Perfect Squares

Problem Statement

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.

Leetcode link

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

Code

Python Code

class Solution:
    def numSquares(self, n):
        if n < 2:
            return n
        lst = []
        i = 1
        while i * i <= n:
            lst.append( i * i )
            i += 1
        cnt = 0
        toCheck = {n}
        while toCheck:
            cnt += 1
            temp = set()
            for x in toCheck:
                for y in lst:
                    if x == y:
                        return cnt
                    if x < y:
                        break
                    temp.add(x-y)
            toCheck = temp

        return cnt