Number of Distinct Islands

MediumGraphsdfs

Solve this the way you would in the interview: out loud, on a timer, with an AI interviewer asking follow-ups while you code. You get a scored report at the end.

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Problem

You are given a binary grid where 1 is land and 0 is water. An island is a group of land cells connected horizontally or vertically. Two islands have the same shape if one can be **translated** (shifted up/down/left/right) to cover exactly the other. Rotations and reflections do not count as the same shape. Return the number of distinct island shapes in the grid.

Examples

Input: grid = [[1,1,0,0,0],[1,1,0,0,0],[0,0,0,1,1],[0,0,0,1,1]]
Output: 1
Both islands are 2x2 squares.
Input: grid = [[1,1,0,1,1],[1,0,0,0,0],[0,0,0,0,1],[1,1,0,1,1]]
Output: 3
The top-left L, the two horizontal bars (one shape), and the bottom-right L, which is a rotated copy of the first and therefore a different shape.

Constraints

  • `1 <= m, n <= 50`
  • `grid[i][j]` is `0` or `1`

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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