Matrix — Reasoning Check

1. After clockwise rotation of an n=4 square matrix, the original cell (1,3) is in row 3. What is its new column? Enter one integer.

2. Set Matrix Zeroes receives [[1,2,3],[4,0,6],[7,8,9]]. Why is immediately zeroing each discovered zero's row and column unsafe?

Select one answer.

Zeros written by an earlier update can be mistaken for original causes and erase unrelated rows or columns. Only the original zero cell should change; spreading to its row and column is unnecessary. Rows must be processed from bottom to top for immediate zeroing to become correct.

3. Traverse [[2,4],[6,8],[10,12]] by increasing r+c, reversing direction on each diagonal and starting at the top-left. The first three emitted values are 2,4,6. What is the fourth value? Enter one integer.

4. During Game of Life encoding, a neighboring cell currently stores 2 (binary 10). How should it contribute to another cell's OLD live-neighbor count?

Select one answer.

It contributes two, because its encoded integer value is 2. It contributes zero, because bit 0 records that it was dead. It contributes one, because any nonzero encoded value is alive.

5. A 9-by-9 Sudoku board has a 4 at (0,0) and another 4 at (0,4), with every other cell empty. How many rule families fail: row, column, and box? Enter one integer.

6. In a one-row spiral traversal, the top sweep emits every cell and increments top past bottom. What prevents the reverse bottom sweep from emitting them again?

Select one answer.

Recheck top<=bottom after the top and right sweeps. Reverse the complete output after all four sweeps. Perform the bottom sweep whenever left<=right, regardless of top and bottom.