Manhattan stonewall problem on the concept of Stacks

StoneWall: Cover "Manhattan skyline" using the minimum number of rectangles.

You are going to build a stone wall. The wall should be straight and N meters long, and its thickness should be constant; however, it should have different heights in different places. The height of the wall is specified by an array H of N positive integers. H[I] is the height of the wall from I to I+1 meters to the right of its left end. In particular, H[0] is the height of the wall's left end and H[N−1] is the height of the wall's right end.

The wall should be built of cuboid stone blocks (that is, all sides of such blocks are rectangular). Your task is to compute the minimum number of blocks needed to build the wall.

Write a function:

    def solution(H)

that, given an array H of N positive integers specifying the height of the wall, returns the minimum number of blocks needed to build it.


For example, given array H containing N = 9 integers:
  H[0] = 8    H[1] = 8    H[2] = 5
  H[3] = 7    H[4] = 9    H[5] = 8
  H[6] = 7    H[7] = 4    H[8] = 8

the function should return 7. The figure shows one possible arrangement of seven blocks.



Write an efficient algorithm for the following assumptions:

        N is an integer within the range [1..100,000];
        each element of array H is an integer within the range [1..1,000,000,000].

Taking help from ChatGPT...

Our prompt looks like:

You are a programming guide.

You are going to build a stone wall... 

... the function should return 7.

Please guide how to solve this problem step by step.

Algo

To solve this problem, we can use a stack-based approach. The idea is to traverse through the array of heights and maintain a stack that keeps track of the heights encountered so far. We will also keep track of the number of blocks used.

Here's how we can solve it step by step:

1. Initialize an empty stack and a variable to count the number of blocks used.

2. Iterate through the array of heights.

3. For each height, check whether it is greater than the top of the stack. If it is, push the height onto the stack.

4. If the height is less than the top of the stack, pop heights from the stack until the top of the stack is less than or equal to the current height.

5. For each height popped from the stack, increment the block count by 1, as each height represents a block.

6. If after popping from the stack, the stack is empty or the current height is greater than the top of the stack, push the current height onto the stack.

7. After iterating through all heights, return the block count.

Let's implement this in code:

Code


def solution(H):
    stack = []  # Stack to keep track of heights
    blocks_used = 0  # Counter for blocks used
    
    for height in H:
        # Pop heights from stack until top is less than or equal to current height
        while stack and stack[-1] > height:
            stack.pop()
            blocks_used += 1
        
        # If stack is empty or current height is greater than top of stack, push height
        if not stack or height > stack[-1]:
            stack.append(height)
    
    # Add remaining heights in stack to block count
    blocks_used += len(stack)
    
    return blocks_used

# Example usage
H = [8, 8, 5, 7, 9, 8, 7, 4, 8]
print(solution(H))  # Output should be 7


This algorithm has a time complexity of O(N), where N is the number of elements in the array H, as it iterates through the array once.

Tags: Algorithms,Technology,