POJ 3468 A Simple Problem with Integers-（线段树）

Problem Description

You have N integers, A₁, A₂, ... , A_N. 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

<p>The first line contains two numbers <i>N</i> and <i>Q</i>. 1 ≤ <i>N</i>,<i>Q</i> ≤ 100000.<br>The second line contains <i>N</i> numbers, the initial values of <i>A</i>₁, <i>A</i>₂, ... , <i>A_N</i>. -1000000000 ≤ <i>A_i</i> ≤ 1000000000.<br>Each of the next <i>Q</i> lines represents an operation.<br>"C <i>a</i> <i>b</i> <i>c</i>" means adding <i>c</i> to each of <i>A_a</i>, <i>A_a</i>₊₁, ... , <i>A_b</i>. -10000 ≤ <i>c</i> ≤ 10000.<br>"Q <i>a</i> <i>b</i>" means querying the sum of <i>A_a</i>, <i>A_a</i>₊₁, ... , <i>A_b</i>.</p>

 

Output

<p>You need to answer all <i>Q</i> commands in order. One answer in a line.</p>

 

Sample Input

10 51 2 3 4 5 6 7 8 9 10Q 4 4Q 1 10Q 2 4C 3 6 3Q 2 4

 

Sample Output

455915

这个题用树状数组老是超时，用线段树可以过，这个题目虽然不难，但却是做了很多次才过的题目，比较典型。

代码：

#include<iostream>#include<string>#include<cstdio>#include<algorithm>#include<cmath>#include<iomanip>#include<queue>#include<cstring>#include<map>using namespace std;typedef long long ll;#define M 100005#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1int n,q;ll tree[M<<2];ll col[M<<2];inline void pushup(int rt){    tree[rt]=tree[rt<<1]+tree[rt<<1|1];}void build(int l,int r,int rt){    if(l==r)    {        col[rt]=0;        scanf("%I64d",&tree[rt]);        return;    }    int m=(l+r)>>1;    build(lson);    build(rson);    pushup(rt);}void pushdown(int rt,ll x){    if(col[rt])    {        col[rt<<1|1]+=col[rt];        col[rt<<1]+=col[rt];        tree[rt<<1]+=col[rt]*(x-(x>>1));        tree[rt<<1|1]+=col[rt]*(x>>1);        col[rt]=0;    }}void update(int L,int R,ll c,int l,int r,int rt){    if(L<=l&&r<=R)    {        col[rt]+=c;        tree[rt]+=(ll)(r-l+1)*c;        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 sum(int L,int R,int l,int r,int rt){    if(L<=l&&r<=R)    {        return tree[rt];    }    pushdown(rt,r-l+1);    int m=(l+r)>>1;    ll ret=0;    if(L<=m) ret+=sum(L,R,lson);    if(R>m) ret+=sum(L,R,rson);    pushup(rt);    return ret;}int main(){    int a,b;    ll c;    char ch;    while(scanf("%d%d",&n,&q)!=EOF)    {        build(1,n,1);        while(q--)        {            getchar();            ch=getchar();            if(ch=='C')            {                scanf("%d%d%I64d",&a,&b,&c);                update(a,b,c,1,n,1);            }            else            {                scanf("%d%d",&a,&b);                printf("%I64d\n",sum(a,b,1,n,1));            }        }    }    return 0;}