Trapping Rain Water Using Stack in DSA C - Time & Space Complexity

Time Complexity: Trapping Rain Water Using Stack

O(n)

Understanding Time Complexity

We want to understand how the time needed to calculate trapped rain water changes as the input size grows.

Specifically, how the steps increase when using a stack to solve this problem.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

This code calculates how much rain water can be trapped between bars using a stack to track boundaries.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The outer while loop runs through each bar once.
• Inner loop: The inner while loop pops bars from the stack when current bar is taller.
• How many times: Each bar is pushed and popped at most once, so total operations scale with input size.

How Execution Grows With Input

As the number of bars increases, each bar is processed a limited number of times.

Input Size (n)	Approx. Operations
10	About 20 (push and pop each bar once)
100	About 200
1000	About 2000

Pattern observation: The operations grow roughly in a straight line with input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to compute trapped water grows directly with the number of bars.

Common Mistake

[X] Wrong: "The inner loop causes the time to be quadratic (O(n²)) because it is nested inside the outer loop."

[OK] Correct: Each bar is pushed and popped only once, so total inner loop executions across all iterations add up to n, not n².

Interview Connect

Understanding this time complexity shows you can analyze stack-based solutions and explain why they are efficient, a valuable skill in interviews.

Self-Check

"What if we used a simple nested loop without a stack? How would the time complexity change?"

Practice

1. What is the main purpose of using a stack in the Trapping Rain Water Using Stack algorithm?

easy

A. To reverse the order of the bars

B. To store the total amount of trapped water directly

C. To sort the heights of bars in ascending order

D. To keep track of bars that are not yet processed for water trapping

Solution

1. Step 1: Understand stack role in the algorithm

   The stack stores indices of bars that are waiting to find a right boundary to trap water.

2. Step 2: Clarify what the stack does not do

   The stack does not store water amounts or sort bars; it helps find boundaries for trapped water.

3. Final Answer:

   To keep track of bars that are not yet processed for water trapping -> Option D

4. Quick Check:

   Stack tracks bars for trapping water [OK]

Hint: Stack holds indices of bars waiting for right boundary [OK]

Common Mistakes:

• Thinking stack stores water volume directly
• Assuming stack sorts the bars
• Believing stack reverses bar order

2. Which of the following C code snippets correctly declares a stack to store indices for trapping rain water?

easy

A. int stack[100]; int top = -1;

B. int stack; int top = 0;

C. int *stack = NULL; int top = 1;

D. int stack[] = {}; int top = -1;

Solution

1. Step 1: Check stack declaration syntax

   int stack[100]; int top = -1; declares an integer array with fixed size and initializes top to -1, which is correct for stack implementation.

2. Step 2: Identify incorrect declarations

   Options B, C, and D have wrong types or invalid initializations for stack and top pointer.

3. Final Answer:

   int stack[100]; int top = -1; -> Option A

4. Quick Check:

   Array + top = -1 is correct stack setup [OK]

Hint: Use array and top = -1 for empty stack [OK]

Common Mistakes:

• Using uninitialized or wrong top value
• Declaring stack as single int instead of array
• Using empty array syntax invalid in C

3. What is the output of the following code snippet that calculates trapped rain water using stack?

int height[] = {0,1,0,2,1,0,1,3,2,1,2,1};
int n = 12;
// Assume correct trapping rain water stack code runs here
int trapped = trappingRainWater(height, n);
printf("%d\n", trapped);

medium

A. 5

B. 6

C. 4

D. 7

Solution

1. Step 1: Understand the input heights

   The array represents bar heights where water can be trapped between taller bars.

2. Step 2: Calculate trapped water manually or recall known result

   The known trapped water for this input is 6 units.

3. Final Answer:

   6 -> Option B

4. Quick Check:

   Standard example trapped water = 6 [OK]

Hint: Remember classic example traps 6 units water [OK]

Common Mistakes:

• Miscounting trapped water units
• Confusing indexes or heights
• Assuming output is sum of heights

4. Identify the bug in this snippet of the trapping rain water stack algorithm:

while (top != -1 && height[i] > height[stack[top]]) {
  int topIndex = stack[top--];
  int distance = i - stack[top] - 1;
  int bounded_height = min(height[i], height[stack[top]]) - height[topIndex];
  water += distance * bounded_height;
}

medium

A. Using 'min' function without including its definition or header

B. Incorrect calculation of 'distance' by missing parentheses

C. Wrong decrement of 'top' causing stack underflow

D. Using 'water' variable without initialization

Solution

1. Step 1: Check function usage

   The code uses 'min' function but C standard library does not have 'min' by default; it needs a macro or function definition.

2. Step 2: Verify other parts

   Distance calculation and top decrement are correct; water variable usage depends on context but usually initialized.

3. Final Answer:

   Using 'min' function without including its definition or header -> Option A

4. Quick Check:

   min() undefined in C without custom code [OK]

Hint: Remember C needs custom min function or macro [OK]

Common Mistakes:

• Assuming min() is built-in in C
• Miscalculating distance with wrong parentheses
• Forgetting to initialize water variable

5. Given the heights array {4, 2, 0, 3, 2, 5}, what is the total trapped rain water calculated using the stack method?

hard

A. 8

B. 7

C. 9

D. 6

Solution

1. Step 1: Analyze the heights for trapped water

   Water trapped at each position i is max(0, min(left_max[i], right_max[i]) - height[i]), where left_max is tallest bar strictly to the left, right_max strictly to the right. Stack method yields same result.

2. Step 2: Calculate trapped water step-by-step

   - i=1: min(4,5)-2 = 2
   - i=2: min(4,5)-0 = 4
   - i=3: min(4,5)-3 = 1
   - i=4: min(4,5)-2 = 2
   Total: 2+4+1+2 = 9 units.

3. Final Answer:

   9 -> Option C

4. Quick Check:

   Total trapped water = 9 [OK]

Hint: Sum water trapped between boundaries carefully [OK]

Common Mistakes:

• Double counting trapped water
• Ignoring zero height bars
• Misidentifying boundaries