How to Find Max Consecutive Ones in an Array?

Finding the maximum number of consecutive ones in a binary array is a common problem that tests both logical thinking and coding skills in software developer interviews. This problem typically requires iterating through the array to track sequences of ones and counting their lengths.

Problem Statement

Given a binary array, your task is to determine the longest contiguous subarray that contains only the number 1.

Example

Consider the binary array:

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The longest sequence of consecutive ones is 3, which appears at the end of the array.

Naive Approach

A straightforward way to solve the problem would be using two nested loops. However, this approach is not efficient, especially for larger arrays.

Naive Method Implementation:

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Optimal Approach

Instead of using two loops, a single pass through the array can be achieved using a simple counter. This reduces the time complexity from O(n^2) to O(n), making it more efficient.

Steps to Implement

1. Initialize a counter to keep track of the current sequence of ones.
2. Initialize a variable to store the maximum length found so far.
3. Iterate through the array:
   • If the current element is 1, increment the current counter.
   • If it is 0, compare the current counter with the maximum count and reset the current counter.
4. After the loop, ensure to check the current counter once more, since the array might end with ones.

Optimal Method Implementation:

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Interview Questions

Here are typical interview questions related to the max consecutive ones problem:

1. What is the time complexity of your solution?

   • The optimal solution runs in O(n) time complexity, where n is the length of the input array. This is because we traverse the array only once.

2. How would you modify your code if the input could include additional numbers?

   • One could easily adjust the solution by defining a condition for what constitutes an acceptable value while counting the consecutive sequence. For instance, if allowed values include 2, one would need to modify the condition.

3. Can you solve this problem using a sliding window approach?

   • While the sliding window technique is often used for different problems, in this case, it might not provide significant benefits over the linear pass solution, since we are interested in counting uninterrupted sequences rather than managing a dynamic range.

Common Edge Cases

• Input with only zeros: [0, 0, 0] should return 0.
• Input with only ones: [1, 1, 1] should return 3.
• Empty input: [] should also return 0.

The max consecutive ones problem offers a good chance to display coding skills, thought processes, and problem-solving abilities during an interview.