#694 - Number of Distinct Islands

Medium • View on LeetCode • View on GitHub

Hash Table Depth-First Search Breadth-First Search Union Find Hash Function

Problem Description

You are given an m x n binary matrix grid. An island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.

An island is considered to be the same as another if and only if one island can be translated (and not rotated or reflected) to equal the other.

Return the number of distinct islands.

Solution

/**
 * @param {number[][]} grid
 * @return {number}
 */
var numDistinctIslands = function(grid) {
  const rows = grid.length;
  const cols = grid[0].length;
  const visited = Array.from({ length: rows }, () => new Array(cols).fill(false));
  const islandShapes = new Set();

  for (let i = 0; i < rows; i++) {
    for (let j = 0; j < cols; j++) {
      if (grid[i][j] === 1 && !visited[i][j]) {
        const shape = [];
        dfs(i, j, i, j, shape);
        islandShapes.add(shape.join('|'));
      }
    }
  }

  return islandShapes.size;

  function dfs(row, col, baseRow, baseCol, shape) {
    if (row < 0 || row >= rows || col < 0 || col >= cols
      || visited[row][col] || grid[row][col] === 0) {
      return;
    }

    visited[row][col] = true;
    shape.push(`${row - baseRow},${col - baseCol}`);

    dfs(row + 1, col, baseRow, baseCol, shape);
    dfs(row - 1, col, baseRow, baseCol, shape);
    dfs(row, col + 1, baseRow, baseCol, shape);
    dfs(row, col - 1, baseRow, baseCol, shape);
  }
};