A15214. Yet Another Problem About Pairs Satisfying an Inequality
编程题
普及/提高-
知识点
题目描述
You are given an array $a_1, a_2, \dots a_n$ . Count the number of pairs of indices $1 \leq i, j \leq n$ such that $a_i < i < a_j < j$ .
输入格式
The first line contains an integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases.
The first line of each test case contains an integer $n$ ( $2 \leq n \leq 2 \cdot 10^5$ ) — the length of the array.
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \leq a_i \leq 10^9$ ) — the elements of the array.
It is guaranteed that the sum of $n$ across all test cases does not exceed $2 \cdot 10^5$ .
The first line of each test case contains an integer $n$ ( $2 \leq n \leq 2 \cdot 10^5$ ) — the length of the array.
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \leq a_i \leq 10^9$ ) — the elements of the array.
It is guaranteed that the sum of $n$ across all test cases does not exceed $2 \cdot 10^5$ .
输出格式
For each test case, output a single integer — the number of pairs of indices satisfying the condition in the statement.
Please note, that the answer for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++).
Please note, that the answer for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++).
输入输出样例
输入 #1
5 8 1 1 2 3 8 2 1 4 2 1 2 10 0 2 1 6 3 4 1 2 8 3 2 1 1000000000 3 0 1000000000 2
输出 #1
3 0 10 0 1
说明/提示
For the first test cases the pairs are $(i, j)$ = $\{(2, 4), (2, 8), (3, 8)\}$ .
- The pair $(2, 4)$ is true because $a_2 = 1$ , $a_4 = 3$ and $1 < 2 < 3 < 4$ .
- The pair $(2, 8)$ is true because $a_2 = 1$ , $a_8 = 4$ and $1 < 2 < 4 < 8$ .
- The pair $(3, 8)$ is true because $a_3 = 2$ , $a_8 = 4$ and $2 < 3 < 4 < 8$ .
- The pair $(2, 4)$ is true because $a_2 = 1$ , $a_4 = 3$ and $1 < 2 < 3 < 4$ .
- The pair $(2, 8)$ is true because $a_2 = 1$ , $a_8 = 4$ and $1 < 2 < 4 < 8$ .
- The pair $(3, 8)$ is true because $a_3 = 2$ , $a_8 = 4$ and $2 < 3 < 4 < 8$ .