perfect-squares.py

# Time:  O(n * sqrt(n))
# Space: O(n)
#
# Given a positive integer n, find the least number of perfect
# square numbers (for example, 1, 4, 9, 16, ...) which sum to n.
#
# For example, given n = 12, return 3 because 12 = 4 + 4 + 4;
# given n = 13, return 2 because 13 = 4 + 9.
#

class Solution(object):
    _num = [0]
    def numSquares(self, n):
        """
        :type n: int
        :rtype: int
        """
        num = self._num
        while len(num) <= n:
            num += min(num[-i*i] for i in xrange(1, int(len(num)**0.5+1))) + 1,
        return num[n]