外挂---线段树懒标记板子+简单数学推理

题目链接

#include <iostream>
#include <cstring>
#include <algorithm>

using namespace std;
#define int long long
const int N = 100010;

int n, m;
int w[N];
struct node
{
    
	int l, r;
	int sum, sum2;
	int add;
}tr[N*4];


void pushup(int u)
{
    
    tr[u].sum = tr[u<<1].sum + tr[u<<1|1].sum;
    tr[u].sum2 = tr[u<<1].sum2 + tr[u<<1|1].sum2;
}

void cal(node &t,int add)
{
    
    t.sum2 = t.sum2 + 2ll * t.sum * add + (t.r - t.l + 1) * add * add; 
    t.sum = t.sum + (t.r - t.l + 1) * add;
}

void pushdown(int u)
{
    
	if(tr[u].add)
	{
    
        cal(tr[u<<1], tr[u].add);
        cal(tr[u<<1|1], tr[u].add);
        
        tr[u<<1].add += tr[u].add;
        tr[u<<1|1].add += tr[u].add;
		tr[u].add = 0;
	}
}

void build(int u,int l,int r)
{
    
	if(l == r)tr[u] = {
    l, r, w[l], w[l]*w[l], 0};
	else
	{
    
		tr[u] = {
    l,r};
		int mid = l + r >> 1;
		build(u<<1, l, mid);
		build(u<<1|1, mid+1, r);	
		pushup(u);
	}
}

void modify(int u,int l,int r,int v)
{
    
	if(tr[u].l >= l && tr[u].r <= r)
	{
    
		cal(tr[u], v);
        tr[u].add += v;
		return ;
	}
	pushdown(u);
	int mid = tr[u].l + tr[u].r >> 1;
	if(l <= mid) modify(u<<1, l, r, v);
	if(r > mid) modify(u<<1|1, l, r, v);
	pushup(u);
}

pair<int,int> query(int u,int l,int r)
{
    
	if(tr[u].l >= l && tr[u].r <= r)return {
    tr[u].sum, tr[u].sum2};
	int sum1 = 0, sum2 = 0;
	int mid=tr[u].l + tr[u].r >> 1;
	pushdown(u);
	if(l <= mid)
    {
    
        pair<int,int> t = query(u<<1, l, r);
        sum1 += t.first;
        sum2 += t.second;
    }
	if(r>mid)
    {
    
        pair<int,int> t = query(u<<1|1, l, r);
        sum1 += t.first;
        sum2 += t.second;
    }
	return {
    sum1,sum2};
}

signed main()
{
    
	cin>>n>>m;
    for(int i=1;i<=n;i++)cin>>w[i];
    build(1, 1, n);
	int op,l,r;
	while(m--)
    {
    
    	cin>>op>>l>>r;
    	if(op==1)
    	{
    
    		int k;cin>>k;
    		modify(1, l, r, k);
		}
		else 
        {
    
            pair<int,int> t = query(1, l, r);
            cout<<(t.first * t.first - t.second) / 2 <<'\n';
        }
	}
}