Calculate total wall area of houses painted

Given integers N, L and W representing number of rows and length and width of houses in each row, and an array Heights[], representing the height of each house, the task is to find the total area of the outer walls required to be painted if the adjacent houses share a common wall.

Examples:

Input: N = 4, W = 1, L = 1, Heights[] = {1, 2, 3, 4}
Output: 28
Explanation:
The area of house-1 painted = 2 * 1 + 1 * 1 = 3 
The area of house-2 painted = 2 * 2 + 1 * 1 = 5 
The area of house-3 painted = 2 * 3 + 1 * 1 = 7 
The area of house-4 painted = 2 * 4 + 1 * 1 + 1 * 4 = 13 
Therefore, the total area painted = 28 

Input: N = 7, W = 1, L = 1, Heights[] = {4, 3, 1, 2, 3, 4, 2}
Output: 52

Approach: The problem can be solved using Greedy technique. Follow the steps below to solve the problem:

• The total area of the wall of the first house painted is equal to 2 * w * h₁ + l * (h₁ + max(0, h₂ – h₁)).
• The total area of the wall of the last house painted is equal to 2 * w * h_n + l * (h_n + max(0, h_n – h_n-1)).
• The total area of the wall of the house painted other than the first and the last houses is equal to 2 * w * h_i + l * (max(0, h_i – h_{i + 1}) + max(0, h_i – h_i-1)).
• Therefore, the total area of all the houses painted will be calculated using the following formula: 
  

Total area printed = 2 * w(h₁ + …+h_n) + l(h₁ + h_n) + l * Σabs(h_i – h_i-1). 

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the total area
// of walls painted in N row-houses
void areaToPaint(int N, int W, int L,
                 int Heights[])
{

    // Stores total area of N row-houses
    // that needs to be painted
    int total = 0;

    // Traverse the array of wall heights
    for (int i = 0; i < N; i++) {

        // Update total area painted
        total += 2 * Heights[i] * W;
    }

    // Update total
    total += L * (Heights[0]
                  + Heights[N - 1]);

    // Traverse all the houses and
    // print the shared walls
    for (int i = 1; i < N; i++) {

        // Update total
        total += L * abs(Heights[i]
                         - Heights[i - 1]);
    }

    // Print total area needs to paint
    cout << total;
}

// Driver Code
int main()
{

    // Given N, W & L
    int N = 7, W = 1, L = 1;

    // Given heights of houses
    int Heights[N]
        = { 4, 3, 1, 2, 3, 4, 2 };

    // Function Call
    areaToPaint(N, W, L, Heights);
}

Java

// Java code of above approach
import java.util.*;
class GFG {

  // Function to find the total area
  // of walls painted in N row-houses
  static void areaToPaint(int N, int W, int L,
                          int Heights[])
  {

    // Stores total area of N row-houses
    // that needs to be painted
    int total = 0;

    // Traverse the array of wall heights
    for (int i = 0; i < N; i++) {

      // Update total area painted
      total += 2 * Heights[i] * W;
    }

    // Update total
    total += L * (Heights[0]
                  + Heights[N - 1]);

    // Traverse all the houses and
    // print the shared walls
    for (int i = 1; i < N; i++) {

      // Update total
      total += L * Math.abs(Heights[i]
                            - Heights[i - 1]);
    }

    // Print total area needs to paint
    System.out.print(total);
  }

  // Driver code
  public static void main(String[] args)
  {
    // Given N, W & L
    int N = 7, W = 1, L = 1;

    // Given heights of houses
    int Heights[]
      = { 4, 3, 1, 2, 3, 4, 2 };

    // Function Call
    areaToPaint(N, W, L, Heights);
  }
}

// This code is contributed by offbeat

Python3

# Python 3 program for the above approach

# Function to find the total area
# of walls painted in N row-houses
def areaToPaint(N, W, L, Heights):

    # Stores total area of N row-houses
    # that needs to be painted
    total = 0

    # Traverse the array of wall heights
    for i in range(N):

        # Update total area painted
        total += 2 * Heights[i] * W

    # Update total
    total += L * (Heights[0]
                  + Heights[N - 1])

    # Traverse all the houses and
    # print the shared walls
    for i in range(1, N):

        # Update total
        total += L * abs(Heights[i]
                         - Heights[i - 1])

    # Print total area needs to paint
    print(total)


# Driver Code
if __name__ == "__main__":

    # Given N, W & L
    N = 7
    W = 1
    L = 1

    # Given heights of houses
    Heights = [4, 3, 1, 2, 3, 4, 2]

    # Function Call
    areaToPaint(N, W, L, Heights)

    # This code is contributed by chitranayal.

C#

// C# program for the above approach
using System;

class GFG{

// Function to find the total area
// of walls painted in N row-houses
static void areaToPaint(int N, int W, int L, int[] Heights)
{
    // Stores total area of N row-houses
    // that needs to be painted
    int total = 0;

    // Traverse the array of wall heights
    for (int i = 0; i < N; i++) {

        // Update total area painted
        total += 2 * Heights[i] * W;
    }

    // Update total
    total += L * (Heights[0] + Heights[N - 1]);

    // Traverse all the houses and
    // print the shared walls
    for (int i = 1; i < N; i++) {

        // Update total
        total += L * Math.Abs(Heights[i] - Heights[i - 1]);
    }

    // Print total area needs to paint
    Console.Write(total);
}

// Driver Code
public static void Main(String[] args)
{

    // Given N, W & L
    int N = 7, W = 1, L = 1;

    // Given heights of houses
    int[] Heights = { 4, 3, 1, 2, 3, 4, 2 };

    // Function Call
    areaToPaint(N, W, L, Heights);
}
}

// This code is contributed by aditya942003patil

Javascript

<script>

// JavaScript code of above approach

// Function to find the total area
  // of walls painted in N row-houses
function areaToPaint(N,W,L,Heights)
{
    // Stores total area of N row-houses
    // that needs to be painted
    let total = 0;

    // Traverse the array of wall heights
    for (let i = 0; i < N; i++) {

      // Update total area painted
      total += 2 * Heights[i] * W;
    }

    // Update total
    total += L * (Heights[0]
                  + Heights[N - 1]);

    // Traverse all the houses and
    // print the shared walls
    for (let i = 1; i < N; i++) {

      // Update total
      total += L * Math.abs(Heights[i]
                            - Heights[i - 1]);
    }

    // Print total area needs to paint
    document.write(total);
}

// Driver code
// Given N, W & L
let N = 7, W = 1, L = 1;

// Given heights of houses
let Heights
= [ 4, 3, 1, 2, 3, 4, 2 ];

// Function Call
areaToPaint(N, W, L, Heights);


// This code is contributed by avanitrachhadiya2155

</script>

Output:

52

Time Complexity: O(N)
Auxiliary Space: O(1)