finish 85

Author: BaffinLee

001-100/85. Maximal Rectangle.md

@@ -0,0 +1,77 @@
+# 85. Maximal Rectangle
+
+- Difficulty: Hard.
+- Related Topics: Array, Hash Table, Dynamic Programming, Stack.
+- Similar Questions: Largest Rectangle in Histogram, Maximal Square.
+
+## 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
+
+```javascript
+/**
+ * @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](./largest-rectangle-in-histogram.html).
+
+**Complexity:**
+
+* Time complexity : O(n^2).
+* Space complexity : O(n).