AcWing 243. 一个简单的整数问题2 （树状数组）打卡

题目：https://www.acwing.com/problem/content/244/

题意：区间加，区间查询

思路：我们把原先那个差分数组分解一下

∑i=1x∑j=1ib[j]=∑i=1x(x−i+1)×b[i]=(x+1)∑i=1xb[i]−∑i=1xi×b[i]

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define lowbit(x) x&(-x)
const int N=2e5;
ll c1[N],c2[N],n,m,a[N];
ll add(ll x,ll y)
{
    for(ll i=x;i<=n;i+=lowbit(i))
    {
        c1[i]+=y;
        c2[i]+=x*y;
    }
}
ll ask(ll x)
{
    ll ans=0;
    for(ll i=x;i;i-=lowbit(i))
        ans+=(x+1)*c1[i]-c2[i];
    return ans;
}
int main()
{
    scanf("%lld%lld
",&n,&m);
    for(ll i=1;i<=n;i++)
    {
        scanf("%lld",&a[i]);
        add(i,a[i]-a[i-1]);
    }
    getchar();
    while(m--)
    {
        char ch=getchar();
        if (ch=='Q')
        {
            ll x,y;
            scanf("%lld%lld
",&x,&y);
            cout<<ask(y)-ask(x-1)<<endl;
        }
        if (ch=='C')
        {
            ll x,y,d;
            scanf("%lld%lld%lld
",&x,&y,&d);
            add(x,d);
            add(y+1,-d);
        }
    }
    return 0;
}