Watch 10 video solutions for Building Boxes, a hard level problem involving Math, Binary Search, Greedy. This walkthrough by Fireship has 1,342,640 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
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:
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