1267. Count Servers that Communicate - Detailed Explanation
Problem Statement
You are given a 2D grid where each cell is either 0 or 1. A cell with a 1 represents a server, while a cell with a 0 means no server exists there. Two servers can communicate if they are in the same row or the same column.
Task:
Return the number of servers that can communicate with at least one other server. In other words, count every server that is not isolated in both its row and its column.
Example 1:
- Input:
grid = [ [1, 0], [0, 1] ] - Output:
0 - Explanation:
Each server is isolated because there is only one server in each row and each column. No server can communicate with another.
Example 2:
- Input:
grid = [ [1, 0], [1, 1] ] - Output:
3 - Explanation:
- The server at (0,0) can communicate with the server at (1,0) (same column).
- The server at (1,0) can communicate with both (0,0) and (1,1).
- The server at (1,1) can communicate with (1,0) (same row).
All three servers can communicate with at least one other server.
Hints to Solve the Problem
-
Counting by Row and Column:
- Traverse the grid to count the number of servers in each row and in each column.
- A server can communicate if either its row or its column has more than one server.
-
Two-Pass Approach:
- First pass: Go through the grid to build two arrays (or dictionaries) for row counts and column counts.
- Second pass: Iterate through the grid again, and for every cell with a server (value
1), check if its row count or column count is greater than one. If yes, include it in the final count.
-
Time and Space Considerations:
- The two-pass solution is efficient with a time complexity of O(m*n) and uses O(m+n) extra space, where m and n are the grid’s dimensions.
-
Alternate Idea – DFS for Connected Components:
- Although overkill for this problem, you can also use DFS (or BFS) to find connected components (servers in the same row or column) and count those in components with size greater than one.
Detailed Explanation
The simplest and most intuitive approach is to count servers per row and per column:
-
Step 1: Traverse the grid once to count the number of servers in each row (using an array
rowCount[]) and each column (using an arraycolCount[]). -
Step 2: Traverse the grid again. For every cell with a server (
grid[i][j] == 1), check ifrowCount[i] > 1orcolCount[j] > 1. If so, then this server can communicate with at least one other server, and we increment our answer.
This method works because if a server is the only one in its row and its column (i.e. rowCount[i] == 1 and colCount[j] == 1), it cannot communicate with any other server. Otherwise, if either count is greater than one, communication is possible.
Python Implementation
Java Implementation
Edge Cases
-
Grid with No Servers:
- Scenario: The grid contains only 0’s.
- Impact: Since there are no servers at all, the output should be 0.
-
Grid with a Single Server:
- Scenario: If the grid has exactly one cell with a 1, that server cannot communicate with anyone else.
- Impact: The answer should be 0.
-
Grid with One Row or One Column:
- Scenario: When the grid is a single row or a single column, the logic still applies. For example, if the row is
[1, 1, 0, 1], then each server that is adjacent to another should be counted.
- Scenario: When the grid is a single row or a single column, the logic still applies. For example, if the row is
-
Isolated Servers:
- Scenario: Servers that are the only ones in their row and column.
- Impact: These servers should not be counted since they have no other server in the same row or column.
-
All Servers in One Row or Column:
- Scenario: If all the servers are located in the same row or the same column, every server communicates with every other server.
- Impact: All these servers should be counted.
Common Mistakes
-
Counting Isolated Servers:
- Mistake: Adding every server to the final count regardless of whether there is another server in its row or column.
- Tip: Always check that either the row count or the column count for a given server is more than one before incrementing the result.
-
Incorrect Indexing When Iterating:
- Mistake: Off-by-one errors when iterating through rows and columns, leading to either missing a server or accessing an invalid index.
- Tip: Use clear loop boundaries (e.g.,
for i in range(m)andfor j in range(n)).
-
Not Handling Single Row/Column Cases Correctly:
- Mistake: Assuming that the grid has multiple rows and columns can lead to errors when the grid is only 1 row or 1 column.
- Tip: Test your solution on grids with minimal dimensions.
-
Overcounting:
- Mistake: Counting a server multiple times (for example, once when checking its row and again when checking its column).
- Tip: Count each server exactly once by performing a single pass over the grid and checking if it meets the condition (row count > 1 or column count > 1).
-
Not Precomputing Counts:
- Mistake: Recalculating row and column counts repeatedly in a nested loop, which can degrade performance.
- Tip: Use two separate passes—one to compute counts for each row and column, and a second to determine the result.
Alternate Problems & Related Challenges
-
Number of Islands:
- Description: Count the number of connected components (islands) in a grid where islands are formed by adjacent 1’s (usually considering four-directional adjacency).
- Relation: Both problems involve processing a grid and determining connectivity. In Count Servers, connectivity is defined across entire rows or columns, whereas in Number of Islands it is defined by adjacent positions.
-
Surrounded Regions:
- Description: Modify a grid by capturing regions that are completely surrounded by another element.
- Relation: This problem also deals with grid connectivity and region identification, requiring careful traversal and boundary checking.
-
Rearrange String k Distance Apart:
- Description: Rearrange characters in a string so that the same characters are at least k positions apart.
- Relation: Although not a grid problem, it shares the concept of spacing out elements (or tasks) so that similar items do not appear too close to each other.
-
Connected Components in Graphs:
- Description: Find and count the connected components in an undirected graph.
- Relation: In some alternate interpretations, you can think of servers as nodes and communication (being in the same row or column) as edges; counting communicative servers is analogous to determining connectivity in a graph.
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