poj 3468(成端更新，区间求和)

最新推荐文章于 2019-05-13 18:38:38 发布

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最新推荐文章于 2019-05-13 18:38:38 发布

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分类专栏：线段树

本文链接：https://blog.youkuaiyun.com/q451792269/article/details/79252278

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本文介绍了一种经典的线段树区间修改问题解决方案，并通过一个具体的编程实例详细展示了如何使用线段树进行区间加法操作及求区间和，旨在帮助读者理解和掌握线段树的应用。

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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.

题解：

经典的线段树区间修改
参考Acdreamer

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

const int maxn = 1e6+100;
typedef long long LL;
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1

LL add[maxn<<2];
LL sum[maxn<<2];

void PushUp(int rt)
{
    sum[rt]=sum[rt<<1]+sum[rt<<1|1];
}

void PushDown(int rt,int m)
{
    if(add[rt])
    {
        add[rt<<1]+=add[rt];
        add[rt<<1|1]+=add[rt];
        sum[rt<<1]+=(m-(m>>1))*add[rt];
        sum[rt<<1|1]+=(m>>1)*add[rt];
        add[rt]=0;
    }
}

void Build(int l,int r,int rt)
{
    add[rt]=0;
    if(l==r)
    {
        scanf("%I64d",&sum[rt]);
        return;
    }
    int m = (l+r)>>1;
    Build(lson);
    Build(rson);
    PushUp(rt);
}

void Update(int L,int R,int c,int l,int r,int rt)
{
    if(L<=l&&R>=r)
    {
        add[rt]+=c;
        sum[rt]+=(LL)c*(r-l+1);
        return;
    }
    PushDown(rt,r-l+1);
    int m = (l+r)>>1;
    if(L<=m) Update(L,R,c,lson);
    if(R>m) Update(L,R,c,rson);
    PushUp(rt);
}

LL Query(int L,int R,int l,int r,int rt)
{
    if(L<=l&&R>=r)
         return sum[rt];
    PushDown(rt,r-l+1);
    int m = (l+r)>>1;
    LL ret = 0;
    if(L<=m) ret+=Query(L,R,lson);
    if(R>m) ret+=Query(L,R,rson);
    return ret;
}

int main()
{
    int m,n;
    scanf("%d%d",&n,&m);
    Build(1,n,1);
    while(m--)
    {
        char s[5];
        int a,b,c;
        scanf("%s",s);
        if(s[0]=='Q')
        {
            scanf("%d%d",&a,&b);
            printf("%I64d\n",Query(a,b,1,n,1));
        }
        else
        {
            scanf("%d%d%d",&a,&b,&c);
            Update(a,b,c,1,n,1);
        }
    }
    return 0;
}