Mobile phones(POJ_1195)

Description

Suppose that the fourth generation mobile phone base stations in the Tampere area operate as follows. The area is divided into squares. The squares form an S * S matrix with the rows and columns numbered from 0 to S-1. Each square contains a base station. The number of active mobile phones inside a square can change because a phone is moved from a square to another or a phone is switched on or off. At times, each base station reports the change in the number of active phones to the main base station along with the row and the column of the matrix.

Write a program, which receives these reports and answers queries about the current total number of active mobile phones in any rectangle-shaped area.

Input

The input is read from standard input as integers and the answers to the queries are written to standard output as integers. The input is encoded as follows. Each input comes on a separate line, and consists of one instruction integer and a number of parameter integers according to the following table.

The values will always be in range, so there is no need to check them. In particular, if A is negative, it can be assumed that it will not reduce the square value below zero. The indexing starts at 0, e.g. for a table of size 4 * 4, we have 0 <= X <= 3 and 0 <= Y <= 3.

Table size: 1 * 1 <= S * S <= 1024 * 1024
Cell value V at any time: 0 <= V <= 32767
Update amount: -32768 <= A <= 32767
No of instructions in input: 3 <= U <= 60002
Maximum number of phones in the whole table: M= 2^30

Output

Your program should not answer anything to lines with an instruction other than 2. If the instruction is 2, then your program is expected to answer the query by writing the answer as a single line containing a single integer to standard output.

Sample Input

0 4
1 1 2 3
2 0 0 2 2
1 1 1 2
1 1 2 -1
2 1 1 2 3
3

Sample Output

3
4

A了这题才感觉树状数组的原理理解的差不多了，但是对于那些不像这题一样明显的题还是无法一眼看出需要用树状数组。一开始写二维的树状数组时运行一直没有结果，仔细研究了一下发现是因为自己二维树状数组下标是从0开始的，这样的话求(0, 0)点的sum会进入死循环，所以注意下标一定要从1开始。

代码

#include <iostream>
#include <cstdio>
#include <cstring>
#define lowbit(x) (x & -x)

using namespace std;

int s;
int c[1030][1030];

void add(int x, int y, int z)
{
    for(int i = x; i <= s; i += lowbit(i))
    {
        for(int j = y; j <= s; j+= lowbit(j))
        {
            c[i][j] += z;
        }
    }
}

int sum(int x, int y)
{
    int ret = 0;
    for(int i = x; i > 0; i -= lowbit(i))
    {
        for(int j = y; j > 0; j -= lowbit(j))
        {
            ret += c[i][j];
        }
    }
    return ret;
}

int main()
{
    int n;
    memset(c, 0, sizeof(c));
    while(scanf("%d", &n) && n != 3)
    {
        if(n == 0)
            scanf("%d", &s);
        else if(n == 1)
        {
            int x, y, z;
            scanf("%d%d%d", &x, &y, &z);
            add(x + 1, y + 1, z);
        }
        else
        {
            int x1, y1, x2, y2;
            scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
            printf("%d\n", sum(x2 + 1, y2 + 1) - sum(x2 + 1, y1) - sum(x1, y2 + 1) + sum(x1, y1));
        }
    }
    return 0;
}