Trapping Rain Water Using Stack in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind using a stack to solve the Trapping Rain Water problem?

Use a stack to keep track of bars that are bounded by higher bars on both sides. When a higher bar is found, calculate trapped water with the bars in the stack.

beginner

In the stack approach, what does each element in the stack represent?

Each element represents the index of a bar in the elevation map, helping to find boundaries for trapped water.

intermediate

Why do we pop from the stack when the current bar height is greater than the height of the bar at the top of the stack?

Because we found a right boundary taller than the bar at the top, allowing us to calculate trapped water between boundaries.

intermediate

How is the width of trapped water calculated in the stack method?

Width is the distance between the current index and the new top of the stack minus one, representing the horizontal space between boundaries.

beginner

What is the time complexity of the Trapping Rain Water solution using a stack?

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

What does the stack store in the Trapping Rain Water problem?

A Indices of bars

B Heights of bars

C Water trapped at each bar

D Widths between bars

The stack stores indices of bars to help calculate trapped water between boundaries.

When do we calculate trapped water in the stack approach?

A Before pushing any bar

B When current bar is shorter than top of stack

C At the end of the array only

D When current bar is taller than top of stack

We calculate trapped water when the current bar is taller than the bar at the top of the stack.

What does popping from the stack represent in this problem?

A Removing a boundary bar

B Calculating trapped water between boundaries

C Finding a valley to trap water

D Resetting the stack

Popping helps calculate trapped water between the current bar and the new top of the stack.

How is the trapped water height calculated after popping from the stack?

A Sum of current and top bar heights minus popped bar height

B Maximum of current and top bar heights minus popped bar height

C Minimum of current and top bar heights minus popped bar height

D Difference between current and popped bar heights

Height is the minimum of current and top bar heights minus the popped bar height.

What is the overall time complexity of the stack solution for trapping rain water?

A O(n)

B O(n log n)

C O(log n)

D O(n^2)

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

Explain step-by-step how the stack helps calculate trapped rain water in the elevation map.

Think about how boundaries form valleys to hold water.

Describe how to calculate the width and height of trapped water when popping from the stack.

Focus on how boundaries define the trapped water area.