Furthest Point From Origin

Furthest Point From Origin

What is this problem about?

The Furthest Point From Origin coding problem is a simple simulation on a 1D number line. You start at position 0. You are given a string containing the characters 'L' (move left 1 unit), 'R' (move right 1 unit), and '_' (move either left or right 1 unit). Your goal is to determine the maximum possible absolute distance you can reach from the origin after executing all the commands.

Why is this asked in interviews?

Companies like Barclays use this String and Counting coding problem as a quick introductory question. It evaluates a candidate's basic logical deduction. It tests whether you can avoid simulating all possible paths for the '' characters and instead recognize that to maximize distance, all '' characters should simply move in the same direction as the dominant fixed moves.

Algorithmic pattern used

This problem relies on a straightforward Counting and Math pattern.

1. Count the total number of 'L' moves.
2. Count the total number of 'R' moves.
3. Count the total number of '_' (wildcard) moves.
4. The base distance achieved by the fixed moves is the absolute difference: abs(L_count - R_count).
5. To maximize the final distance, all wildcards should be used to extend the dominant direction.
6. Result: abs(L_count - R_count) + wildcard_count.

Example explanation

String: "L_RL__R"

1. Count 'L': 2
2. Count 'R': 2
3. Count '_': 3
4. Base distance: abs(2 - 2) = 0. The fixed moves cancel each other out.
5. Wildcards: Since base is 0, we can move all 3 wildcards in either direction (all L or all R) to reach a maximum distance of 3. Result: 0 + 3 = 3.

String: "_R__LL_"

1. 'L': 2, 'R': 1, '_': 4.
2. Base distance: abs(2 - 1) = 1 (Net movement is left).
3. To maximize, make all wildcards 'L'.
4. Total distance: 1 + 4 = 5.

Common mistakes candidates make

• Recursive Simulation: Trying to use backtracking or recursion to explore every possible assignment for the '_' characters, which leads to an exponential $O(2^N)$ time complexity and Time Limit Exceeded errors.
• Absolute Value Logic Error: Calculating abs(L + wildcards - R) versus abs(L - (R + wildcards)) manually instead of just adding the wildcards to the absolute difference of the fixed moves.

Interview preparation tip

Always look for the "greedy" math shortcut in easy array/string problems. If you have wildcards and want to maximize a sum or distance, applying all wildcards in the direction of the current majority is almost always the optimal choice.