Introduction

In this blog post, we will explore how to solve the LeetCode problem "279" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

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. 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

Here's the breakdown of the solution:

• Dynamic Programming: Use a DP table dp where dp[i] stores the minimum number of perfect squares that sum to i.
• Bottom-Up Approach: Iterate from 1 to n, and for each i, find the minimum number of perfect squares by considering all perfect squares less than or equal to i. Update dp[i] with the minimum value found.

• Optimization: The core optimization comes from pre-calculating the perfect squares up to n.

• Runtime Complexity: O(n sqrt(n)), *Storage Complexity: O(n)

Code

    def numSquares(n: int) -> int:
    """
    Given an integer n, return the least number of perfect square numbers that sum to n.
    """

    dp = [float('inf')] * (n + 1)
    dp[0] = 0

    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]