CF 701B Cells Not Under Attack（想法题）

题目链接: 传送门

Cells Not Under Attack

time limit per test:2 second     memory limit per test:256 megabytes

Description

Vasya has the square chessboard of size n × n and m rooks. Initially the chessboard is empty. Vasya will consequently put the rooks on the board one after another.
The cell of the field is under rook's attack, if there is at least one rook located in the same row or in the same column with this cell. If there is a rook located in the cell, this cell is also under attack.
You are given the positions of the board where Vasya will put rooks. For each rook you have to determine the number of cells which are not under attack after Vasya puts it on the board.

Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 100 000, 1 ≤ m ≤ min(100 000, n2)) — the size of the board and the number of rooks.
Each of the next m lines contains integers xi and yi (1 ≤ xi, yi ≤ n) — the number of the row and the number of the column where Vasya will put the i-th rook. Vasya puts rooks on the board in the order they appear in the input. It is guaranteed that any cell will contain no more than one rook.

Output

Print m integer, the i-th of them should be equal to the number of cells that are not under attack after first i rooks are put.

Sample Input

3 3
1 1
3 1
2 2
5 2
1 5
5 1
100000 1
300 400

Sample Output

4 2 0
16 9
9999800001 

解题思路：

题目大意：N*N的棋盘大小，往（x，y）放一棋子，则x行y列的棋格都会被攻击，每次放下一个棋子，问剩下还有多少没被攻击的棋格。
这道题如果根据棋子放下位置去特判计算显得很复杂，可以按行、列来做，我首先先做列的，每次放下的棋子如果在新的一列那么肯定要减号N个棋格，如果之前已经有行被减掉，那么就不能减去N个棋格那么多，不然会有重复减，加个变量记录有几行被减去计算一下就好了，行同理。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
typedef __int64 LL;
int main()
{
    LL N,M;
    while (~scanf("%I64d%I64d",&N,&M))
    {
        LL sum = N*N;
        LL x,y,xcnt = 0,ycnt = 0;
        bool r[100005],c[100005];
        memset(r,false,sizeof(r));
        memset(c,false,sizeof(c));
        bool first = true;
        while (M--)
        {
            scanf("%I64d%I64d",&x,&y);
            if (!c[y])
            {
                sum -= (N - xcnt);
                c[y] = true;
                ycnt++;
            }
            if (!r[x])
            {
                sum -= (N - ycnt);
                r[x] = true;
                xcnt++;
            }
            first?printf("%I64d",sum):printf(" %I64d",sum);
            first = false;
        }
        printf("\n");
    }
    return 0;
}