Trapping Rain Water Using Stack in DSA C - Execution Trace

Concept Flow - Trapping Rain Water Using Stack

Start with empty stack

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Iterate over height array

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While stack not empty and current height > height at stack top

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Pop top

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Calculate trapped water

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Add water to total

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Push current index to stack

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Move to next index

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End when all bars processed

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Return total trapped water

We use a stack to keep indexes of bars. When current bar is higher than stack top, we pop and calculate trapped water between bars.

Execution Sample

DSA C

int trap(int* height, int heightSize) {
    int stack[heightSize];
    int top = -1, water = 0, i = 0;
    while (i < heightSize) {
        while (top != -1 && height[i] > height[stack[top]]) {
            int topIndex = stack[top--];
            if (top == -1) break;
            int distance = i - stack[top] - 1;
            int bounded_height = (height[i] < height[stack[top]] ? height[i] : height[stack[top]]) - height[topIndex];
            water += distance * (bounded_height > 0 ? bounded_height : 0);
        }
        stack[++top] = i++;
    }
    return water;
}

This code calculates trapped rain water using a stack to track bars and compute trapped water when a higher bar is found.

Execution Table

Step	Operation	Current Index (i)	Stack Content (indexes)	Popped Index	Distance	Bounded Height	Water Added	Total Water	Visual State
1	Push index 0	0	[0]	-	-	-	0	0	Height: [0:0] Stack: [0] Water: 0
2	Pop index 0 (height 0 < current height 1? Yes)	1	[]	0	-	-	0	0	Height: [0:0,1:1] Stack: [] Water: 0
3	Push index 1	1	[1]	-	-	-	0	0	Height: [0:0,1:1] Stack: [1] Water: 0
4	Push index 2	2	[1,2]	-	-	-	0	0	Height: [0:0,1:1,2:0] Stack: [1,2] Water: 0
5	Pop index 2 (height 0 < current height 3? Yes)	3	[1]	2	3 - 1 - 1 = 1	min(3,1) - 0 = 1	1*1=1	1	Height: [0:0,1:1,2:0,3:3] Stack: [1] Water: 1
6	Pop index 1 (height 1 < current height 3? Yes)	3	[]	1	-	-	0	1	Height: [0:0,1:1,2:0,3:3] Stack: [] Water: 1
7	Push index 3	3	[3]	-	-	-	0	1	Height: [0:0,1:1,2:0,3:3] Stack: [3] Water: 1
8	Push index 4	4	[3,4]	-	-	-	0	1	Height: [0:0,1:1,2:0,3:3,4:0] Stack: [3,4] Water: 1
9	Pop index 4 (height 0 < current height 2? Yes)	5	[3]	4	5 - 3 - 1 = 1	min(2,3) - 0 = 2	1*2=2	3	Height: [0:0,1:1,2:0,3:3,4:0,5:2] Stack: [3] Water: 3
10	Push index 5	5	[3,5]	-	-	-	0	3	Height: [0:0,1:1,2:0,3:3,4:0,5:2] Stack: [3,5] Water: 3
11	Push index 6	6	[3,5,6]	-	-	-	0	3	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1] Stack: [3,5,6] Water: 3
12	Pop index 6 (height 1 < current height 4? Yes)	7	[3,5]	6	7 - 5 - 1 = 1	min(4,2) - 1 = 1	1*1=1	4	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4] Stack: [3,5] Water: 4
13	Pop index 5 (height 2 < current height 4? Yes)	7	[3]	5	7 - 3 - 1 = 3	min(4,3) - 2 = 1	3*1=3	7	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4] Stack: [3] Water: 7
14	Pop index 3 (height 3 < current height 4? Yes)	7	[]	3	-	-	0	7	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4] Stack: [] Water: 7
15	Push index 7	7	[7]	-	-	-	0	7	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4] Stack: [7] Water: 7
16	Push index 8	8	[7,8]	-	-	-	0	7	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4,8:0] Stack: [7,8] Water: 7
17	Pop index 8 (height 0 < current height 2? Yes)	9	[7]	8	9 - 7 - 1 = 1	min(2,4) - 0 = 2	1*2=2	9	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4,8:0,9:2] Stack: [7] Water: 9
18	Push index 9	9	[7,9]	-	-	-	0	9	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4,8:0,9:2] Stack: [7,9] Water: 9
19	Pop index 9 (height 2 < current height 3? Yes)	10	[7]	9	10 - 7 - 1 = 2	min(3,4) - 2 = 1	2*1=2	11	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4,8:0,9:2,10:3] Stack: [7] Water: 11
20	Push index 10	10	[7,10]	-	-	-	0	11	Height: [0:0,1:1,2:0,3:3,4:0,5:2,6:1,7:4,8:0,9:2,10:3] Stack: [7,10] Water: 11

💡 All bars processed, total trapped water calculated

Variable Tracker

Variable	Start	After Step 1	After Step 5	After Step 9	After Step 13	After Step 18	Final
i	0	1	3	5	7	10	11
stack (indexes)	[]	[0]	[1]	[3]	[3]	[7,9]	[7,10]
water	0	0	1	3	7	9	11

Key Moments - 3 Insights

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

Because trapped water can only be formed when we find a right boundary higher than the previous bars. This is shown in execution_table rows 5 and 9 where popping happens only when current height is greater.

Why do we calculate distance as i - stack[top] - 1?

Distance is the width between the current bar and the new top of stack after popping. The '-1' excludes the popped bar itself. See execution_table rows 5 and 9 for distance calculation.

Why do we break if stack becomes empty after popping?

If stack is empty, there is no left boundary to trap water. So we stop calculating water for that popped bar. This is shown in execution_table row 6 where break happens after popping.

Visual Quiz - 3 Questions

Look at the execution_table at step 5, what is the amount of water added?

A 1

B 0

C 2

D 3

💡 Hint

Check the 'Water Added' column at step 5 in execution_table.

At which step does the total trapped water first become greater than zero?

A Step 1

B Step 5

C Step 9

D Step 13

💡 Hint

Look at the 'Total Water' column in execution_table to find when it changes from 0.

If the height at index 3 was lower, how would that affect the water trapped at step 13?

A Water trapped would increase

B Water trapped would stay the same

C Water trapped would decrease

D No water would be trapped at all

💡 Hint

Step 13 depends on height at index 3 as left boundary; lower height reduces bounded height.

Concept Snapshot

Trapping Rain Water Using Stack:
- Use a stack to store indexes of bars.
- Iterate bars, pop when current bar is higher than stack top.
- Calculate trapped water using distance and bounded height.
- Add trapped water to total.
- Push current index to stack.
- Return total water after processing all bars.

Full Transcript

This visualization shows how to calculate trapped rain water using a stack. We start with an empty stack and iterate over the height array. When the current bar is higher than the bar at the top of the stack, we pop the stack to find trapped water between bars. We calculate the distance between the current bar and the new top of the stack and find the bounded height to compute trapped water. We add this water to the total. We continue pushing indexes to the stack and repeat until all bars are processed. The total trapped water is returned at the end.