[POJ3468 A Simple Problem with Integers]

[题目来源]：POJ Monthly--2007.11.25, Yang Yi

[关键字]：线段树

[题目大意]：对于给定区间进行整体添加数值，或询问操作，对于每个询问操作输出该区间数字之和。

//=====================================================================================================

[分析]：对于线段树的操作，没有技巧只是要注意延迟操作和int64。原先写的时候思路并不清楚也没有真正弄明白，下面给出一个比较优美的版本。

[代码]：

View Code

  1 type
  2   rec = record
  3     x, y, lc, rc: longint;
  4     dat, last: int64;
  5   end;
  6 var
  7   n, q, tot: longint;
  8   ans: int64;
  9   tree: array[0..500100] of rec;
 10   a: array[0..100100] of longint;
 11 
 12 procedure build(l, r: longint);
 13 var
 14   now: longint;
 15 begin
 16   inc(tot);
 17   now := tot;
 18   tree[now].x := l;
 19   tree[now].y := r;
 20   if l+1 <= r then
 21     begin
 22       tree[now].lc := tot+1;
 23       build(l,(l+r) div 2);
 24       tree[now].rc := tot+1;
 25       build((l+r) div 2+1,r);
 26       tree[now].dat := tree[tree[now].lc].dat+tree[tree[now].rc].dat;
 27     end
 28   else
 29     tree[now].dat := a[l];
 30 end;
 31 
 32 procedure init;
 33 var
 34   i: longint;
 35 begin
 36   readln(n,q);
 37   for i := 1 to n do read(a[i]);
 38   readln;
 39   build(1,n);
 40 end;
 41 
 42 procedure ins(v, x, y: longint;d: int64);
 43 begin
 44   if (x = tree[v].x) and (tree[v].y = y) then
 45     begin
 46       tree[v].last := tree[v].last+d;
 47       exit;
 48     end;
 49   tree[v].dat := tree[v].dat+(y-x+1)*d;
 50   if tree[tree[v].lc].y >= y then ins(tree[v].lc,x,y,d)
 51     else
 52       if tree[tree[v].rc].x <= x then ins(tree[v].rc,x,y,d)
 53         else
 54           begin
 55             ins(tree[v].lc,x,tree[tree[v].lc].y,d);
 56             ins(tree[v].rc,tree[tree[v].rc].x,y,d);
 57           end;
 58 end;
 59 
 60 procedure find(v, x, y: longint);
 61 begin
 62   if tree[v].last <> 0 then
 63     begin
 64       tree[tree[v].lc].last := tree[tree[v].lc].last+tree[v].last;
 65       tree[tree[v].rc].last := tree[tree[v].rc].last+tree[v].last;
 66       tree[v].dat := tree[v].dat+(tree[v].y-tree[v].x+1)*tree[v].last;
 67       tree[v].last := 0;
 68     end;
 69   if (x = tree[v].x) and (tree[v].y = y) then
 70     begin
 71       ans := ans+tree[v].dat;
 72       exit;
 73     end;
 74   if tree[tree[v].lc].y >= y then find(tree[v].lc,x,y)
 75     else
 76       if tree[tree[v].rc].x <= x then find(tree[v].rc,x,y)
 77         else
 78           begin
 79             find(tree[v].lc,x,tree[tree[v].lc].y);
 80             find(tree[v].rc,tree[tree[v].rc].x,y);
 81           end;
 82 end;
 83 
 84 procedure work;
 85 var
 86   i, x, y: longint;
 87   d: int64;
 88   ch: char;
 89 begin
 90   for i := 1 to q do
 91     begin
 92       read(ch);
 93       case ch of
 94         'Q': begin
 95                readln(x,y);
 96                ans := 0;
 97                find(1,x,y);
 98                writeln(ans);
 99              end;
100         'C': begin
101                readln(x,y,d);
102                ins(1,x,y,d);
103              end;
104       end;
105     end;
106 end;
107 
108 begin
109   init;
110   work;
111 end.

优美版（推荐）

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

const int MAXN=600000;

struct node
{
       int rc,lc,x,y;
       long long dat,yan;
}tree[MAXN];
int n,q,tot;
long long ans;
long long sum[MAXN];

void Build(int l,int r)
{
     int now=++tot;
     tree[now].x=l,tree[now].y=r;
     tree[now].dat=sum[r]-sum[l-1];
     if (tree[now].x+1<=tree[now].y)
     {
                                    tree[now].lc=tot+1;
                                    Build(l,(l+r)/2);
                                    tree[now].rc=tot+1;
                                    Build((l+r)/2+1,r);
     }
}

void Lazy(int v)
{
     if (tree[v].yan)
     {
                     int temp=tree[v].lc;
                     tree[temp].dat+=tree[v].yan*(tree[temp].y-tree[temp].x+1);
                     tree[temp].yan+=tree[v].yan;
                     temp=tree[v].rc;
                     tree[temp].dat+=tree[v].yan*(tree[temp].y-tree[temp].x+1);                     
                     tree[temp].yan+=tree[v].yan;
     }
     tree[v].yan=0;
}

void Insert(int v,int a,int b,int c)
{
     Lazy(v);
     if (tree[v].x==a && tree[v].y==b)
     {
                      tree[v].dat+=c*(tree[v].y-tree[v].x+1);
                      tree[v].yan+=c;
                      return;
     }
     if (tree[tree[v].lc].y>=b) Insert(tree[v].lc,a,b,c); else
     if (tree[tree[v].rc].x<=a) Insert(tree[v].rc,a,b,c); else
     {
                                Insert(tree[v].lc,a,tree[tree[v].lc].y,c);
                                Insert(tree[v].rc,tree[tree[v].rc].x,b,c);
     }
     tree[v].dat=tree[tree[v].lc].dat+tree[tree[v].rc].dat;
}

void Find(int v,int a,int b)
{
     Lazy(v);
     //printf("%d %d %d %d\n",a,b,tree[v].x,tree[v].y);
     if (tree[v].x==a && tree[v].y==b)
     {
                      ans+=tree[v].dat;
                      //printf("%d\n",tree[v].dat);
                      return;
     }
     if (tree[tree[v].lc].y>=b) Find(tree[v].lc,a,b); else
     if (tree[tree[v].rc].x<=a) Find(tree[v].rc,a,b); else
     {
                                Find(tree[v].lc,a,tree[tree[v].lc].y);
                                Find(tree[v].rc,tree[tree[v].rc].x,b);
     }
}

int main()
{
    int x,a,b,c;
    char ch;
    scanf("%d%d",&n,&q);
    for (int i=1;i<=n;++i)
    {
        scanf("%d",&x);
        sum[i]=sum[i-1]+x;
    }
    Build(1,n);
    scanf("%c",&ch);
    for (int i=1;i<=q;++i)
    {
        scanf("%c",&ch);
        if (ch=='C')
        {
                  scanf("%d%d%d%c",&a,&b,&c,&ch);
                  Insert(1,a,b,c);
        }
        if (ch=='Q')
        {
                    scanf("%d%d%c",&a,&b,&ch);
                    ans=0;
                    Find(1,a,b);
                    printf("%I64d\n",ans);
        }
    }
    return 0;
}