Largest Rectangle in Histogram Using Stack in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind using a stack to find the largest rectangle in a histogram?

Use a stack to keep track of bars in increasing height order. When a smaller bar appears, calculate areas for taller bars popped from the stack to find the largest rectangle.

beginner

Why do we push the index of bars onto the stack instead of their heights?

Storing indices helps calculate the width of rectangles easily by using the current index and the index on the stack top.

intermediate

What triggers the calculation of area for bars in the stack during the algorithm?

When the current bar is shorter than the bar at the top of the stack, we pop from the stack and calculate the area for the popped bar.

intermediate

How do you calculate the width of the rectangle when popping a bar from the stack?

Width = current index - index of new stack top - 1. If stack is empty, width = current index.

beginner

What is the time complexity of the Largest Rectangle in Histogram algorithm using a stack?

O(n), because each bar is pushed and popped at most once.

What data structure is used to solve the Largest Rectangle in Histogram problem efficiently?

A Linked List

B Queue

C Stack

D Hash Map

A stack helps track bars in increasing height order to calculate areas efficiently.

When do we pop bars from the stack during the algorithm?

A When the current bar is shorter than the top of the stack

B When the stack is empty

C At the end of the array only

D When the current bar is taller than the top of the stack

We pop bars when the current bar is shorter to calculate areas for taller bars.

What does the stack store in the Largest Rectangle in Histogram algorithm?

A Indices of bars

B Heights of bars

C Widths of bars

D Areas of rectangles

Stack stores indices to calculate widths easily.

How is the width calculated when popping a bar from the stack?

A Popped index + current index

B Current index - popped index

C Stack top index - current index

D Current index - stack top index - 1

Width is current index minus new stack top index minus one.

What is the overall time complexity of this stack-based algorithm?

A O(n log n)

B O(n)

C O(n^2)

D O(log n)

Each bar is pushed and popped once, so time complexity is O(n).

Explain step-by-step how the stack helps find the largest rectangle in a histogram.

Think about how the stack keeps track of bars and when you calculate areas.

Describe how to calculate the width of the rectangle when popping a bar from the stack.

Width depends on the distance between bars around the popped bar.