很明显的线段树，果然比用伸展树舒服多了，没有太多的思路，就是区间成段的更新  还有 区间 求和操作，直接看代码

#include<iostream>
#include<cstdio>
#include<list>
#include<algorithm>
#include<cstring>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<vector>
#include<cmath>
#include<memory.h>
#include<set>

#define ll long long

#define eps 1e-7

#define inf 0xfffffff
const ll INF = 1ll<<61;

using namespace std;

//vector<pair<int,int> > G;
//typedef pair<int,int > P;
//vector<pair<int,int> > ::iterator iter;
//
//map<ll,int >mp;
//map<ll,int >::iterator p;
//


typedef struct {
	int l,r;
	ll sum;
	ll add;
}Node;

int n,m;
ll num[200000 + 5];
Node tree[200005 * 2];

ll build(int root,int left,int right) {
	int mid;
	ll x,y;
	tree[root].l = left;
	tree[root].r = right;
	tree[root].add = 0;
	if(left == right) {
		tree[root].sum = num[left];
		return num[left];
	}
	mid = (left + right)/2;
	x = build(root * 2,left,mid);
	y = build(root * 2 + 1,mid + 1,right);
	return tree[root].sum = x + y;
}

void insert(int root,int left,int right,int add) {
	if(left <= tree[root].l && tree[root].r <= right) {
		tree[root].add  += add;
		tree[root].sum += add*(tree[root].r - tree[root].l + 1);
		return ;
	}
	if(tree[root].add) {
		tree[root * 2].sum += tree[root].add * (tree[root * 2].r - tree[root * 2].l + 1);
		tree[root * 2 + 1].sum += tree[root].add * (tree[root * 2 + 1].r - tree[root * 2 + 1].l + 1);
		tree[root * 2 ].add += tree[root].add;
		tree[root * 2 + 1].add += tree[root].add;
		tree[root].add = 0;
	}
	if(left <= (tree[root].l + tree[root].r)/2)
		insert(root * 2,left,right,add);
	if(right > (tree[root].l + tree[root].r)/2)
		insert(root * 2 + 1,left,right,add);
	tree[root].sum = tree[root * 2].sum + tree[root * 2 + 1].sum;
}

ll find(int root,int left,int right) {
	ll x = 0,y = 0;
	if(left <= tree[root].l && tree[root].r <= right)
		return tree[root].sum;
	if(tree[root].add) {
		tree[root * 2].sum += tree[root].add * (tree[root * 2].r -tree[root * 2].l + 1);
		tree[root * 2 + 1].sum += tree[root].add * (tree[root * 2 + 1].r - tree[root * 2 + 1].l + 1);
		tree[root * 2 ].add += tree[root].add;
		tree[root * 2 + 1].add += tree[root].add;
		tree[root].add = 0;
	}
	if(left <= (tree[root].l + tree[root].r)/2)
		x = find(root * 2,left,right);
	if(right > (tree[root].l + tree[root].r)/2)
		y = find(root * 2 + 1,left,right);
	return x + y; 
}

int main() {
	char s[2];
	int a,b,c;
	while(scanf("%d %d",&n,&m) == 2) {
		for(int i=1;i<=n;i++)
			scanf("%I64d",&num[i]);
		build(1,1,n);
		for(int i=0;i<m;i++) {
			scanf("%s",s);
			if(s[0] == ‘C‘) {
				scanf("%d %d %d",&a,&b,&c);
				if(a > b) {
					int tmp = a;
					a = b;
					b = tmp;
				}
				insert(1,a,b,c);
			}
			else {
				scanf("%d %d",&a,&b);
				if(a > b){
					int tmp = a;
					a = b;
					b = tmp;
				}
				printf("%I64d\n",find(1,a,b));
			}
		}
	}
	return EXIT_SUCCESS;
}

POJ3468 A Simple Problem with Integers 线段树 区间成段更新+区间求和