number-of-unequal-triplets-in-array

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Algorithms

You are given a 0-indexed array of positive integers <code>nums</code>. Find the number of triplets <code>(i, j, k)</code> that meet the following conditions:

<ul>
	<li><code>0 &lt;= i &lt; j &lt; k &lt; nums.length</code></li>
	<li><code>nums[i]</code>, <code>nums[j]</code>, and <code>nums[k]</code> are pairwise distinct.
	<ul>
		<li>In other words, <code>nums[i] != nums[j]</code>, <code>nums[i] != nums[k]</code>, and <code>nums[j] != nums[k]</code>.</li>
	</ul>
	</li>
</ul>

Return the number of triplets that meet the conditions.

&nbsp;
Example 1:

<pre>
Input: nums = [4,4,2,4,3]
Output: 3
Explanation: The following triplets meet the conditions:
- (0, 2, 4) because 4 != 2 != 3
- (1, 2, 4) because 4 != 2 != 3
- (2, 3, 4) because 2 != 4 != 3
Since there are 3 triplets, we return 3.
Note that (2, 0, 4) is not a valid triplet because 2 &gt; 0.
</pre>

Example 2:

<pre>
Input: nums = [1,1,1,1,1]
Output: 0
Explanation: No triplets meet the conditions so we return 0.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>3 &lt;= nums.length &lt;= 100</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
</ul>

unequalTriplets

Number of Unequal Triplets in Array

Count Good Triplets

count-good-triplets

统计好三元组

Count Square Sum Triples

count-square-sum-triples

统计平方和三元组的数目

Number of Arithmetic Triplets

number-of-arithmetic-triplets

等差三元组的数目

Array

Hash Table

Sorting

给你一个下标从 0 开始的正整数数组 <code>nums</code> 。请你找出并统计满足下述条件的三元组 <code>(i, j, k)</code> 的数目：

<ul>
	<li><code>0 &lt;= i &lt; j &lt; k &lt; nums.length</code></li>
	<li><code>nums[i]</code>、<code>nums[j]</code> 和 <code>nums[k]</code> 两两不同 。
	<ul>
		<li>换句话说：<code>nums[i] != nums[j]</code>、<code>nums[i] != nums[k]</code> 且 <code>nums[j] != nums[k]</code> 。</li>
	</ul>
	</li>
</ul>

返回满足上述条件三元组的数目。

&nbsp;

示例 1：

<pre>
输入：nums = [4,4,2,4,3]
输出：3
解释：下面列出的三元组均满足题目条件：
- (0, 2, 4) 因为 4 != 2 != 3
- (1, 2, 4) 因为 4 != 2 != 3
- (2, 3, 4) 因为 2 != 4 != 3
共计 3 个三元组，返回 3 。
注意 (2, 0, 4) 不是有效的三元组，因为 2 &gt; 0 。
</pre>

示例 2：

<pre>
输入：nums = [1,1,1,1,1]
输出：0
解释：不存在满足条件的三元组，所以返回 0 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>3 &lt;= nums.length &lt;= 100</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
</ul>