feat: Largest Rectangle in Histogram

Author: hongbo-miao

JavaScript/0084. Largest Rectangle in Histogram.js

@@ -0,0 +1,70 @@
+// Given n non-negative integers representing the histogram's bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.
+//
+//       |
+//     | |
+//     | |
+//     | |   |
+// |   | | | |
+// | | | | | |
+//
+// Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].
+// The largest rectangle is shown in the shaded area, which has area = 10 unit.
+//
+// Example:
+//
+// Input: [2,1,5,6,2,3]
+// Output: 10
+
+/**
+ * @param {number[]} heights
+ * @return {number}
+ */
+
+/** Monotonic Stack */
+// https://youtu.be/KkJrGxuQtYo?t=479
+// Time O(n)
+// Space O(n)
+//
+// Last pop() is hIdx
+// Then peak() is lIdx
+//
+// st     hIdx lIdx rIdx h w area max
+// [0]
+// []      0   U    1    2 1  2    2
+// [1]
+// [1,2]
+// [1,2,3]
+// [1,2]   3   2    4    6 1  6    6
+// [1]     2   1    4    5 2  10   10
+// [1,4]
+// [1,4,5]
+// [1,4]   5   4    6    3 1  3    10
+// [1]     4   1    6    2 4  8    10
+// []      1   U    6    1 6  6    10
+const largestRectangleArea = (heights) => {
+  const st = [];
+
+  const getArea = (rIdx) => {
+    const hIdx = st.pop();
+    const h = heights[hIdx];
+
+    const lIdx = st[st.length - 1];
+
+    const w = st.length ? rIdx - lIdx - 1 : rIdx;
+    return w * h;
+  };
+
+  let max = 0;
+  for (let rIdx = 0; rIdx < heights.length; rIdx++) {
+    while (st.length && heights[rIdx] < heights[st[st.length - 1]]) {
+      const area = getArea(rIdx);
+      max = Math.max(max, area);
+    }
+    st.push(rIdx);
+  }
+  while (st.length) {
+    const area = getArea(heights.length);
+    max = Math.max(max, area);
+  }
+  return max;
+};