CodeForces 616C The Labyrinth(DFS)

本文介绍了一种算法,用于计算二维矩阵中,当移除特定障碍点后,剩余部分形成的连通块的大小。算法通过深度优先搜索(DFS)遍历矩阵,并在每个障碍点移除后计算其连通块大小。

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题意给你n行m列的矩阵,矩阵*表示障碍,.表示空地对于每一个障碍,让你输出去掉这个障碍之后,这个点所在的连通块的大小是多少

思路:DFS...


#include<bits/stdc++.h>
using namespace std;
const int maxn = 1005;
char mp[maxn][maxn];
int cc[maxn][maxn];
int num[maxn*maxn];
int vis[maxn][maxn];
int dir[4][2]={{0,1},{0,-1},{1,0},{-1,0}};
int n,m;
set<int>s;
set<int>::iterator it;
void dfs(int x,int y,int c)
{
	cc[x][y]=c;
	num[c]++;
	for (int i = 0;i<4;i++)
	{
		int dx = x+dir[i][0];
		int dy = y+dir[i][1];
		if (dx>=n || dx<0 || dy<0 || dy>=m)
			continue;
		if (cc[dx][dy] || mp[dx][dy]!='.')
			continue;
		vis[dx][dy]=1;
		dfs(dx,dy,c);
	}
}
int solve(int x,int y)
{
	s.clear();
	int ans = 0;
	for (int i = 0;i<4;i++)
	{
		int dx = x+dir[i][0];
		int dy = y+dir[i][1];
		if (dx>=n || dx<0 || dy<0 || dy>=m)
			continue;
		if (mp[dx][dy]!='.')
			continue;
		s.insert(cc[dx][dy]);
	}
	for (it = s.begin();it!=s.end();it++)
	{
		ans+=num[*it];
	}
	return ans;
}
int main()
{
     scanf("%d%d",&n,&m);
	 for (int i = 0;i<n;i++)
		 scanf("%s",mp[i]);
	 int c = 1;
	 for (int i = 0;i<n;i++)
		 for (int j = 0;j<m;j++)
			 if (cc[i][j]==0 && mp[i][j]=='.')
			 {
				 num[c]=0;
				 dfs(i,j,c);
				 c++;
			 }
	 for (int i = 0;i<n;i++)
		 for (int j = 0;j<m;j++)
			 if (mp[i][j]=='*')
			 {
				 int ans = (solve(i,j)+1)%10;
				 mp[i][j]='0'+ans;
			 }
	 for (int i = 0;i<n;i++)
		 printf("%s\n",mp[i]);
}


Description

You are given a rectangular field of n × m cells. Each cell is either empty or impassable (contains an obstacle). Empty cells are marked with '.', impassable cells are marked with '*'. Let's call two empty cells adjacent if they share a side.

Let's call a connected component any non-extendible set of cells such that any two of them are connected by the path of adjacent cells. It is a typical well-known definition of a connected component.

For each impassable cell (x, y) imagine that it is an empty cell (all other cells remain unchanged) and find the size (the number of cells) of the connected component which contains (x, y). You should do it for each impassable cell independently.

The answer should be printed as a matrix with n rows and m columns. The j-th symbol of the i-th row should be "." if the cell is empty at the start. Otherwise the j-th symbol of the i-th row should contain the only digit —- the answer modulo 10. The matrix should be printed without any spaces.

To make your output faster it is recommended to build the output as an array of n strings having length m and print it as a sequence of lines. It will be much faster than writing character-by-character.

As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use scanf/printf instead ofcin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.

Input

The first line contains two integers n, m (1 ≤ n, m ≤ 1000) — the number of rows and columns in the field.

Each of the next n lines contains m symbols: "." for empty cells, "*" for impassable cells.

Output

Print the answer as a matrix as described above. See the examples to precise the format of the output.

Sample Input

Input
3 3
*.*
.*.
*.*
Output
3.3
.5.
3.3
Input
4 5
**..*
..***
.*.*.
*.*.*
Output
46..3
..732
.6.4.
5.4.3

Hint

In first example, if we imagine that the central cell is empty then it will be included to component of size 5 (cross). If any of the corner cell will be empty then it will be included to component of size 3 (corner).



CodeForces - 616D是一个关于找到一个序列中最长的第k好子段的起始位置和结束位置的问题。给定一个长度为n的序列和一个整数k,需要找到一个子段,该子段中不超过k个不同的数字。题目要求输出这个序列最长的第k好子段的起始位置和终止位置。 解决这个问题的方法有两种。第一种方法是使用尺取算法,通过维护一个滑动窗口来记录\[l,r\]中不同数的个数。每次如果这个数小于k,就将r向右移动一位;如果已经大于k,则将l向右移动一位,直到个数不大于k。每次更新完r之后,判断r-l+1是否比已有答案更优来更新答案。这种方法的时间复杂度为O(n)。 第二种方法是使用枚举r和双指针的方法。通过维护一个最小的l,满足\[l,r\]最多只有k种数。使用一个map来判断数的种类。遍历序列,如果当前数字在map中不存在,则将种类数sum加一;如果sum大于k,则将l向右移动一位,直到sum不大于k。每次更新完r之后,判断i-l+1是否大于等于y-x+1来更新答案。这种方法的时间复杂度为O(n)。 以上是两种解决CodeForces - 616D问题的方法。具体的代码实现可以参考引用\[1\]和引用\[2\]中的代码。 #### 引用[.reference_title] - *1* [CodeForces 616 D. Longest k-Good Segment(尺取)](https://blog.youkuaiyun.com/V5ZSQ/article/details/50750827)[target="_blank" data-report-click={"spm":"1018.2226.3001.9630","extra":{"utm_source":"vip_chatgpt_common_search_pc_result","utm_medium":"distribute.pc_search_result.none-task-cask-2~all~insert_cask~default-1-null.142^v91^koosearch_v1,239^v3^insert_chatgpt"}} ] [.reference_item] - *2* [Codeforces616 D. Longest k-Good Segment(双指针+map)](https://blog.youkuaiyun.com/weixin_44178736/article/details/114328999)[target="_blank" data-report-click={"spm":"1018.2226.3001.9630","extra":{"utm_source":"vip_chatgpt_common_search_pc_result","utm_medium":"distribute.pc_search_result.none-task-cask-2~all~insert_cask~default-1-null.142^v91^koosearch_v1,239^v3^insert_chatgpt"}} ] [.reference_item] [ .reference_list ]
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