Constellation

題目描述

A star map in Berland is a checked field $n\times m$ squares. In each square there is or there is not a star. The favorite constellation of all Berland’s astronomers is the constellation of the Cross. This constellation can be formed by any 5 stars so, that for some integer $x$ (radius of the constellation) the following is true:

• the 2nd is on the same vertical line as the 1st, but $x$ squares up
• the 3rd is on the same vertical line as the 1st, but $x$ squares down
• the 4th is on the same horizontal line as the 1st, but $x$ squares left
• the 5th is on the same horizontal line as the 1st, but $x$ squares right

Such constellations can be very numerous, that’s why they are numbered with integers from 1 on the following principle: when two constellations are compared, the one with a smaller radius gets a smaller index; if their radii are equal — the one, whose central star if higher than the central star of the other one; if their central stars are at the same level — the one, whose central star is to the left of the central star of the other one.

Your task is to find the constellation with index $k$ by the given Berland’s star map.

輸入格式

The first line contains three integers $n$ , $m$ and $k$ ( $1<=n,m<=300,1<=k<=3\times 10^7$ ) — height and width of the map and index of the required constellation respectively. The upper-left corner has coordinates $(1,1)$ , and the lower-right — $(n,m)$ . Then there follow $n$ lines, $m$ characters each — description of the map. $j$ -th character in $i$ -th line is “*”, if there is a star in the corresponding square, and “.” if this square is empty.

輸出格式

If the number of the constellations is less than $k$ , output -1. Otherwise output 5 lines, two integers each — coordinates of the required constellation. Output the stars in the following order: central, upper, lower, left, right.

題面翻譯

題目描述

一個Berland星空圖填充了一個 $N\times M$ 的矩形。Berland的十字星座是所有的天文學家最喜歡的星座。這個星座由 $5$ 個星星組成。對于星座的半徑 $x$，$5$ 個星星的位置關系有以下原則：

第二個和第一個在同一條垂直線上，但是在第一個的上邊 $x$ 單位處。

第三個和第一個在同一條垂直線上，但是在第一個的下邊 $x$ 單位處。

第四個和第一個在同一水平線上，但是在第一個的左邊 $x$ 單位處。

第五個和第一個在同一水平線上，但是在第一個的右邊 $x$ 單位處。

對于星座的索引：更小的半徑會有更小的索引。如果它們的半徑相等，位于更上邊更左邊的中心恒星所在的十字星座索引更小。

你的任務是找到索引為 $K$ 的星座的Berland星空圖。

輸入格式

第一行包含三個整數 $N,M$ 和 $K$($1\le N,M\le 300，1\le K\le 3\times 10^7$)，分別為地圖的高，寬和所求星座的索引。下面輸入 $N$ 行，$M$ 列的字符來描述星空圖。左上角坐標為 $(1,1)$，右下角坐標為 $(N,M)$。

輸出格式

如果星座索引小于 $k$，輸出 $?1$。否則輸出 $5$ 行，每行分別兩個整數，即星座的每一個星星的坐標。按照中心、上、下、左、右的順序輸出星星。

樣例 #1

樣例輸入 #1

5 6 1
....*.
...***
....*.
..*...
.***..

樣例輸出 #1

2 5
1 5
3 5
2 4
2 6

樣例 #2

樣例輸入 #2

5 6 2
....*.
...***
....*.
..*...
.***..

樣例輸出 #2

-1

樣例 #3

樣例輸入 #3

7 7 2
...*...
.......
...*...
*.***.*
...*...
.......
...*...

樣例輸出 #3

4 4
1 4
7 4
4 1
4 7

原題

Codeforces——傳送門
洛谷——傳送門

代碼

#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
typedef long long ll;int main()
{ios::sync_with_stdio(0);cin.tie(0);int n, m, k;cin >> n >> m >> k;vector<vector<char>> g(n + 1, vector<char>(m + 1, 0)); // 存圖for (int i = 1; i <= n; i++){for (int j = 1; j <= m; j++){cin >> g[i][j];}}int cnt = 0;                                             // 當前十字星座個數for (int r = 1; r <= max((n - 1) / 2, (m - 1) / 2); r++) // 枚舉半徑{// 枚舉中心星的坐標for (int i = 1 + r; i <= n - r; i++){for (int j = 1 + r; j <= m - r; j++){// 十字星座的五個頂點均為'*'if (g[i][j] == '*' && g[i - r][j] == '*' && g[i + r][j] == '*' && g[i][j - r] == '*' && g[i][j + r] == '*'){cnt++;        // 星座個數++if (cnt == k) // 找到第k個星座，直接輸出答案{cout << i << ' ' << j << '\n';cout << i - r << ' ' << j << '\n';cout << i + r << ' ' << j << '\n';cout << i << ' ' << j - r << '\n';cout << i << ' ' << j + r << '\n';return 0;}}}}}// 星座數小于k，輸出-1cout << -1 << '\n';return 0;
}