279. Perfect Squares

第一种做法是动态规划，用一个数组perfect[i]来记录到perfect[i]数目，perfect[0]=0，对于i来说，任意一个i-jj + jj = i，所以prefect[i] = min(perfect[i], perfect[i-j*j] + 1),把所有perfect[i]初始化为n。代码如下：

import math
class Solution(object):
    def numSquares(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 0:
            return 0
        perfect = [n for i in range(n+1)]
        perfect[0] = 0
        for i in range(n+1):
            for j in range(1,int(math.sqrt(i)+1)):
                perfect[i] = min(perfect[i],perfect[i-j*j]+1)
        return perfect[-1]

第二种做法是静态动态规划。

import math
class Solution(object):
    def numSquares(self, n):
        """
        :type n: int
        :rtype: int
        """
        perfect = []
        perfect.append(0)
        
        while len(perfect) <= n:
            m = len(perfect)
            minc = n
            for i in range(1, int(math.sqrt(m))+1):
                minc = min(minc,perfect[m-i*i] + 1)
            perfect.append(minc)
        return perfect[-1]