Given an array of integers, print a sum triangle from it such that the first level has all array elements. From then, at each level number of elements is one less than the previous level and elements at the level is be the Sum of consecutive two elements in the previous level.
Example :

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)

Approach :

1. Recursion is the key. At each iteration create a new array which contains the Sum of consecutive elements in the array passes as parameter.
2. Make a recursive call and pass the newly created array in the previous step.
3. While back tracking print the array (for printing in reverse order).

 
Below is implementation of the above approach :


C++








// C++ program to create Special triangle. #include<bits/stdc++.h> 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

PHP








<?php // PHP program to create // Special triangle.    // Function to generate // Special Triangle function printTriangle($A , $n)     {                // Base case         if ($n < 1)             return;            // Creating new array which          // contains the Sum of          // consecutive elements in         // the array passes as parameter.         $temp[$n - 1] = 0;         for ($i = 0; $i < $n - 1; $i++)         {             $x = $A[$i] + $A[$i + 1];             $temp[$i] = $x;         }            // Make a recursive call and          // pass the newly created array         printTriangle($temp, $n - 1);            // Print current array in the         // end so that smaller arrays          // are printed first         for ($i = 0; $i < $n ; $i++)         {             if($i == $n - 1)                 echo $A[$i] , " ";             else             echo $A[$i] , ", ";         }                            echo "\n";     }    // Driver Code $A = array( 1, 2, 3, 4, 5 ); $n = sizeof($A);    printTriangle($A, $n);    // This code is contributed // by nitin mittal.  ?>

Output :

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

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