P2956 [USACO09OCT]机器人犁田The Robot Plow

题目描述

Farmer John has purchased a new robotic plow in order to relieve him from the drudgery of plowing field after field after field. It achieves this goal but at a slight disadvantage: the robotic plow can only plow in a perfect rectangle with sides of integer length.

Because FJ's field has trees and other obstacles, FJ sets up the plow to plow many different rectangles, which might end up overlapping. He's curious as to just how many squares in his field are actually plowed after he programs the plow with various plow instructions, each of which describes a rectangle by giving its lower left and upper right x,y coordinates.

As usual, the field is partitioned into squares whose sides are parallel to the x and y axes. The field is X squares wide and Y squares high (1 <= X <= 240; 1 <= Y <= 240). Each of the I (1 <= I <= 200) plow instructions comprises four integers: Xll, Yll, Xur, and Yur (1 <= Xll <= Xur; Xll <= Xur <= X; 1 <= Yll <= Yur; Yll <= Yur <= Y) which are the lower left and upper right coordinates of the rectangle to be plowed. The plow will plow all the field's squares in the range (Xll..Xur, Yll..Yur) which might be one more row and column than would initially be assumed (depending on how you go about your assumptions, of course).

Consider a field that is 6 squares wide and 4 squares high. As FJ issues a pair of plowing instructions (shown), the field gets plowed as shown by '*' and '#' (normally plowed field all looks the same, but '#' shows which were most recently plowed):

......             **....             #####. 
......  (1,1)(2,4) **....  (1,3)(5,4) #####. 
......             **....             **.... 
......             **....             **.... 

A total of 14 squares are plowed.

POINTS: 25

Farmer John为了让自己从无穷无尽的犁田工作中解放出来，于是买了个新机器人帮助他犁田。这个机器人可以完成犁田的任务，可惜有一个小小的缺点：这个犁田机器人一次只能犁一个边的长度是整数的长方形的田地。

因为FJ的田地有树和其它障碍物，所以FJ设定机器人去犁很多不同的长方形。这些长方形允许重叠。他给机器人下了P个指令，每个指令包含一个要犁长方形的地。这片田地由长方形的左下角和右上角坐标决定。他很好奇最后到底有多少个方格的地被犁过了。

一般来说，田地被分割为很多小方格。这些方格的边和x轴或y轴平行。田地的宽度为X个方格，高度为Y个方格 (1 <= X <= 240; 1 <= Y <= 240). FJ执行了I (1 <= I <= 200)个指令，每个指令包含4个整数：Xll, Yll, Xur, Yur (1 <= Xll <= Xur; Xll <= Xur <=X; 1 <= Yll <= Yur; Yll <= Yur <= Y), 分别是要犁的长方形的左下角坐标和右上角坐标。机器人会犁所有的横坐标在Xll..Xur并且纵坐标在Yll..Yur范围内的所有方格的地。可能这个长方形会比你想象的多一行一列（就是说从第Xll列到第Xur列一共有Xur - Xll + 1列而不是Xur - Xll列）。

考虑一个6方格宽4方格高的田地。FJ进行了2个操作（如下），田地就被犁成"*"和"#"了。虽然一般被犁过的地看起来都是一样的。但是标成"#"可以更清晰地看出最近一次被犁的长方形。

一共14个方格的地被犁过了。

输入输出格式

输入格式：

 

• Line 1: Three space-separated integers: X, Y, and I

• Lines 2..I+1: Line i+1 contains plowing instruction i which is described by four integers: Xll, Yll, Xur, and Yur

 

输出格式：

 

• Line 1: A single integer that is the total number of squares plowed

 

输入输出样例

输入样例#1：

6 4 2 
1 1 2 4 
1 3 5 4 

输出样例#1：

14 

说明

As in the task's example.

 

用差分维护区间和，最后统计。这样就避免了重复。

#include<iostream>
#include<cstdio>
#include<string.h>
#include<algorithm>
#include<math.h>
#include<cmath>
using namespace std;
int n,m,q;
int a[250][250],ans;
int main()
{
    scanf("%d%d%d",&n,&m,&q);
    for(int i=1,x,y,xx,yy;i<=q;i++)
    {
        scanf("%d%d%d%d",&x,&y,&xx,&yy);
        for(int i=y;i<=yy;i++)
            a[x][i]++,a[xx+1][i]--;        
    }
    for(int j=1;j<=m;j++)
    {
        int tot=0;
        for(int i=1;i<=n;i++)
        {
            tot+=a[i][j];
            if(tot>0) ans++;
        }
    }
    cout<<ans;
    return 0;
}