PAT 1009. Triple Inversions (35) 数状数组

Given a list of N integers A₁, A₂, A₃,...A_N, there's a famous problem to count the number of inversions in it. An inversion is defined as a pair of indices i < j such that A_i > A_j.

Now we have a new challenging problem. You are supposed to count the number of triple inversions in it. As you may guess, a triple inversion is defined as a triple of indices i < j < k such that A_i > A_j > A_k. For example, in the list {5, 1, 4, 3, 2} there are 4 triple inversions, namely (5,4,3), (5,4,2), (5,3,2) and (4,3,2). To simplify the problem, the list A is given as a permutation of integers from 1 to N.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N in [3, 10⁵]. The second line contains a permutation of integers from 1 to N and each of the integer is separated by a single space.

Output Specification:

For each case, print in a line the number of triple inversions in the list.

Sample Input:

22
1 2 3 4 5 16 6 7 8 9 10 19 11 12 14 15 17 18 21 22 20 13

Sample Output:

8

题意：给定1~n的无序数列，求其中长度=3连续递减的字串个数，如样例：(16,14,13)。
思路：愚蠢！愚蠢！刚开始找的是三个数中的最前一个，然而判断连续递减就有点困难（这题时间限制为300ms）。
其实可以找中间的那个数，再向左查询比中间数大的数的个数，向右查询比中间数小的个数, 两侧相乘就是解了。
最大的问题是如何记录大小，因为给定的是1~n连续的数，甚至不需用离散化，通过遍历到某个数，找比它小或大的是否已经被标记了，再标记这个数。
快速求和操作显然要用到树状数组。
噢，还有这题注意结果使用long long 为此而WA。

#include <stdio.h>
#include <iostream>
#include <string.h>
#include <algorithm>
#define LL long long
using namespace std;


int n, c[100010], a[100010];
LL l[100010], r[100010];
void add(int x)  //增加操作 
{
    while(x <= n)
    {
        c[x]++;
        x += x & (-x);
    }
}

int get(int x) //获取和 
{
    int ans = 0;
    while(x)
    {
        ans +=c[x];
        x -= x & (-x);
    }
    return ans;
}
int main()
{
    LL ans;
    while(cin >> n)
    {
        ans = 0;
        for(int i = 1; i <= n; i++)
        {
            scanf("%d", a + i);
            c[i] = 0;
        }
        for(int i = 1; i <= n; i++)
        {
            l[i] = i - 1 - get(a[i]);
            add(a[i]);
        }
        for(int i = 1; i <= n; i++)
            c[i] = 0;
        for(int i = 1; i <= n; i++)
        {
            r[i] = a[i] - 1 - get(a[i]);//为value - 左侧大于它的个数 
            add(a[i]);
        }

        for(int i = 1; i <= n; i++)
            ans += l[i]*r[i];

        printf("%lld
", ans);
    }
}