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.
Solution：
思路：
Time Complexity: O(mn) Space Complexity: O(N)
Solution Code：
class Solution {
// dp[i] : the fewest number of coins that need to make up amount i
public int coinChange(int[] coins, int amount) {
if(amount < 1) return 0;
int[] dp = new int[amount + 1];
int sum = 0;
while(++sum <= amount) {
int min = -1;
for(int coin : coins) {
if(sum >= coin && dp[sum - coin] != -1) {
int temp = dp[sum - coin] + 1;
min = min < 0 ? temp : (temp < min ? temp : min);
}
}
dp[sum] = min;
}
return dp[amount];
}
}
