UVALA 4329 - Ping pong 树状数组+组合原理

点击打开题目链接 UVALA 4329

题意与分析：

代码：

#include <cstdio>
#include <iostream>
#include <cstring>
using namespace std;

const int MAXN = 20000 + 10;
const int MAXM = 100000 +10;
int num[MAXN];
int c[MAXN], d[MAXN], x[MAXM];

//x 的二进制表达式中最右边的1所对应的值
int lobit(int x)
{
    return x & -x;
}
//前缀和
int sum(int k)
{
    int ret = 0;
    while(k > 0)
    {
        ret += x[k];
        k -= lobit(k);
    }
    return ret;
}
//更新 x 数组
void add(int k)
{
    while (k <= 100000)
    {
        x[k] += 1;
        k += lobit(k);
    }
}

int main()
{
    int t, n;
    scanf("%d", &t);
    while (t--)
    {
        scanf("%d", &n);
        for (int i = 1; i <= n; i++)
        {
            scanf("%d", &num[i]);
        }
        memset(x, 0, sizeof(x));
        for (int i = 1; i <= n; i++)    //正序求c[i]
        {
            add(num[i]);
            c[i] = sum(num[i] - 1);
        }

        memset(x, 0, sizeof(x));
        for (int i = n; i >= 1; i--)    //逆序求d[i]
        {
            add(num[i]);
            d[i] = sum(num[i] - 1);
        }

        long long ans = 0;
        for (int i = 1; i <= n; i++)
        {
            ans += (long long)c[i] * (n - i - d[i]) + d[i] * (i - 1 - c[i]);
        }
        printf("%lld\n", ans);
    }
    return 0;
}