LeetCode 279. Perfect Squares

Description

https://leetcode.com/problems/perfect-squares/

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

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, 149, 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

Explanation

Dynamic programming dp[i] means what is the minimum number of square numbers to add up to equal to i.

Python Solution

class Solution:
    def numSquares(self, n: int) -> int:
        
        square_nums = [i**2 for i in range(0, int(sqrt(n)) + 1)]
        
        
        dp = [float('inf')] * (n + 1)
        
        
        dp[0] = 0
        
        
        for i in range(1, n + 1):
            for square in square_nums:
                if i < square:
                    break
                    
                dp[i] = min(dp[i], dp[i - square] + 1)
                
        return dp[n]
  • Time Complexity: O(N).
  • Space Complexity: O(N).

where Q is the length of queries and N is the length of colors.

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