Perfect 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
SOLUTION:
import math

class Solution:
    def numSquaresRec(self, n: int) -> int:
        if n <= 1:
            return n
        if n in self.memo:
            return self.memo[n]
        root = int(math.sqrt(n))
        minSquares = float('inf')
        for k in range(1, root + 1):
            minSquares = min(minSquares, 1 + self.numSquaresRec(n - k * k))
        self.memo[n] = minSquares
        return minSquares

    def numSquares(self, n: int) -> int:
        self.memo = {}
        return self.numSquaresRec(n)

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