AcWing 楼蓝图腾(树状数组维护逆序对)

Posted 2022-07-15 mb62d0ca5a0a625

链接

题意：

给出你一段序列，让你找出yig9ong多少先增后减和多少先减后增的三元组。

分析：

用树状数组维护逆序对。先正序维护一个逆序对，再倒序维护逆序对，两两相乘再求和即可。

#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int maxn= 2e5+7;

ll n;
ll a[maxn];
ll tree[maxn];

ll lowbit(ll x)
    return x&(-x);

void update(ll x,ll d)
    while(x<=n)
        tree[x]+=d;
        x+=lowbit(x);
    

ll query(ll x)
    ll ans=0;
    while(x>0)
        ans+=tree[x];
        x-=lowbit(x);
    
    return ans;

ll l[maxn],r[maxn];
int main()
    scanf("%lld",&n);
    for(int i=1;i<=n;i++)
        scanf("%lld",&a[i]);
        l[i]=query(a[i]-1);
        r[i]=query(n)-query(a[i]);
        update(a[i],1);
    
    ll ans1=0;
    ll ans2=0;
    memset(tree,0,sizeof tree);
    for(int i=n;i>=1;i--)
        ans1+=l[i]*query(a[i]-1);
        ans2+=r[i]*(query(n)-query(a[i]));
        update(a[i],1);
    
    cout<<ans2<<" "<<ans1<<endl;

    return 0;