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.

递推方程  dp[i]=min{dp[i-j]}+1     1<j<=i

public static int coinChange(int[] coins, int amount)
{
int len=coins.length;
if(len<1)
return -1;

long[] dp=new long[amount+1];
for(int i=0;i<len;i++)
{
int num=coins[i];
if(num<=amount)
dp[num]=1;
}

for(int i=1;i<=amount;i++)
{
long min=Integer.MAX_VALUE;
for(int j=0;j<len;j++)
if(i-coins[j]>=0)
min=Math.min(min, dp[i-coins[j]]+1);
dp[i]=min;
}

long ret=dp[amount];
return (int) (ret==Integer.MAX_VALUE?-1:ret);
}