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Luogu P1637 三元上升子序列

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题目描述

https://www.luogu.com.cn/problem/P1637

简单题意：求满足 a[i]<a[j]<a[k]的点集(i,j,k)的个数

Solution

我们按照用树状数组求逆序对时的思路

做两遍树状数组即可

时间复杂度 $O(nlogn)$ 

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#include <iostream>
#include <cstdio>
#include <algorithm>
#define maxn 30010
#define ll long long
#define lowbit(i) ((i) & (-i)) 
using namespace std;

int n, a[maxn];

int b[maxn], cnt; 
void init_hash() { 
    for (int i = 1; i <= n; ++i) b[i] = a[i];
    sort(b + 1, b + n + 1); cnt = unique(b + 1, b + n + 1) - b - 1;
    for (int i = 1; i <= n; ++i) a[i] = lower_bound(b + 1, b + cnt + 1, a[i]) - b;
}

struct Bit {
    int n, Bit[maxn]; 

    inline void add(int i, int v) { while (i <= n) Bit[i] += v, i += lowbit(i); }

    inline int get_sum(int i) {
        int s = 0;
        while (i) s += Bit[i], i -= lowbit(i);
        return s;
    }
} B1, B2; 

int main() {
    cin >> n;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    init_hash(); B1.n = B2.n = cnt; ll ans = 0; 
    for (int i = 1; i <= n; ++i) {
        B2.add(a[i], B1.get_sum(a[i] - 1));
        B1.add(a[i], 1);
        ans += B2.get_sum(a[i] - 1); 
    }
    cout << ans << endl; 
    return 0;
}