Perfect Squares Python Solution with Tests

LeetCode 279, Medium. Topics: Math, Dynamic Programming, Breadth-First Search. View on LeetCode. Generate this problem as a practice environment: tested reference solution, 17 parametrized pytest cases, and a playground notebook:

lcpy gen -n 279   # by problem number
lcpy gen -s perfect_squares   # by problem name

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. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.

Examples

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

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

Constraints

1 <= n <= 10^4

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(n * sqrt(n))
    # Space: O(n)
    def num_squares(self, n: int) -> int:
        dp = [0] + [n + 1] * n
        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]

Complexity

Time	Space
O(n * sqrt(n))	O(n)

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Perfect Squares Python Solution with Tests

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