# Leetcode Largest Rectangle in Histogram problem solution

In this Leetcode Largest Rectangle in Histogram problem solution we have Given an array of integers heights representing the histogram's bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.

## Problem solution in Python.

```class Solution:
def largestRectangleArea(self, arr: List[int]) -> int:
stack,pos,maxA=[],0,0
n=len(arr)
for i in range(n):

while(stack and arr[stack[-1]]>arr[i]):
pos= stack.pop()
if stack:
area=arr[pos]*(i-stack[-1]-1)
maxA=max(maxA,area)
else:
area=arr[pos]*(i-0)
maxA=max(maxA,area)

stack.append(i)

while stack:

pos= stack.pop()
if stack:
area=arr[pos]*(n-stack[-1]-1)
maxA=max(maxA,area)
else:
area=arr[pos]*(n-0)
maxA=max(maxA,area)

return maxA
```

## Problem solution in Java.

```class Solution {
public int largestRectangleArea(int[] heights) {
Stack < Integer > stack = new Stack < > ();
int[] left = new int[heights.length];
int[] right = new int[heights.length];
Arrays.fill(right,heights.length);
Arrays.fill(left,-1);
for(int i = 0;i<heights.length;i++){
while(!stack.empty()&&heights[stack.peek()]>heights[i]){
right[stack.peek()] = i;
stack.pop();
}
stack.push(i);
}

stack = new Stack<>();
for(int i = heights.length-1;i>=0;i--){
while(!stack.empty()&&heights[stack.peek()]>heights[i]){
left[stack.peek()] = i;
stack.pop();
}
stack.push(i);
}

int maxArea = 0;
for (int i = 0; i < heights.length; ++i) {
maxArea = Math.max(maxArea,(right[i]-left[i]-1)*heights[i]);
}

return maxArea;
}
}
```

## Problem solution in C++.

```int largestRectangleArea(vector<int>& arr) {
int n=arr.size();
if(n==0) return 0;
stack<int> s;
int i=0,area=INT_MIN;
while(i<n)
{
if(s.empty()||arr[s.top()]<=arr[i])
{
s.push(i);i++;
}
else
{
int num=s.top();s.pop();
int l=s.empty()?-1:s.top();
area=max(area,arr[num]*(i-l-1));
}
}
while(!s.empty())
{
int num=s.top();s.pop();
int l=s.empty()?-1:s.top();
area=max(area,arr[num]*(i-l-1));
}
return area;
}
```

## Problem solution in C.

```struct tagStackObj{
int height;
int width;
};

int largestRectangleArea(int* heights, int heightsSize){
int maxSize = 0;
int squareSize = 0;
int i;
int *p = heights;
int index = 0;
int stride = 0;
struct tagStackObj *pStack = NULL;

if (0 == heightsSize)
return 0;

pStack = malloc(heightsSize * sizeof(struct tagStackObj));
pStack[index].width = 1;
pStack[index].height = heights[0];

for (i = 1; i < heightsSize; i++){
if (p[i] >= pStack[index].height){
index++;
pStack[index].height = p[i];
pStack[index].width = 1;
}
else{
stride = 0;
while ((index >= 0) && (pStack[index].height > p[i])){
stride += pStack[index].width;
squareSize = stride * pStack[index].height;
maxSize = squareSize > maxSize ? squareSize : maxSize;
index--;
}

pStack[++index].height = p[i];
pStack[index].width = stride + 1;
}
}

stride = 0;
while ((index >= 0) && (pStack[index].height > -1)){
stride += pStack[index].width;
squareSize = stride * pStack[index].height;
maxSize = squareSize > maxSize ? squareSize : maxSize;
index--;
}

return maxSize;
}
```