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Sum triangle from array
  • Difficulty Level : Easy
  • Last Updated : 21 Dec, 2018

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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