[POJ1195 Mobile phones]

[题目来源]：IOI 2001

[关键字]：线段树

[题目大意]：对于一个矩形，一开始全是0，然后会有操作：1、在（x，y）加上某个数；2、查找（l，r）到（b，t）这一子矩形中数字的和。

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[分析]：用线段树或树状数组进行区间的变更或求和操作，由于是一个二维的所以将每个区间的值改成一个数组记录另一维。每次插入都回直接插入到树的叶子上，所以只要在回溯时顺便更新就行，不用延迟。

[代码]：

线段树

 1 program Project1;
 2 type
 3   rec = record
 4     x, y, lc, rc: longint;
 5     dat: array[0..1200] of longint;
 6   end;
 7 var
 8   n, ans, tot: longint;
 9   tree: array[0..5000] of rec;
10   
11 procedure build(l, r: longint);
12 var
13   now: longint;
14 begin
15   inc(tot);
16   now := tot;
17   tree[now].x := l;
18   tree[now].y := r;
19   if l+1 <= r then
20     begin
21       tree[now].lc := tot+1;
22       build(l,(l+r) div 2);
23       tree[now].rc := tot+1;
24       build((l+r) div 2+1,r);
25     end;
26 end;
27 
28 procedure ins(v, x, y, dat: longint);
29 begin
30   if (y = tree[v].x) and (tree[v].y = y) then
31     begin
32       tree[v].dat[x] := tree[v].dat[x]+dat;
33       exit;
34     end;
35 //  writeln(tree[v].x,'',tree[v].y);
36   if y <= (tree[v].x+tree[v].y) div 2 then ins(tree[v].lc,x,y,dat);
37   if y > (tree[v].x+tree[v].y) div 2 then ins(tree[v].rc,x,y,dat);
38   tree[v].dat[x] := tree[v].dat[x]+dat;
39 end;
40 
41 procedure find(v, l, r, b, t: longint);
42 var
43   i: longint;
44 begin
45   if (b <= tree[v].x) and (tree[v].y <= t) then
46     begin
47       for i := l to r do
48         ans := ans+tree[v].dat[i];
49       //writeln(tree[v].x,'',tree[v].y,'',ans);
50       exit;
51     end;
52   //writeln(tree[v].x,'',tree[v].y);
53   if b <= (tree[v].x+tree[v].y) div 2 then find(tree[v].lc,l,r,b,t);
54   if t > (tree[v].x+tree[v].y) div 2 then find(tree[v].rc,l,r,b,t);
55 end;
56 
57 procedure init;
58 var
59   s, x, y, dat, l, r, b, t: longint;
60 begin
61   while 1 = 1 do
62     begin
63       read(s);
64       case s of
65         0: begin
66              readln(n);
67              tot := 0;
68              build(1,n);
69            end;
70         1: begin
71              readln(x,y,dat);
72              ins(1,x+1,y+1,dat);
73            end;
74         2: begin
75              readln(l,b,r,t);
76              ans := 0;
77              find(1,l+1,r+1,b+1,t+1);
78              writeln(ans);
79            end;
80         3: exit;
81       end;
82    end;
83 end;
84 
85 begin
86   init;
87 end.

树状数组

 1 program Project1;
 2 var
 3   ans, n: longint;
 4   tree: array[0..2000,0..2000] of longint;
 5 
 6 procedure ins(x, y, dat: longint);
 7 var
 8   k: longint;
 9 begin
10   k := y;
11   while k <= n do
12     begin
13       tree[k,x] := tree[k,x]+dat;
14       k := k+k and -k;
15     end;
16 end;
17 
18 function find(l, r, y: longint):longint;
19 var
20   sum, k, i: longint;
21 begin
22   k := y;
23   sum := 0;
24   while k >= 1 do
25     begin
26       for i := l to r do
27         sum := sum+tree[k,i];
28       k := k-k and -k;
29     end;
30   exit(sum);
31 end;
32 
33 procedure init;
34 var
35   s, x, y, dat, l, r, b, t: longint;
36 begin
37   while 1 = 1 do
38     begin
39       read(s);
40       case s of
41         0: readln(n);
42         1: begin
43              readln(x,y,dat);
44              ins(x+1,y+1,dat);
45            end;
46         2: begin
47              readln(l,b,r,t);
48              ans := find(l+1,r+1,t+1);
49              ans := ans-find(l+1,r+1,b);
50              writeln(ans);
51            end;
52         3: exit;
53       end;
54    end;
55 end;
56 
57 begin
58   init;
59 end.