k-inverse-pairs-array

java

python

python3

mysql

mssql

oraclesql

csharp

javascript

typescript

bash

swift

kotlin

dart

golang

ruby

scala

rust

racket

erlang

elixir

pythondata

postgresql

cangjie

Algorithms

For an integer array <code>nums</code>, an inverse pair is a pair of integers <code>[i, j]</code> where <code>0 &lt;= i &lt; j &lt; nums.length</code> and <code>nums[i] &gt; nums[j]</code>.

Given two integers n and k, return the number of different arrays consisting of numbers from <code>1</code> to <code>n</code> such that there are exactly <code>k</code> inverse pairs. Since the answer can be huge, return it modulo <code>109 + 7</code>.

&nbsp;
Example 1:

<pre>
Input: n = 3, k = 0
Output: 1
Explanation: Only the array [1,2,3] which consists of numbers from 1 to 3 has exactly 0 inverse pairs.
</pre>

Example 2:

<pre>
Input: n = 3, k = 1
Output: 2
Explanation: The array [1,3,2] and [2,1,3] have exactly 1 inverse pair.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
	<li><code>0 &lt;= k &lt;= 1000</code></li>
</ul>

kInversePairs

K Inverse Pairs Array

Count the Number of Inversions

count-the-number-of-inversions

统计逆序对的数目

Dynamic Programming

对于一个整数数组&nbsp;<code>nums</code>，逆序对是一对满足 <code>0 &lt;= i &lt; j &lt; nums.length</code> 且&nbsp;<code>nums[i] &gt; nums[j]</code>的整数对&nbsp;<code>[i, j]</code>&nbsp;。

给你两个整数&nbsp;<code>n</code>&nbsp;和&nbsp;<code>k</code>，找出所有包含从&nbsp;<code>1</code>&nbsp;到&nbsp;<code>n</code>&nbsp;的数字，且恰好拥有&nbsp;<code>k</code>&nbsp;个 逆序对 的不同的数组的个数。由于答案可能很大，只需要返回对 <code>109&nbsp;+ 7</code> 取余的结果。

&nbsp;

示例 1：

<pre>
输入：n = 3, k = 0
输出：1
解释：
只有数组 [1,2,3] 包含了从1到3的整数并且正好拥有 0 个逆序对。
</pre>

示例 2：

<pre>
输入：n = 3, k = 1
输出：2
解释：
数组 [1,3,2] 和 [2,1,3] 都有 1 个逆序对。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
	<li><code>0 &lt;= k &lt;= 1000</code></li>
</ul>