#305 - Number of Islands II

Problem Description

You are given an empty 2D binary grid grid of size m x n. The grid represents a map where 0's represent water and 1's represent land. Initially, all the cells of grid are water cells (i.e., all the cells are 0's).

We may perform an add land operation which turns the water at position into a land. You are given an array positions where positions[i] = [ri, ci] is the position (ri, ci) at which we should operate the ith operation.

Return an array of integers answer where answer[i] is the number of islands after turning the cell (ri, ci) into a land.

An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.

Solution

/**
 * @param {number} m
 * @param {number} n
 * @param {number[][]} positions
 * @return {number[]}
 */
var numIslands2 = function(m, n, positions) {
  const parent = new Map();
  const rank = new Map();
  const result = [];
  const directions = [[-1, 0], [1, 0], [0, -1], [0, 1]];
  let islandCount = 0;

  for (const [row, col] of positions) {
    const current = row * n + col;
    if (parent.has(current)) {
      result.push(islandCount);
      continue;
    }
    islandCount++;
    parent.set(current, current);
    rank.set(current, 0);

    for (const [dr, dc] of directions) {
      const newRow = row + dr;
      const newCol = col + dc;
      if (newRow >= 0 && newRow < m && newCol >= 0 && newCol < n) {
        const neighbor = newRow * n + newCol;
        if (parent.has(neighbor)) {
          union(current, neighbor);
        }
      }
    }
    result.push(islandCount);
  }

  return result;

  function find(node) {
    if (!parent.has(node)) {
      parent.set(node, node);
      rank.set(node, 0);
    }
    if (parent.get(node) !== node) {
      parent.set(node, find(parent.get(node)));
    }
    return parent.get(node);
  }

  function union(node1, node2) {
    const root1 = find(node1);
    const root2 = find(node2);
    if (root1 === root2) return;
    const rank1 = rank.get(root1);
    const rank2 = rank.get(root2);
    if (rank1 < rank2) {
      parent.set(root1, root2);
    } else if (rank1 > rank2) {
      parent.set(root2, root1);
    } else {
      parent.set(root2, root1);
      rank.set(root1, rank1 + 1);
    }
    islandCount--;
  }
};