Distinct Islands Problem Statement

Given a two-dimensional array/list consisting of integers 0s and 1s, where 1 represents land and 0 represents water, determine the number of distinct islands. A group of connected 1s (horizontally or vertically) forms an island.

Note:

Two islands are considered the same if one can be translated to overlap the other without rotation or reflection. If this condition is satisfied, they are considered identical.

Example:

Input:

 1 1 0
 0 0 1
 0 0 1

Output:

2

Explanation:

Here, two islands exist and they cannot be translated to overlap each other, thus they are distinct.

Example:

Input:

 1 1 0 0 0
 1 1 0 0 0
 0 0 0 1 1
 0 0 0 1 1

Output:

1

Explanation:

These islands can be translated to overlap each other, thus they are not distinct. Only one distinct island exists.

Input:

N, M

The first two numbers are the dimensions of the array: 'N' rows and 'M' columns.

The subsequent 'N' lines provide the values for each row, with each row containing 'M' space-separated values of the array.

Output:

Total number of distinct islands.

Constraints:

• 0 ≤ N ≤ 1000
• 0 ≤ M ≤ 1000
• Array elements are either 0 or 1
• Time Limit: 1 sec