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Algorithms

You have a cubic storeroom where the width, length, and height of the room are all equal to <code>n</code> units. You are asked to place <code>n</code> boxes in this room where each box is a cube of unit side length. There are however some rules to placing the boxes:

<ul>
	<li>You can place the boxes anywhere on the floor.</li>
	<li>If box <code>x</code> is placed on top of the box <code>y</code>, then each side of the four vertical sides of the box <code>y</code> must either be adjacent to another box or to a wall.</li>
</ul>

Given an integer <code>n</code>, return the minimum possible number of boxes touching the floor.

&nbsp;
Example 1:

<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/3-boxes.png" style="width: 135px; height: 143px;" />

<pre>
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.
</pre>

Example 2:

<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/4-boxes.png" style="width: 135px; height: 179px;" />

<pre>
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.
</pre>

Example 3:

<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/10-boxes.png" style="width: 271px; height: 257px;" />

<pre>
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.</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 109</code></li>
</ul>

minimumBoxes

Building Boxes

Block Placement Queries

block-placement-queries

物块放置查询

Greedy

Math

Binary Search

有一个立方体房间，其长度、宽度和高度都等于 <code>n</code> 个单位。请你在房间里放置 <code>n</code> 个盒子，每个盒子都是一个单位边长的立方体。放置规则如下：

<ul>
	<li>你可以把盒子放在地板上的任何地方。</li>
	<li>如果盒子 <code>x</code> 需要放置在盒子 <code>y</code> 的顶部，那么盒子 <code>y</code> 竖直的四个侧面都 必须 与另一个盒子或墙相邻。</li>
</ul>

给你一个整数 <code>n</code> ，返回接触地面的盒子的 最少 可能数量。

 

示例 1：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/01/24/3-boxes.png" style="width: 135px; height: 143px;" />

<pre>
输入：n = 3
输出：3
解释：上图是 3 个盒子的摆放位置。
这些盒子放在房间的一角，对应左侧位置。
</pre>

示例 2：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/01/24/4-boxes.png" style="width: 135px; height: 179px;" />

<pre>
输入：n = 4
输出：3
解释：上图是 3 个盒子的摆放位置。
这些盒子放在房间的一角，对应左侧位置。
</pre>

示例 3：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/01/24/10-boxes.png" style="width: 271px; height: 257px;" />

<pre>
输入：n = 10
输出：6
解释：上图是 10 个盒子的摆放位置。
这些盒子放在房间的一角，对应后方位置。</pre>

 

提示：

<ul>
	<li><code>1 <= n <= 109</code></li>
</ul>