Perfect Squares — LeetCode 279 Python Solution

The problem

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.

Example

Input

n = 12

Output

3

Explanation

12 = 4 + 4 + 4.

Python solution

class Solution:
    def numSquares(self, n: int) -> int:
        m = int(sqrt(n))
        f = [[inf] * (n + 1) for _ in range(m + 1)]
        f[0][0] = 0
        for i in range(1, m + 1):
            for j in range(n + 1):
                f[i][j] = f[i - 1][j]
                if j >= i * i:
                    f[i][j] = min(f[i][j], f[i][j - i * i] + 1)
        return f[m][n]

Complexity

Pattern: Breadth-First Search

Expand outward level by level, so the first time you arrive is the shortest way. LeetCode 279. Perfect Squares is filed here because LeetCode tags it Breadth-First Search, which is the vocabulary this hub collects.

The breadth-first search guide has the Python template for the pattern and the 233 LeetCode problems that use it.

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