树状数组笔记

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用来放自己的板子。

单点修改区间查询：

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#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int N = 1e6 + 10;

int n;
ll t[N],a[N];
int lowbit(int x)
{
    return x & -x;
}
void init()
{
     for(int i = 1;i <= n;i++)
    {
        t[i] += a[i];
        int j = i + lowbit(i);
        if(j <= n) t[j] += t[i];
    }
}
void add(int x,int k)
{
    while(x <= n)
    {
        t[x] += k;
        x += lowbit(x);
    }
}
ll getsum(int x)
{
    ll res = 0;
    while(x >= 1)
    {
        res += t[x];
        x -= lowbit(x);
    }
    return res;
}
int main()
{
    int T;
    scanf("%d%d",&n,&T);
    for(int i = 1;i <= n;i++)
        scanf("%lld",a + i);
    init();
    while(T--)
    {
        int op;
        scanf("%d",&op);
        if(op == 1)
        {
            int x,k;
            scanf("%d%d",&x,&k);
            add(x,k);
        }
        else 
        {
            int l,r;
            scanf("%d%d",&l,&r);
            printf("%lld\n",getsum(r) - getsum(l - 1));
        }
    }
    return 0;
}

区间修改单点查询：

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#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int N = 1e6 + 10;

int n;
ll t[N],a[N];
int lowbit(int x)
{
    return x & -x;
}
void init()
{
    for(int i = 1;i <= n;i++)
    {
        t[i] += a[i] - a[i - 1];
        int j = i + lowbit(i);
        if(j <= n) t[j] += t[i];
    }
}
void add(int x,int k)
{
    while(x <= n)
    {
        t[x] += k;
        x += lowbit(x);
    }
}
ll getsum(int x)
{
    ll res = 0;
    while(x >= 1)
    {
        res += t[x];
        x -= lowbit(x);
    }
    return res;
}
int main()
{
    int T;
    scanf("%d%d",&n,&T);
    for(int i = 1;i <= n;i++)
        scanf("%lld",a + i);
    init();
    while(T--)
    {
        int op;
        scanf("%d",&op);
        if(op == 1)
        {
            int l,r,k;
            scanf("%d%d%d",&l,&r,&k);
            add(l,k);add(r + 1,-k);
        }
        else 
        {
            int x;
            scanf("%d",&x);
            printf("%lld\n",getsum(x));
        }
    }
    return 0;
}

区间修改区间查询：

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#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int N = 1e6 + 10;

int n;
ll t1[N],t2[N],a[N];
int lowbit(int x)
{
    return x & -x;
}
void init()
{
    for(int i = 1;i <= n;i++)
    {
        ll k = a[i] - a[i - 1];
        t1[i] += k;t2[i] += k * (i - 1);
        int j = i + lowbit(i);
        if(j <= n) 
            t1[j] += t1[i],
            t2[j] += t2[i];
    }
}
void add(int x,ll k)
{
    ll i = x - 1;
    while(x <= n)
    {
        t1[x] += k;
        t2[x] += k * i;
        x += lowbit(x);
    }
}
ll getsum(int x)
{
    ll res = 0,i = x;
    while(x >= 1)
    {
        res += i * t1[x] - t2[x];
        x -= lowbit(x);
    }
    return res;
}
int main()
{
    int T;
    scanf("%d%d",&n,&T);
    for(int i = 1;i <= n;i++)
        scanf("%lld",a + i);
    init();
    while(T--)
    {
        int op,l,r;
        scanf("%d%d%d",&op,&l,&r);
        if(op == 1)
        {
            ll k;
            scanf("%lld",&k);
            add(l,k);add(r + 1,-k);
        }
        else 
        {
            printf("%lld\n",getsum(r) - getsum(l - 1));
        }
    }
    return 0;
}