Leftmost Column with at Least a One

Leftmost Column with at Least a One

What is this problem about?

The "Leftmost Column with at Least a One interview question" is an interactive problem involving a binary matrix. In this matrix, each row is sorted in non-decreasing order (meaning all 0s come before all 1s). You cannot access the matrix directly; instead, you use an API to query individual cells. Your goal is to find the index of the leftmost column that contains at least one '1'. If no such column exists, return -1. This "Leftmost Column with at Least a One coding problem" challenges you to minimize the number of API calls.

Why is this asked in interviews?

Companies like Uber and Meta ask this to test your ability to optimize search strategies in a constrained environment. It's a great test of "Binary Search interview pattern" and "Matrix interview pattern" knowledge. Because you are limited in how you can access the data, you must think about the structure of the matrix to avoid unnecessary queries.

Algorithmic pattern used

There are two main approaches. One is performing a Binary Search on each row to find the first '1'. However, the more optimized approach is the "Staircase Search" or "Top-Right to Bottom-Left" traversal. You start at the top-right corner. If you see a '0', move down (since this row won't have a '1' further left). If you see a '1', move left to see if there's an even earlier '1' in another row. This ensures an O(M + N) complexity, where M is rows and N is columns.

Example explanation

Matrix: [[0, 0, 1], [0, 1, 1], [0, 0, 0]]

1. Start at (0, 2). It's a '1'. Leftmost found so far is col 2. Move left to (0, 1).
2. (0, 1) is '0'. Move down to (1, 1).
3. (1, 1) is '1'. Leftmost found so far is col 1. Move left to (1, 0).
4. (1, 0) is '0'. Move down to (2, 0).
5. (2, 0) is '0'. We are at the bottom row. The smallest column index we found was 1.

Common mistakes candidates make

• Brute force: Iterating through every single cell, which leads to too many API calls.
• Incorrect Binary Search range: Not properly updating the "best" column found so far when doing binary search on rows.
• Not handling the -1 case: Forgetting to return -1 if the entire matrix consists of 0s.

Interview preparation tip

Whenever you see a matrix where rows or columns are sorted, think about how you can "navigate" the grid rather than just scanning it. The staircase walk is a very powerful technique for sorted matrices.