阵列中的三角形总和

给定一个整数数组，从中打印一个总和三角形，以使第一级具有所有数组元素。从那时起，每个级别上的元素数量比上一个级别少一个，并且该级别上的元素是上一个级别中连续两个元素的总和。
例子 ：

Input : A = {1, 2, 3, 4, 5}
Output : [48]
         [20, 28] 
         [8, 12, 16] 
         [3, 5, 7, 9] 
         [1, 2, 3, 4, 5] 

Explanation :
Here,   [48]
        [20, 28] -->(20 + 28 = 48)
        [8, 12, 16] -->(8 + 12 = 20, 12 + 16 = 28)
        [3, 5, 7, 9] -->(3 + 5 = 8, 5 + 7 = 12, 7 + 9 = 16)
        [1, 2, 3, 4, 5] -->(1 + 2 = 3, 2 + 3 = 5, 3 + 4 = 7, 4 + 5 = 9)

方法 ：

1. 递归是关键。在每次迭代时，创建一个新数组，其中包含该数组遍历中连续元素的总和作为参数。
2. 进行递归调用，并在上一步中传递新创建的数组。
3. 反向跟踪时，打印阵列(以相反顺序打印)。

   下面是上述方法的实现：

   C++

   // C++ program to create Special triangle.
   #include
   using namespace std;
     
   // Function to generate Special Triangle
   void printTriangle(int A[] , int n)
       {
           // Base case
           if (n < 1)
               return;
     
           // Creating new array which contains the
           // Sum of consecutive elements in
           // the array passes as parameter.
           int temp[n - 1];
           for (int i = 0; i < n - 1; i++)
           {
               int x = A[i] + A[i + 1];
               temp[i] = x;
           }
     
           // Make a recursive call and pass
           // the newly created array
           printTriangle(temp, n - 1);
     
           // Print current array in the end so
           // that smaller arrays are printed first
           for (int i = 0; i < n ; i++)
           {
               if(i == n - 1)
                   cout << A[i] << " ";
               else
               cout << A[i] << ", ";
           }
                     
           cout << endl;
       }
     
       // Driver function
       int main()
       {
           int A[] = { 1, 2, 3, 4, 5 };
           int n = sizeof(A) / sizeof(A[0]);
             
           printTriangle(A, n);
       }
         
   // This code is contributed by Smitha Dinesh Semwal

   Java

   // Java program to create Special triangle.
   import java.util.*;
   import java.lang.*;
     
   public class ConstructTriangle
   {
       // Function to generate Special Triangle.
       public static void printTriangle(int[] A)
       {
           // Base case
           if (A.length < 1)
               return;
     
           // Creating new array which contains the
           // Sum of consecutive elements in
           // the array passes as parameter.
           int[] temp = new int[A.length - 1];
           for (int i = 0; i < A.length - 1; i++)
           {
               int x = A[i] + A[i + 1];
               temp[i] = x;
           }
     
           // Make a recursive call and pass
           // the newly created array
           printTriangle(temp);
     
           // Print current array in the end so
           // that smaller arrays are printed first
           System.out.println(Arrays.toString(A));
       }
     
       // Driver function
       public static void main(String[] args)
       {
           int[] A = { 1, 2, 3, 4, 5 };
           printTriangle(A);
       }
   }

   Python3

   # Python3 program to create Special triangle.
   # Function to generate Special Triangle.
   def printTriangle(A):
             
           # Base case
           if (len(A) < 1):
               return
     
           # Creating new array which contains the
           # Sum of consecutive elements in
           # the array passes as parameter.
           temp = [0] * (len(A) - 1)
           for i in range( 0, len(A) - 1):
             
               x = A[i] + A[i + 1]
               temp[i] = x
             
     
           # Make a recursive call and pass
           # the newly created array
           printTriangle(temp)
             
           # Print current array in the end so
           # that smaller arrays are printed first
           print(A)
         
     
   # Driver function
   A = [ 1, 2, 3, 4, 5 ]
   printTriangle(A)
     
   # This code is contributed by Smitha Dinesh Semwal

   C#

   // C# program to create Special triangle.
      
   using System;
                         
   public class ConstructTriangle
   {
   // Function to generate Special Triangle
   static void printTriangle(int []A, int n)
       {
           // Base case
           if (n < 1)
               return;
      
           // Creating new array which contains the
           // Sum of consecutive elements in
           // the array passes as parameter.
           int []temp = new int[n - 1];
           for (int i = 0; i < n - 1; i++)
           {
               int x = A[i] + A[i + 1];
               temp[i] = x;
           }
      
           // Make a recursive call and pass
           // the newly created array
           printTriangle(temp, n - 1);
      
           // Print current array in the end so
           // that smaller arrays are printed first
           for (int i = 0; i < n ; i++)
           {
               if(i == n - 1)
                   Console.Write(A[i] + " ");
               else
               Console.Write(A[i] + ", ");
           }
                      
           Console.WriteLine();
       }
      
       // Driver function
       public static void Main()
       {
           int[] A = { 1, 2, 3, 4, 5 };
           int n = A.Length;
           printTriangle(A,n);
       }
   }
     
   //This code contributed by 29AjayKumar

   输出 ：

   [48]
   [20, 28]
   [8, 12, 16]
   [3, 5, 7, 9]
   [1, 2, 3, 4, 5]