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# Coin Change

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Problem Statement
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

```Input: coins = [1, 2, 5], amount = 11
Output: 3
Explanation: 11 = 5 + 5 + 1
```

Example 2

```Input: coins = , amount = 3
Output: -1
```

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

Solution

```class Solution {
public int coinChange(int[] coins, int amount) {
final int MAX = 1000;
int n = coins.length;

// dp[i] = minimum number of coins to make up amount i
int[] dp = new int[amount+1];
dp = 0;

for (int a=1; a<=amount; a++){
dp[a] = MAX;
}

for (int coin:coins) {
if (coin <= amount) {
dp[coin] = 1;
}
}

for (int a=1; a<=amount; a++){
for (int coin:coins) {
if (a-coin >= 0) {
dp[a] = Math.min(dp[a-coin]+1, dp[a]);
}
}
}

if (dp[amount] != MAX) {
return dp[amount];
} else {
return -1;
}
}
}
```