UVA 11134 - Fabled Rooks(贪心+优先队列)

We would like to place  n  rooks, 1 ≤  n  ≤ 5000, on a  n×n  board subject to the following restrictions

• The i-th rook can only be placed within the rectangle given by its left-upper corner (xl_i, yl_i) and its right-lower corner (xr_i, yr_i), where 1 ≤ i ≤ n, 1 ≤ xl_i ≤ xr_i ≤ n, 1 ≤ yl_i ≤ yr_i ≤ n.
• No two rooks can attack each other, that is no two rooks can occupy the same column or the same row.

The input consists of several test cases. The first line of each of them contains one integer number, n, the side of the board. n lines follow giving the rectangles where the rooks can be placed as described above. The i-th line among them gives xl_i, yl_i, xr_i, and yr_i. The input file is terminated with the integer `0' on a line by itself.

Your task is to find such a placing of rooks that the above conditions are satisfied and then output n lines each giving the position of a rook in order in which their rectangles appeared in the input. If there are multiple solutions, any one will do. Output IMPOSSIBLE if there is no such placing of the rooks.

Sample input

8
1 1 2 2
5 7 8 8
2 2 5 5
2 2 5 5
6 3 8 6
6 3 8 5
6 3 8 8
3 6 7 8
8
1 1 2 2
5 7 8 8
2 2 5 5
2 2 5 5
6 3 8 6
6 3 8 5
6 3 8 8
3 6 7 8
0

Output for sample input

1 1
5 8
2 4
4 2
7 3
8 5
6 6
3 7
1 1
5 8
2 4
4 2
7 3
8 5
6 6
3 7

题意：给定n辆车可以放在棋盘的区间，求能否放满且所有车不受攻击。

思路：贪心+优先队列，把行列分开去贪心。。

代码：

#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
using namespace std;

const int N = 5005;

int n, ans1[N], ans2[N];
struct Car {
    int l, r, p, id;
    friend bool operator < (Car a, Car b) {
	return a.r > b.r;
    }
} c1[N], c2[N];

bool cmp(Car a, Car b) {
    return a.l < b.l;
}

bool cmpid(Car a, Car b) {
    return a.id < b.id;
}
void init() {
    for (int i = 1; i <= n; i ++) {
	scanf("%d%d%d%d", &c1[i].l, &c2[i].l, &c1[i].r, &c2[i].r);
	c1[i].id = c2[i].id = i;
    }
    sort(c1 + 1, c1 + 1 + n, cmp);
    sort(c2 + 1, c2 + 1 + n, cmp);
}

bool judge(Car *c, int *ans) {
    priority_queue<Car> Q;
    int num = 1;
    for (int i = 1; i <= n; i ++) {
	while (c[num].l <= i  && c[num].r >= i && num <= n) {Q.push(c[num++]);}
	if (Q.empty()) return false;
	Car s = Q.top(); Q.pop();
	if (i > s.r) return false;
	ans[s.id] = i;
    }
    return true;
}

void solve() {
    if (!judge(c1, ans1) || !judge(c2, ans2)) {printf("IMPOSSIBLE\n"); return;}
    for (int i = 1; i <= n; i ++)
	printf("%d %d\n", ans1[i], ans2[i]);
}

int main() {
    while (~scanf("%d", &n) && n) {
	init();
	solve();
    }
    return 0;
}