85. Maximal Rectangle

Problem

Given a 2D binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return its area.

Example:

Input:
[
  ["1","0","1","0","0"],
  ["1","0","1","1","1"],
  ["1","1","1","1","1"],
  ["1","0","0","1","0"]
]
Output: 6

Solution

/**
 * @param {character[][]} matrix
 * @return {number}
 */
var maximalRectangle = function(matrix) {
  var n = matrix.length;
  var m = (matrix[0] || []).length;
  var max = 0;
  var heights = Array(m);
  var stack = [];
  var h = 0;
  var w = 0;

  for (var i = 0; i < n; i++) {
    stack = [];

    for (var j = 0; j < m; j++) {
      if (matrix[i][j] === '1') {
        heights[j] = i === 0 ? 1 : heights[j] + 1;
      } else {
        heights[j] = 0;
      }

      while (stack.length && heights[j] <= heights[stack[stack.length - 1]]) {
        h = heights[stack.pop()];
        w = stack.length === 0 ? j : j - stack[stack.length - 1] - 1;
        max = Math.max(max, h * w);
      }

      stack.push(j);
    }

    while (stack.length) {
      h = heights[stack.pop()];
      w = stack.length === 0 ? m : m - stack[stack.length - 1] - 1;
      max = Math.max(max, h * w);
    }
  }

  return max;
};

Explain:

see Largest Rectangle in Histogram.

Complexity:

• Time complexity : O(n^2).
• Space complexity : O(n).