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#1739 - Building Boxes
Problem Description
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.
Solution
/**
* @param {number} n
* @return {number}
*/
var minimumBoxes = function(n) {
if (n < 4) return n;
let baseSize = 0;
let totalBoxes = 0;
const triangular = k => k * (k + 1) / 2;
while (totalBoxes + triangular(baseSize + 1) <= n) {
baseSize++;
totalBoxes += triangular(baseSize);
}
const remaining = n - totalBoxes;
let extraFloor = 0;
while (triangular(extraFloor) < remaining) extraFloor++;
return triangular(baseSize) + extraFloor;
};