LeetCode——Coin Change

Question

You are given coins of different denominations and a total amount of money amount. Write a function to compute the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.

Example 1:

coins = [1, 2, 5], amount = 11

return 3 (11 = 5 + 5 + 1)

Example 2:

coins = [2], amount = 3

return -1.

Note:

You may assume that you have an infinite number of each kind of coin.

Credits:

Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

Solution

动态规划。依次计算出组成1～amount所需要的硬币数目。

dp[i] = min(dp[i], dp[i - coins[j]] + 1)，因为是依次求解的，那么求dp[i]的时候，dp[i - coins[j]]已经求解过了。

Code

class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        vector<int> dp(amount + 1, amount + 1);
        dp[0] = 0;
        for (int i = 1; i <= amount; i++) {
            for (int j = 0; j < coins.size(); j++) {
                if (coins[j] <= i) {
                    dp[i] = min(dp[i], dp[i - coins[j]] + 1);
                }
            }
        }
        return dp[amount] < amount + 1 ? dp[amount] : -1;
    }
};