poj 3468 A Simple Problem with Integers(區間查詢區間更新)

題目：

You have N integers, A1, A2, … , AN. You need to deal with two kinds of operations. One type of operation is to add some given number to each number in a given interval. The other is to ask for the sum of numbers in a given interval.

Input
The first line contains two numbers N and Q. 1 ≤ N,Q ≤ 100000.
The second line contains N numbers, the initial values of A1, A2, … , AN. -1000000000 ≤ Ai ≤ 1000000000.
Each of the next Q lines represents an operation.
“C a b c” means adding c to each of Aa, Aa+1, … , Ab. -10000 ≤ c ≤ 10000.
“Q a b” means querying the sum of Aa, Aa+1, … , Ab.

Output
You need to answer all Q commands in order. One answer in a line.
Sample Input
10 5
1 2 3 4 5 6 7 8 9 10
Q 4 4
Q 1 10
Q 2 4
C 3 6 3
Q 2 4
Sample Output
4
55
9
15
Hint
The sums may exceed the range of 32-bit integers.

題意：

給你一個序列，要你進行區間修改以及區間查詢.

ps:

模板題，lazy標記的使用，沒啥說的，注意lazy是累加，還有sum更新的方法是加上區間長乘以更新值，還有一個地方坑了我好久找bug，寫在代碼註釋裏了。

代碼：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define ls (rt<<1)
#define rs (rt<<1|1)
#define lson L,mid,ls
#define rson mid+1,R,rs
#define def_mid int mid=(L+R)>>1
#define ll long long
#define INF 0x3f3f3f3f
using namespace std;

const int maxn = 123456;
ll sum[maxn<<2],lazy[maxn<<2];
ll a[maxn];

void pushup(int rt)
{
    sum[rt]=sum[ls]+sum[rs];
}

void pushlazy(int lz,int len,int rt)
{
    sum[rt]+=(ll)lz*len;//被這裏坑了兩個int類型相乘會爆int所以在這裏要強轉爲ll
    lazy[rt]+=lz;
}

void pushdown(int L,int R,int rt)
{
    if(lazy[rt]!=0)
    {
        def_mid;
        pushlazy(lazy[rt],mid-L+1,ls);
        pushlazy(lazy[rt],R-mid,rs);
        lazy[rt]=0;
    }
    return;
}

void build(int L,int R,int rt)
{
    lazy[rt]=0;
    if(L==R)
    {
        sum[rt]=a[L];
        return;
    }
    def_mid;
    build(lson);
    build(rson);
    pushup(rt);
}

void update(int l,int r,int L,int R,int rt,int k)
{
    if(l<=L&&r>=R)
    {
        sum[rt]+=k*(R-L+1);
        lazy[rt]+=k;
        return;
    }
    pushdown(L,R,rt);
    def_mid;
    if(l<=mid)
        update(l,r,lson,k);
    if(r>mid)
        update(l,r,rson,k);
    pushup(rt);
}

ll querysum(int l,int r,int L,int R,int rt)
{
    if(l<=L&&r>=R)
        return sum[rt];
    pushdown(L,R,rt);
    def_mid;
    ll ret=0;
    if(l<=mid)
        ret+=querysum(l,r,lson);
    if(r>mid)
        ret+=querysum(l,r,rson);
    return ret;
}

int main()
{
    int n,q,k;
    while(scanf("%d%d",&n,&q)!=EOF)
    {
        memset(lazy,0,sizeof(lazy));
        memset(sum,0,sizeof(sum));
        memset(a,0,sizeof(a));
        char op[3];
        int l,r;
        for(int i=1;i<=n;i++)
            scanf("%lld",&a[i]);
        build(1,n,1);
        while(q--)
        {
            scanf("%s%d%d",op,&l,&r);
            if(op[0]=='Q')
                printf("%lld\n",querysum(l,r,1,n,1));
            else
            {
                scanf("%d",&k);
                update(l,r,1,n,1,k);
            }
        }
    }
    return 0;
}