A Simple Problem with Integers

A Simple Problem with Integers - POJ 3468 - 线段树 区间更新

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

Sample Output

455915

  题意：给你n个数，下标1~n，有m个询问：C a b c代表把区间[a,b]中的每一个数都加上c。Q a b代表查询区间[a,b]间的总和。

  思路：可以用树状数组，也可以用线段树。因为树状数组我基本不会，所以只写了线段树版本。

  写了结构体版本和数组版本两种，两种写法时间复杂度相同，数组稍微快一点点，但在空间复杂度上数组版本就很占优了。

  还有一个小问题就是我写数组版本的时候怎么样都是WA，问了问学长，发现是爆int了。不知道为什么写结构体的时候鬼使神差般全用的long long，写数组就全用int了。

  Lazy标记什么的详见我的另一篇博客：线段树 - Lazy标记 - 单点/区间更新 - 模板

  特别的，lazy在我的数组版本里是laz在结构体版本里是add。

结构体版本AC代码：

////  main.cpp//  L////  Created by LucienShui on 2017/5/24.//  Copyright © 2017年 LucienShui. All rights reserved.//#include <iostream>#include <algorithm>#include <set>#include <string>#include <vector>#include <queue>#include <map>#include <iomanip>#include <cstdio>#include <cstring>#include <cmath>#include <cctype>#define memset(a,b) memset(a,b,sizeof(a))#define il inline#define ull unsigned long long#define ll long longusing namespace std;#define ls (u<<1)#define rs (u<<1|1)const int maxn = 200000+7;ll n,m,ans;struct node {    ll l,r,sum,add;}tree[maxn<<2];il void pushup(ll u) {    tree[u].sum = tree[ls].sum + tree[rs].sum;}il void pushdown(ll u) {    tree[ls].add += tree[u].add;    tree[rs].add += tree[u].add;    tree[ls].sum += tree[u].add*(tree[ls].r-tree[ls].l+1);    tree[rs].sum += tree[u].add*(tree[rs].r-tree[rs].l+1);    tree[u].add = 0;}il void build(ll u, ll l, ll r) {    tree[u].l = l;    tree[u].r = r;    tree[u].add = 0;    if(l==r) {        scanf("%lld",&tree[u].sum);        return ;    }    ll mid = (l+r) >> 1;    build(ls,l,mid);    build(rs,mid+1,r);    pushup(u);}il void update(ll u, ll l, ll r, ll num) {    if(r<tree[u].l || l>tree[u].r) return ;    if(l <= tree[u].l && r >= tree[u].r) {        tree[u].add += num;        tree[u].sum += num * (tree[u].r-tree[u].l+1);        return ;    }    if(tree[u].add) pushdown(u);    update(ls,l,r,num);    update(rs,l,r,num);    pushup(u);}il void query(ll u, ll l, ll r) {    if(r < tree[u].l || l > tree[u].r) return ;    if(l <= tree[u].l && r >= tree[u].r) {        ans += tree[u].sum;        return ;    }    if(tree[u].add) pushdown(u);    ll mid = (tree[u].l+tree[u].r)>>1;    if(r<=mid) query(ls,l,r);    else if(l>mid) query(rs,l,r);    else {        query(ls,l,mid);        query(rs,mid+1,r);    }}int main (){#ifndef ONLINE_JUDGE    freopen("in.txt","r",stdin);#endif // ONLINE_JUDGE    while(~scanf("%lld %lld",&n,&m))    {        build(1,1,n);        char str[5];        while(m--)        {            scanf("%s",str);            if(str[0]=='Q')            {                ll l,r;                scanf("%lld %lld",&l,&r);                ans=0;                query(1,l,r);                printf("%lld\n",ans);            }            else            {                ll l,r,c;                scanf("%lld %lld %lld",&l,&r,&c);                update(1,l,r,c);            }        }    }    return 0;}

数组版本AC代码：

////  main.cpp//  L////  Created by LucienShui on 2017/5/26.//  Copyright © 2017年 LucienShui. All rights reserved.//#include <iostream>#include <algorithm>#include <set>#include <string>#include <vector>#include <queue>#include <map>#include <iomanip>#include <cstdio>#include <cstring>#include <cmath>#include <cctype>#define memset(a,b) memset(a,b,sizeof(a))#define il inline#define ull unsigned long long#define ll long longusing namespace std;#define ls (u<<1)#define rs (u<<1|1)const int maxn = 200000+7;ll n,m,ans;ll node[maxn<<2],laz[maxn<<2];//node是树节点，laz是lazy标记il void pushdown(ll u, ll l, ll r) {    ll mid = (l+r)>>1;    laz[ls] += laz[u];    laz[rs] += laz[u];    node[ls] += laz[u]*(mid-l+1);    node[rs] += laz[u]*(r-mid);    laz[u] = 0;}il void build(ll u, ll l, ll r) {    if(l==r) {        scanf("%lld",node+u);        return ;    }    ll mid = (l+r)>>1;    build(ls,l,mid);    build(rs,mid+1,r);    node[u] = node[ls] + node[rs];}il void update(ll u, ll l, ll r, ll b, ll e, ll num) {    if(e<l || b>r) return ;    if(b<=l && r<=e) {        laz[u] += num;        node[u] += num * (r-l+1);        return ;    }    if(laz[u]) pushdown(u,l,r);    ll mid = (l+r)>>1;    update(ls,l,mid,b,e,num);    update(rs,mid+1,r,b,e,num);    node[u] = node[ls] + node[rs];}il void query(ll u, ll l, ll r, ll b, ll e) {    if(e<l || b>r) return ;    if(b<=l && r<=e) {        ans += node[u];        return ;    }    if(laz[u]) pushdown(u,l,r);    ll mid = (l+r)>>1;    if(e<=mid) query(ls,l,mid,b,e);    else if(b>mid) query(rs,mid+1,r,b,e);    else {        query(ls,l,mid,b,e);        query(rs,mid+1,r,b,e);    }}int main (){#ifndef ONLINE_JUDGE    freopen("in.txt","r",stdin);#endif // ONLINE_JUDGE    ll l,r,c;    while(~scanf("%lld %lld",&n,&m)) {        build(1,1,n);        char str[5];        while(m--)        {            scanf(" %s",str);            if(str[0]=='Q')            {                scanf("%lld %lld",&l,&r);                ans=0;                query(1,1,n,l,r);                printf("%lld\n",ans);            }            else            {                scanf("%lld %lld %lld",&l,&r,&c);                update(1,1,n,l,r,c);            }        }    }    return 0;}