微软技术面试：矩阵算法伪代码问题求助

Hey there, let’s break down this interview question step by step to help you understand where you might have missed the mark, and get you ready for next time. I’ll walk through each of the interviewer’s questions with precise explanations that align with what they were likely looking for:

1. What’s wrong with the code, and how to fix it? #

Your callout about the array index out-of-bounds error (when x=3, x+1=4 exceeds the 0-3 index range of the 4x4 matrix) is correct. But there are two other critical issues the interviewer probably cared about more:

• Incorrect equality check syntax: The line IF a[x+1][y] = a[x][y] uses an assignment operator (=) instead of an equality check. In pseudo-code, this should be == (or equivalent) to compare values, not overwrite them.
• Flawed logic order that breaks functionality: The current code tries to handle merging and shifting in the same loop iteration, which leads to inconsistent results. For example:
  • If a column has [NULL, 2, 2, NULL], the code would first shift the first 2 up to index 0 when x=0, then when x=1, it would shift the second 2 up to index 1—but it would never merge the two 2s because the merge check only runs when a[x+1][y] != NULL and a[x][y] wasn’t NULL before shifting.

Fix steps: #

1. Adjust the inner loop range: Change x = 0 to 3 to x = 0 to 2 so x+1 never exceeds 3.
2. Split into two separate loops:
   • First loop: Shift all non-NULL elements in each column to the top (push NULLs to the bottom).
   • Second loop: Merge adjacent identical elements starting from the top (double the value of the upper element, set the lower one to NULL).
3. Fix the equality check: Replace = with == in the merge condition.

2. What does the corrected foo() function do? #

After fixing the issues, foo() implements the column-wise upward merge logic from the 2048 game for a 4x4 matrix. Specifically:

• For each column, first gather all non-NULL values at the top of the column (empty positions represented by NULL move to the bottom).
• Then, starting from the top of the column, merge any two adjacent identical values into one value (double the original number), and set the lower position to NULL.

Using your sample input:

Original state:
[[2, NULL, 2, NULL],
 [2, NULL, 2, NULL],
 [NULL, NULL, NULL, NULL],
 [NULL, NULL, NULL, NULL]]

After running the corrected foo(), the result becomes:

[[4, NULL, 4, NULL],
 [NULL, NULL, NULL, NULL],
 [NULL, NULL, NULL, NULL],
 [NULL, NULL, NULL, NULL]]

3. How to make foo() more generic? (Up to 3 directions) #

Here are three practical generalization strategies:

• Support arbitrary matrix sizes: Instead of hardcoding the 4x4 dimensions, pass the number of rows and columns as parameters to foo(). The loops would use these parameters to dynamically set their ranges, so the function works with any NxM matrix.
• Support all merge directions: Currently, it only handles upward merges. Add a direction parameter (e.g., "up", "down", "left", "right") and adjust the loop order and index logic accordingly. For example:
  • For downward merges, iterate from the bottom of the column upward.
  • For left/right merges, iterate across rows instead of columns.
• Customize empty values and merge rules: Let users define what counts as an "empty" value (instead of hardcoding NULL) and provide a custom merge function (instead of always doubling the value). For example, you could pass empty_value and merge_func parameters—so the function could use 0 as empty and merge values by adding them, if needed.

内容的提问来源于stack exchange，提问作者Ajay