计算涂漆房屋的总墙面积

给定整数N、L和W，表示每行房屋的行数和长宽，以及一个数组Heights[] ，代表每栋房屋的高度，任务是找到所需的外墙总面积如果相邻的房屋共用一堵墙，则涂漆。

例子：

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

方法：该问题可以使用贪心技术解决。请按照以下步骤解决问题：

• 涂漆的第一所房子的墙壁总面积等于 2 * w * h ₁ + l * (h ₁ + max(0, h ₂ – h ₁ ))。
• 最后一栋房子的墙壁总面积等于 2 * w * h _n + l * (h _n + max(0, h _n – h _n-1 ))。
• 除第一个和最后一个房屋外，房屋墙壁的总面积等于 2 * w * h _i + l * (max(0, h _i – h _{i + 1} ) + max(0, h _i – h _i-1 ))。
• 因此，所有涂漆房屋的总面积将使用以下公式计算：

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

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
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.

输出：

52

时间复杂度： O(N)
辅助空间： O(N)