## Coin Change

07/18/2016 Dynamic Programming

## 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.

## Solution

Result: Accepted Time: 20 ms

Here should be some explanations.

#define MAXN 65535
int dp[MAXN];
int coinChange(int* coins, int coinsSize, int amount) {
memset(dp,0x3f,sizeof(int)*(amount+1));
dp[0] = 0;
for(int i = 0; i < coinsSize; i++)
for(int j = 0,k = coins[i]; j <= amount; j++,k++)
dp[k] = dp[j] + 1 < dp[k] ? dp[j]+1 : dp[k];
return dp[amount] == 0x3f3f3f3f? -1:dp[amount];
}


Complexity Analytics

• Time Complexity: $O(n^2)$
• Space Complexity: $O(n)$