Introduction

In this blog post, we will explore how to solve the LeetCode problem "1739" 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

You have a cubic storeroom where the width, length, and height of the room are all equal to n units. You are asked to place n boxes in this room where each box is a cube of unit side length. There are however some rules to placing the boxes: You can place the boxes anywhere on the floor. If box x is placed on top of the box y, then each side of the four vertical sides of the box y must either be adjacent to another box or to a wall. Given an integer n, return the minimum possible number of boxes touching the floor. Example 1: Input: n = 3 Output: 3 Explanation: The figure above is for the placement of the three boxes. These boxes are placed in the corner of the room, where the corner is on the left side. Example 2: Input: n = 4 Output: 3 Explanation: The figure above is for the placement of the four boxes. These boxes are placed in the corner of the room, where the corner is on the left side. Example 3: Input: n = 10 Output: 6 Explanation: The figure above is for the placement of the ten boxes. These boxes are placed in the corner of the room, where the corner is on the back side. Constraints: 1 <= n <= 109

Explanation

Here's the breakdown of the solution:

• Layered Pyramid: The most efficient way to stack the boxes is to form a pyramid in the corner of the room. Each layer of the pyramid will be a square.
• Sum of Triangular Numbers: The number of boxes in each layer will follow a triangular number sequence (1, 3, 6, 10,...). The total number of boxes used will be the sum of these triangular numbers. We need to find the minimum number of layers required to reach or exceed n boxes.

• Floor Touch: The number of boxes touching the floor is the number of boxes in the base layer. This is equal to the triangular number corresponding to the number of layers.

• Runtime Complexity: O(cbrt(n)) and Storage Complexity: O(1)

Code

    def minimumBoxes(n: int) -> int:
    k = 0
    total = 0
    while total < n:
        k += 1
        total += k * (k + 1) // 2
    return k * (k + 1) // 2