Microsoft Interview Question — LeetCode 1267

In this post, we are going to discuss leetcode 1267 — Count Servers that Communicate, which is asked in Microsoft interviews.

Problem Analysis

You are given a map of a server center, represented as a m * n integer matrix grid, where 1 means that on that cell there is a server and 0 means that it is no server. Two servers are said to communicate if they are on the same row or on the same column.

Return the number of servers that communicate with any other server.

Example 1:

Input: grid = [[1,0],[0,1]] 
Output: 0 
Explanation: No servers can communicate with others.

Example 2:

Input: grid = [[1,0],[1,1]] 
Output: 3 
Explanation: All three servers can communicate with at least one other server.

Example 3:

Input: grid = [[1,1,0,0],[0,0,1,0],[0,0,1,0],[0,0,0,1]] 
Output: 4 
Explanation: The two servers in the first row can communicate with each other. The two servers in the third column can communicate with each other. The server at right bottom corner can't communicate with any other server.

My Thinking Process

I started with a graph approach, by translating the input into a graph. Then I only need to count the connected components with size of 1.

However, during my implementation, I find I overcomplicate the problem. One node is not connected to others, if and only if there are no nodes on the same row or column. Then why not just keep a map of row_index to a count of nodes on the row, and a map of col_index to a count of nodes on the column? Then with this, we can loop through the nodes, and check how many nodes are on the same row and same column. If this is the only node on this row and column, then we can say this node is not connected to anything.

So the logic of the approach will be below:

1. Loop through the grid, and build a map of row_index to a count of nodes on the row, and a map of col_index to a count of nodes on the column.
2. Loop through the grid again, for each node, if it is the only node on the row and column, this node is not connected to others.
3. Total number of nodes — single nodes will return the result

Code Implementation

Base on the analysis above, below is my implementation of the problem.