a];
+            }
+        }
+        // selecting all possible coins with total amount
+        return dp[coins.size()][amount];
+    }
+};