0279 Number Squares

Given an integer n, return the least number of perfect square numbers that sum to n.

A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.

Example 1:

Input: n = 12
Output: 3
Explanation: 12 = 4 + 4 + 4.

Example 2:

Input: n = 13
Output: 2
Explanation: 13 = 4 + 9.

Constraints:

1 <= n <= 104

import math 
def numSquares(n):
    # dp table
    # dp[i] is the least number of perfect square 
    dp = [float('inf')]*(n+1)
    dp[0] = 0
    dp[1] = 1
    # fill dp
    for i in range(2,n+1):
        for j in range(1, int(math.sqrt(i))+1):
            if j**2 == i:    
                dp[i] = 1
            else:
                dp[i] = min(dp[i], dp[i-j**2] + 1)
    return dp[n]

# test
n = 13
numSquares(n)

2

The above solution has a time limit when n is larger, such as n=6637.

The following code can improve the speed but the time complexity is the same.

def numSquares(n):
    dp = [float('inf')] * (n + 1)
    dp[0] = 0
    for i in range(1, n + 1):
        j = 1
        while j * j <= i:
            dp[i] = min(dp[i], dp[i - j * j] + 1)
            j += 1
    return dp[n]