322. Coin Change

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.

This is a forward DP, by knowing DP[i], calculate DP[i + x]. Note the direction, also here we need to caculate dp[i] + 1, which may overflow. so the MAX value is actually Integer.MAX_VALUE -1, or 0x7ffffffe;

public class Solution {
    public int coinChange(int[] coins, int amount) {
        int dp[] = new int[amount+1];
        for(int i= 1; i<= amount; i++){
            dp[i] = 0x7ffffffe;// why not Integer.MAX_VALUE ??? 
        }

        for(int i= 0; i<= amount; i++){
            for(int c : coins){
                if(i+c <= amount){
                    dp[i + c] = Math.min(dp[i+c], dp[i] + 1); 
                    //casue dp[i] may be Integer.MAX_VALUE, and + 1 make it overflow;
                }
            }
        }
        return dp[amount] == 0x7ffffffe ? -1 : dp[amount];
    }
}