Why Trapping Rain Water Using Stack in DSA C?

The Big Idea

Discover how a simple stack can solve a tricky rainwater puzzle faster than guessing!

The Scenario

Imagine you have a row of buildings with different heights, and after it rains, you want to find out how much water gets trapped between them. Doing this by looking at each building and guessing the water trapped is like trying to count raindrops one by one on a big roof -- slow and confusing.

The Problem

Manually checking each building and comparing it with every other building to find trapped water takes a lot of time and can easily lead to mistakes. It's like trying to solve a puzzle by testing every piece with every other piece -- it quickly becomes overwhelming and error-prone.

The Solution

Using a stack helps us keep track of buildings in a smart way. We can quickly find where water can be trapped by remembering the heights and positions of buildings we have seen. This method is faster and less confusing, like having a helper who points out where water will collect as you walk along the buildings.

Before vs After

✗ Before

int trappedWater(int heights[], int size) {
    int water = 0;
    for (int i = 1; i < size - 1; i++) {
        int maxLeft = 0, maxRight = 0;
        for (int j = i; j >= 0; j--) maxLeft = (maxLeft > heights[j]) ? maxLeft : heights[j];
        for (int j = i; j < size; j++) maxRight = (maxRight > heights[j]) ? maxRight : heights[j];
        water += (maxLeft < maxRight ? maxLeft : maxRight) - heights[i];
    }
    return water;
}

✓ After

int trappedWater(int heights[], int size) {
    int water = 0, top, current = 0;
    int stack[size];
    int stackTop = -1;
    while (current < size) {
        while (stackTop != -1 && heights[current] > heights[stack[stackTop]]) {
            top = stack[stackTop--];
            if (stackTop == -1) break;
            int distance = current - stack[stackTop] - 1;
            int bounded_height = (heights[current] < heights[stack[stackTop]] ? heights[current] : heights[stack[stackTop]]) - heights[top];
            water += distance * bounded_height;
        }
        stack[++stackTop] = current++;
    }
    return water;
}

What It Enables

This method lets us quickly and accurately calculate trapped rainwater in complex building arrangements, saving time and avoiding mistakes.

Real Life Example

City planners use this idea to understand how water collects between buildings after rain, helping them design better drainage systems to prevent flooding.

Key Takeaways

Manual checking is slow and error-prone for trapping rainwater.

Stack helps track building heights efficiently to find trapped water.

This approach speeds up calculations and reduces mistakes.

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