https://github.com/emahtab/largest-rectangle-in-a-histogram
Largest rectangle in a histogram
https://github.com/emahtab/largest-rectangle-in-a-histogram
leetcode problems-solving
Last synced: 5 months ago
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Largest rectangle in a histogram
- Host: GitHub
- URL: https://github.com/emahtab/largest-rectangle-in-a-histogram
- Owner: eMahtab
- Created: 2020-03-21T10:46:31.000Z (about 6 years ago)
- Default Branch: master
- Last Pushed: 2020-04-05T05:52:31.000Z (about 6 years ago)
- Last Synced: 2025-06-05T22:19:12.343Z (about 1 year ago)
- Topics: leetcode, problems-solving
- Homepage:
- Size: 16.6 KB
- Stars: 1
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Largest rectangle in a histogram
## https://leetcode.com/problems/largest-rectangle-in-histogram
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.
# Implementation 1 : O(n^2)
```java
class Solution {
public int largestRectangleArea(int[] heights) {
if(heights == null || heights.length == 0)
return 0;
int area = heights[0];
for(int i = 0; i < heights.length; i++) {
int minHeight = heights[i];
area = Math.max(area, heights[i]);
for(int j = i+1; j < heights.length; j++) {
minHeight = Math.min(minHeight, heights[j]);
if(minHeight == 0)
break;
area = Math.max(area, minHeight * (j - i +1));
}
}
return area;
}
}
```
# Implementation 2 : O(n)
```java
class Solution {
public int largestRectangleArea(int[] heights) {
Stack stack = new Stack<>();
int maxArea = 0;
int index = 0;
while (index < heights.length) {
if (stack.empty() || heights[index] >= heights[stack.peek()]) {
stack.push(index++);
} else {
int top = stack.pop();
int width = stack.empty() ? index : index - stack.peek() - 1;
maxArea = Math.max(maxArea, heights[top] * width);
}
}
while (!stack.empty()) {
int top = stack.pop();
int width = stack.empty() ? index : index - stack.peek() - 1;
maxArea = Math.max(maxArea, heights[top] * width);
}
return maxArea;
}
}
```
# References :
1. https://leetcode.com/articles/largest-rectangle-in-histogram
2. https://tech.pic-collage.com/algorithm-largest-area-in-histogram-84cc70500f0c