1. Perfect Squares

Given a positive integern, find the least number of perfect square numbers (for example,1, 4, 9, 16, ...) which sum ton.

For example, givenn=12, return3because12 = 4 + 4 + 4; givenn=13, return2because13 = 4 + 9.

dp[0] = 0 
dp[1] = dp[0]+1 = 1
dp[2] = dp[1]+1 = 2
dp[3] = dp[2]+1 = 3
dp[4] = Min{ dp[4-1*1]+1, dp[4-2*2]+1 } 
      = Min{ dp[3]+1, dp[0]+1 } 
      = 1                
dp[5] = Min{ dp[5-1*1]+1, dp[5-2*2]+1 } 
      = Min{ dp[4]+1, dp[1]+1 } 
      = 2
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dp[13] = Min{ dp[13-1*1]+1, dp[13-2*2]+1, dp[13-3*3]+1 } 
       = Min{ dp[12]+1, dp[9]+1, dp[4]+1 } 
       = 2
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dp[n] = Min{ dp[n - i*i] + 1 },  n - i*i >=0 && i >= 1

public class Solution {
    public int numSquares(int n) {

        if(n <= 0) return 0;

        int[] dp = new int[n + 1];

        for(int i = 1; i <= n; i ++){

            int min = Integer.MAX_VALUE;
            for(int j = 1; j*j <= i; j ++)
                min = Math.min(min, dp[i - j * j] + 1);

            dp[i] = min;
        }

        return dp[n];
    }
}