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‎solution/3200-3299/3200.Maximum Height of a Triangle/README.md

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---
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comments: true
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difficulty: 简单
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edit_url: https://github.com/doocs/leetcode/edit/main/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/README.md
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---
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<!-- problem:start -->
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# [3200. 三角形的最大高度](https://leetcode.cn/problems/maximum-height-of-a-triangle)
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[English Version](/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/README_EN.md)
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## 题目描述
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<!-- description:start -->
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<p>给你两个整数 <code>red</code> 和 <code>blue</code>，分别表示红色球和蓝色球的数量。你需要使用这些球来组成一个三角形，满足第 1 行有 1 个球，第 2 行有 2 个球，第 3 行有 3 个球，依此类推。</p>
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<p>每一行的球必须是 <strong>相同 </strong>颜色，且相邻行的颜色必须<strong> 不同</strong>。</p>
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<p>返回可以实现的三角形的 <strong>最大 </strong>高度。</p>
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<p>&nbsp;</p>
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<p><strong class="example">示例 1：</strong></p>
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<div class="example-block">
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<p><strong>输入：</strong> <span class="example-io">red = 2, blue = 4</span></p>
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<p><strong>输出：</strong> 3</p>
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<p><strong>解释：</strong></p>
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<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/images/brb.png" style="width: 300px; height: 240px; padding: 10px;" /></p>
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<p>上图显示了唯一可能的排列方式。</p>
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</div>
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<p><strong class="example">示例 2：</strong></p>
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<div class="example-block">
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<p><strong>输入：</strong> <span class="example-io">red = 2, blue = 1</span></p>
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<p><strong>输出：</strong> <span class="example-io">2</span></p>
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<p><strong>解释：</strong></p>
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<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/images/br.png" style="width: 150px; height: 135px; padding: 10px;" /><br />
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上图显示了唯一可能的排列方式。</p>
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</div>
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<p><strong class="example">示例 3：</strong></p>
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<div class="example-block">
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<p><strong>输入：</strong> <span class="example-io">red = 1, blue = 1</span></p>
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<p><strong>输出：</strong> <span class="example-io">1</span></p>
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</div>
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<p><strong class="example">示例 4：</strong></p>
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<div class="example-block">
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<p><strong>输入：</strong> <span class="example-io">red = 10, blue = 1</span></p>
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<p><strong>输出：</strong> <span class="example-io">2</span></p>
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<p><strong>解释：</strong></p>
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<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/images/br.png" style="width: 150px; height: 135px; padding: 10px;" /><br />
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上图显示了唯一可能的排列方式。</p>
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</div>
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<p>&nbsp;</p>
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<p><strong>提示：</strong></p>
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<ul>
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<li><code>1 &lt;= red, blue &lt;= 100</code></li>
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</ul>
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<!-- description:end -->
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## 解法
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<!-- solution:start -->
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### 方法一：模拟
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我们可以枚举第一行的颜色，然后模拟构造三角形，计算最大高度。
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时间复杂度 $O(\sqrt{n})$，其中 $n$ 为红色球和蓝色球的数量。空间复杂度 $O(1)$。
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<!-- tabs:start -->
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#### Python3
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```python
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class Solution:
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def maxHeightOfTriangle(self, red: int, blue: int) -> int:
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ans = 0
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for k in range(2):
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c = [red, blue]
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i, j = 1, k
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while i <= c[j]:
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c[j] -= i
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j ^= 1
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ans = max(ans, i)
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i += 1
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return ans
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```
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#### Java
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```java
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class Solution {
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public int maxHeightOfTriangle(int red, int blue) {
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int ans = 0;
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for (int k = 0; k < 2; ++k) {
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int[] c = {red, blue};
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for (int i = 1, j = k; i <= c[j]; j ^= 1, ++i) {
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c[j] -= i;
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ans = Math.max(ans, i);
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}
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}
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return ans;
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}
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}
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```
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#### C++
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```cpp
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class Solution {
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public:
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int maxHeightOfTriangle(int red, int blue) {
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int ans = 0;
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for (int k = 0; k < 2; ++k) {
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int c[2] = {red, blue};
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for (int i = 1, j = k; i <= c[j]; j ^= 1, ++i) {
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c[j] -= i;
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ans = max(ans, i);
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}
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}
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return ans;
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}
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};
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```
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#### Go
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```go
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func maxHeightOfTriangle(red int, blue int) (ans int) {
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for k := 0; k < 2; k++ {
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c := [2]int{red, blue}
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for i, j := 1, k; i <= c[j]; i, j = i+1, j^1 {
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c[j] -= i
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ans = max(ans, i)
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}
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}
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return
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}
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```
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#### TypeScript
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```ts
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function maxHeightOfTriangle(red: number, blue: number): number {
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let ans = 0;
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for (let k = 0; k < 2; ++k) {
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const c: [number, number] = [red, blue];
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for (let i = 1, j = k; i <= c[j]; ++i, j ^= 1) {
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c[j] -= i;
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ans = Math.max(ans, i);
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}
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}
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return ans;
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}
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```
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<!-- tabs:end -->
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<!-- solution:end -->
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<!-- problem:end -->

‎solution/3200-3299/3200.Maximum Height of a Triangle/README_EN.md

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---
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comments: true
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difficulty: Easy
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edit_url: https://github.com/doocs/leetcode/edit/main/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/README_EN.md
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---
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<!-- problem:start -->
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# [3200. Maximum Height of a Triangle](https://leetcode.com/problems/maximum-height-of-a-triangle)
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[中文文档](/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/README.md)
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## Description
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<!-- description:start -->
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<p>You are given two integers <code>red</code> and <code>blue</code> representing the count of red and blue colored balls. You have to arrange these balls to form a triangle such that the 1<sup>st</sup> row will have 1 ball, the 2<sup>nd</sup> row will have 2 balls, the 3<sup>rd</sup> row will have 3 balls, and so on.</p>
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<p>All the balls in a particular row should be the <strong>same</strong> color, and adjacent rows should have <strong>different</strong> colors.</p>
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<p>Return the <strong>maximum</strong><em> height of the triangle</em> that can be achieved.</p>
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<p>&nbsp;</p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">red = 2, blue = 4</span></p>
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<p><strong>Output:</strong> 3</p>
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<p><strong>Explanation:</strong></p>
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<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/images/brb.png" style="width: 300px; height: 240px; padding: 10px;" /></p>
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<p>The only possible arrangement is shown above.</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">red = 2, blue = 1</span></p>
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<p><strong>Output:</strong> <span class="example-io">2</span></p>
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<p><strong>Explanation:</strong></p>
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<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/images/br.png" style="width: 150px; height: 135px; padding: 10px;" /><br />
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The only possible arrangement is shown above.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">red = 1, blue = 1</span></p>
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<p><strong>Output:</strong> <span class="example-io">1</span></p>
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</div>
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<p><strong class="example">Example 4:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">red = 10, blue = 1</span></p>
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<p><strong>Output:</strong> <span class="example-io">2</span></p>
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<p><strong>Explanation:</strong></p>
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<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3200-3299/3200.Maximum%20Height%20of%20a%20Triangle/images/br.png" style="width: 150px; height: 135px; padding: 10px;" /><br />
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The only possible arrangement is shown above.</p>
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</div>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 &lt;= red, blue &lt;= 100</code></li>
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</ul>
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<!-- description:end -->
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## Solutions
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<!-- solution:start -->
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### Solution 1: Simulation
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We can enumerate the color of the first row, then simulate the construction of the triangle, calculating the maximum height.
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The time complexity is $O(\sqrt{n})$, where $n$ is the number of red and blue balls. The space complexity is $O(1)$.
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<!-- tabs:start -->
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#### Python3
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```python
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class Solution:
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def maxHeightOfTriangle(self, red: int, blue: int) -> int:
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ans = 0
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for k in range(2):
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c = [red, blue]
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i, j = 1, k
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while i <= c[j]:
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c[j] -= i
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j ^= 1
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ans = max(ans, i)
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i += 1
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return ans
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```
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#### Java
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```java
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class Solution {
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public int maxHeightOfTriangle(int red, int blue) {
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int ans = 0;
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for (int k = 0; k < 2; ++k) {
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int[] c = {red, blue};
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for (int i = 1, j = k; i <= c[j]; j ^= 1, ++i) {
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c[j] -= i;
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ans = Math.max(ans, i);
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}
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}
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return ans;
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}
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}
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```
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#### C++
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```cpp
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class Solution {
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public:
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int maxHeightOfTriangle(int red, int blue) {
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int ans = 0;
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for (int k = 0; k < 2; ++k) {
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int c[2] = {red, blue};
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for (int i = 1, j = k; i <= c[j]; j ^= 1, ++i) {
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c[j] -= i;
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ans = max(ans, i);
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}
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}
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return ans;
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}
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};
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```
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#### Go
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```go
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func maxHeightOfTriangle(red int, blue int) (ans int) {
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for k := 0; k < 2; k++ {
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c := [2]int{red, blue}
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for i, j := 1, k; i <= c[j]; i, j = i+1, j^1 {
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c[j] -= i
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ans = max(ans, i)
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}
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}
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return
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}
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```
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#### TypeScript
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```ts
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function maxHeightOfTriangle(red: number, blue: number): number {
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let ans = 0;
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for (let k = 0; k < 2; ++k) {
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const c: [number, number] = [red, blue];
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for (let i = 1, j = k; i <= c[j]; ++i, j ^= 1) {
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c[j] -= i;
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ans = Math.max(ans, i);
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}
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}
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return ans;
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}
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```
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<!-- tabs:end -->
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<!-- solution:end -->
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<!-- problem:end -->

‎solution/3200-3299/3200.Maximum Height of a Triangle/Solution.cpp

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class Solution {
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public:
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int maxHeightOfTriangle(int red, int blue) {
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int ans = 0;
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for (int k = 0; k < 2; ++k) {
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int c[2] = {red, blue};
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for (int i = 1, j = k; i <= c[j]; j ^= 1, ++i) {
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c[j] -= i;
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ans = max(ans, i);
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}
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}
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return ans;
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}
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};

‎solution/3200-3299/3200.Maximum Height of a Triangle/Solution.go

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func maxHeightOfTriangle(red int, blue int) (ans int) {
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for k := 0; k < 2; k++ {
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c := [2]int{red, blue}
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for i, j := 1, k; i <= c[j]; i, j = i+1, j^1 {
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c[j] -= i
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ans = max(ans, i)
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}
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}
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return
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}

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