# 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:28Explanation:

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 * h
_{1}+ l * (h_{1}+ max(0, h_{2}– h_{1})). - 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(h

_{1}+ …+h_{n}) + l(h_{1}+ 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.` |

## 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(N)