def num_distinct_islands(grid):
    if not grid:
        return 0

    distinct_islands = set()

    def dfs(row, col, path, direction):
        if row < 0 or row >= len(grid) or col < 0 or col >= len(grid[0]) or grid[row][col] != 1:
            return

        grid[row][col] = 0
        path.append(direction)

        dfs(row - 1, col, path, 'U')
        dfs(row + 1, col, path, 'D')
        dfs(row, col - 1, path, 'L')
        dfs(row, col + 1, path, 'R')

        path.append('B')

    for row in range(len(grid)):
        for col in range(len(grid[0])):
            if grid[row][col] == 1:
                path = []
                dfs(row, col, path, 'O')
                distinct_islands.add(''.join(path))

    return len(distinct_islands)

# Example usage
grid = [
    [1, 1, 0, 0, 0],
    [1, 1, 0, 0, 0],
    [0, 0, 0, 1, 1],
    [0, 0, 0, 1, 1

]
]
print(num_distinct_islands(grid))  # 1