#include <bits/stdc++.h>
#define int long long
using namespace std;
const int N = 100005 , SN = 1005;

int n , m , a[ N ];
int lenb;
int q[ N ] , st[ SN ] , ed[ SN ];
int sum[ SN ] , add[ SN ];

void modify( int l , int r , int v )
{
	int lx = q[ l ] , rx = q[ r ];
	
	if( lx == rx )
	{
		sum[ lx ] += v * ( r - l + 1 );
		for( int i = l ; i <= r ; i ++ )
			a[ i ] += v;
		return;
	}
	
	sum[ lx ] += v * ( ed[ lx ] - l + 1 );
	for( int i = l ; i <= ed[ lx ] ; i ++ )
		a[ i ] += v;
	
	for( int i = lx + 1 ; i <= rx - 1 ; i ++ )
		add[ i ] += v;
	
	sum[ rx ] += v * ( r - st[ rx ] + 1 ); 
	for( int i = st[ rx ] ; i <= r ; i ++ ) 
		a[ i ] += v;
}

int query( int l , int r )
{
	int lx = q[ l ] , rx = q[ r ] , ans = 0;
	
	if( lx == rx )
	{
		ans += add[ lx ] * ( r - l + 1 );
		for( int i = l ; i <= r ; i ++ )
			ans += a[ i ];
		return ans;
	}
	
	ans += add[ lx ] * ( ed[ lx ] - l + 1 );
	for( int i = l ; i <= ed[ lx ] ; i ++ )
		ans += a[ i ];
	
	for( int i = lx + 1 ; i <= rx - 1 ; i ++ )
		ans += sum[ i ] + add[ i ] * lenb;
	
	ans += add[ rx ] * ( r - st[ rx ] + 1 ); 
	for( int i = st[ rx ] ; i <= r ; i ++ )
		ans += a[ i ];
	
	return ans;
}

void init()
{
	lenb = sqrt( n );
	for( int i = 1 ; i <= ceil( 1.0 * n / lenb ) ; i ++ )
	{
		st[ i ] = ( i - 1 ) * lenb + 1;
		ed[ i ] = min( i * lenb , n );
		for( int j = st[ i ] ; j <= ed[ i ] ; j ++ )
			q[ j ] = i , sum[ i ] += a[ j ];
	}
}

signed main()
{
	cin >> n;
	for( int i = 1 ; i <= n ; i ++ )
		scanf( "%lld" , a + i );
	init();
	
	cin >> m;
	while( m -- )
	{
		int opt , l , r , v;
		scanf( "%lld%lld%lld" , & opt , & l , & r );
		
		if( opt == 1 )
		{
			scanf( "%lld" , & v );
			modify( l , r , v );
		}
		
		if( opt == 2 )
		{
			printf( "%lld\n" , query( l , r ) );
		}
	}
	
	return 0;
}

线段树解法代码：

#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5;
int n, q;
long long lazy[maxn<<2], tr[maxn<<2];

#define lson l, mid, rt<<1
#define rson mid+1, r, rt<<1|1
void push_up(int rt) {
	tr[rt] = tr[rt<<1] + tr[rt<<1|1];
}
void push_down(int l, int r, int rt) {
	if (lazy[rt]) {
		int mid = (l + r) / 2;
		tr[rt<<1] += (mid - l + 1) * lazy[rt];
		lazy[rt<<1] += lazy[rt];
		tr[rt<<1|1] += (r - mid) * lazy[rt];
		lazy[rt<<1|1] += lazy[rt];
		lazy[rt] = 0;
	}
}
void build(int l, int r, int rt) {
	if (l == r) {
		scanf("%lld", tr + rt);
		return;
	}
	int mid = (l + r) / 2;
	build(lson);
	build(rson);
	push_up(rt);
}
void update(int L, int R, long long x, int l, int r, int rt) {
	if (L <= l && r <= R) {
		tr[rt] += (r - l + 1) * x;
		lazy[rt] += x;
		return;
	}
	push_down(l, r, rt);
	int mid = (l + r) / 2;
	if (L <= mid) update(L, R, x, lson);
	if (R > mid) update(L, R, x, rson);
	push_up(rt);
}
long long query(int L, int R, int l, int r, int rt) {
	if (L <= l && r <= R)
		return tr[rt];
	push_down(l, r, rt);
	int mid = (l + r) / 2;
	long long res = 0;
	if (L <= mid) res += query(L, R, lson);
	if (R > mid) res += query(L, R, rson);
	return res;
}
int main() {
	scanf("%d", &n);
	build(1, n, 1);
	scanf("%d", &q);
	while (q--) {
		int op, l, r, x;
		scanf("%d%d%d", &op, &l, &r);
		if (op == 1) {
			scanf("%d", &x);
			update(l, r, x, 1, n, 1);
		}
		else 
			printf("%lld\n", query(l, r, 1, n, 1));
	}
	return 0;
}

线段树求区间和

#include<bits/stdc++.h>
#define ll long long
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
using namespace std;
const int N=2e5+5;
ll tr[N<<2],a[N];
ll lazy[N<<2];
void push_up(int rt)
{
	tr[rt]=tr[rt<<1]+tr[rt<<1|1];
}
void push_down(int l,int r,int rt)
{
	if(lazy[rt])
	{
		int mid=(l+r)>>1;
		tr[rt<<1]+=(mid-l+1)*lazy[rt];
		lazy[rt<<1]+=lazy[rt];
		tr[rt<<1|1]+=(r-mid)*lazy[rt];
		lazy[rt<<1|1]+=lazy[rt];
		lazy[rt]=0;
	}
}
void build(int l,int r,int rt)
{
	if(l==r)
	{
		tr[rt]=a[l];
		return;
	}
	int mid=(l+r)>>1;
	build(lson);
	build(rson);
	push_up(rt);
}
void update(int l,int r,int rt,int l1,int r1,int x)
{
	if(l1<=l&&r<=r1)
	{
		tr[rt]+=(r-l+1)*x;
		lazy[rt]+=x;
		return;
	}
	int mid=(l+r)>>1;
	push_down(l,r,rt);
	if(l1<=mid)update(lson,l1,r1,x);
	if(r1>mid)update(rson,l1,r1,x);
	push_up(rt);
}
ll query(int l,int r,int rt,int l1,int r1)
{
	if(l1<=l&&r<=r1)
		return tr[rt];
	int mid=(l+r)>>1;
	ll res=0;
	push_down(l,r,rt);
	if(l1<=mid)res+=query(lson,l1,r1);
	if(r1>mid)res+=query(rson,l1,r1);
	return res;
}
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%lld",&a[i]);
	build(1,n,1);
	int T;
	scanf("%d",&T);
	while(T--)
	{
		int op,l,r;
		scanf("%d%d%d",&op,&l,&r);
		if(op==1)
		{
			int x;
			scanf("%d",&x);
			update(1,n,1,l,r,x);
		}
		else
		{
			printf("%lld\n",query(1,n,1,l,r));
		}
	}
	return 0;
}

#include <bits/stdc++.h> #define int long long using namespace std; const int N = 100005 , SN = 1005;

int n , m , a[ N ]; int lenb; int q[ N ] , st[ SN ] , ed[ SN ]; int sum[ SN ] , add[ SN ];

void modify( int l , int r , int v ) { int lx = q[ l ] , rx = q[ r ];

if( lx == rx )
{
	sum[ lx ] += v * ( r - l + 1 );
	for( int i = l ; i <= r ; i ++ )
		a[ i ] += v;
	return;
}

sum[ lx ] += v * ( ed[ lx ] - l + 1 );
for( int i = l ; i <= ed[ lx ] ; i ++ )
	a[ i ] += v;

for( int i = lx + 1 ; i <= rx - 1 ; i ++ )
	add[ i ] += v;

sum[ rx ] += v * ( r - st[ rx ] + 1 ); 
for( int i = st[ rx ] ; i <= r ; i ++ ) 
	a[ i ] += v;

}

int query( int l , int r ) { int lx = q[ l ] , rx = q[ r ] , ans = 0;

if( lx == rx )
{
	ans += add[ lx ] * ( r - l + 1 );
	for( int i = l ; i <= r ; i ++ )
		ans += a[ i ];
	return ans;
}

ans += add[ lx ] * ( ed[ lx ] - l + 1 );
for( int i = l ; i <= ed[ lx ] ; i ++ )
	ans += a[ i ];

for( int i = lx + 1 ; i <= rx - 1 ; i ++ )
	ans += sum[ i ] + add[ i ] * lenb;

ans += add[ rx ] * ( r - st[ rx ] + 1 ); 
for( int i = st[ rx ] ; i <= r ; i ++ )
	ans += a[ i ];

return ans;

}

void init() { lenb = sqrt( n ); for( int i = 1 ; i <= ( n - 1 ) / lenb + 1 ; i ++ ) { st[ i ] = ( i - 1 ) * lenb + 1; ed[ i ] = min( i * lenb , n ); for( int j = st[ i ] ; j <= ed[ i ] ; j ++ ) q[ j ] = i , sum[ i ] += a[ j ]; } }

signed main() { cin >> n; for( int i = 1 ; i <= n ; i ++ ) scanf( "%lld" , a + i ); init();

cin >> m;
while( m -- )
{
	int opt , l , r , v;
	scanf( "%lld%lld%lld" , & opt , & l , & r );
	
	if( opt == 1 )
	{
		scanf( "%lld" , & v );
		modify( l , r , v );
	}
	
	if( opt == 2 )
	{
		printf( "%lld\n" , query( l , r ) );
	}
}

return 0;

}