Largest Rectangle in Histogram - Leetcode 84

Largest Rectangle in Histogram - Leetcode 84


3 min read

Problem - Leetcode

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.

Example 1:

Input: heights = [2,1,5,6,2,3]
Output: 10
Explanation: The above is a histogram where the width of each bar is 1. The largest rectangle is shown in the red area, which has an area of 10 units.

Example 2:

Input: heights = [2,4]
Output: 4

Solution in Golang

func largestRectangleArea(heights []int) int {
    stack := []StackValue{}
    maxArea := 0
    var start int
    for i,h := range heights {
        start = i
        for len(stack) != 0 && stack[len(stack)-1].height > h {
            index, height := stack[len(stack)-1].index , stack[len(stack)-1].height
            stack = stack[0:len(stack)-1]
            maxArea = max(maxArea, height*(i-index))
            start = index
        stack = append(stack, StackValue{start,h})
    for _, h := range stack {
        maxArea = max(maxArea, h.height*(len(heights)-h.index))
    return maxArea
type StackValue struct {
    index  int
    height int
func max(a,b int) int {
    if a > b {
        return a
    return b

This Go code defines a function largestRectangleArea that calculates the largest area of a rectangle that can be formed within a given histogram represented by an array of integer heights. The code uses a stack data structure to efficiently compute this.

Here's a step-by-step explanation of the code:

  1. stack := []StackValue{}: Initialize an empty stack to keep track of heights and their corresponding indices in the histogram.

  2. maxArea := 0: Initialize a variable maxArea to store the maximum rectangle area found so far.

  3. var start int: Initialize a variable start to keep track of the starting index of a potential rectangle.

  4. Loop through the input heights array using a for loop with i representing the current index and h representing the current height.

  5. Set start to the current index i.

  6. Check if the stack is not empty and the height at the top of the stack (stack[len(stack)-1].height) is greater than the current height h. If this condition is true, it means we can potentially calculate the area of a rectangle.

  7. Inside the loop, pop elements from the stack while the condition in step 6 is met. For each popped element, calculate the area it represents (height times the width, which is the difference between the current index i and the index stored in the popped element). Update maxArea if this area is greater than the current maxArea.

  8. Set start to the index of the last popped element, as this is the starting index of the potential rectangle that includes the current height h.

  9. Push the current index start and height h onto the stack as a StackValue.

  10. After the loop, there might still be elements left in the stack. Loop through these remaining elements and calculate the area for each of them, considering the entire remaining width of the histogram. Update maxArea if any of these areas is greater than the current maxArea.

  11. Finally, return the maxArea, which represents the largest rectangle that can be formed within the given histogram.

The StackValue struct is used to store the index and height of elements pushed onto the stack.

The max function is a simple utility function used to find the maximum of two integers.

This code essentially uses a stack to keep track of ascending heights in the histogram and calculates the maximum rectangle area that can be formed efficiently.

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