Sum triangle from array - GeeksforGeeks

10 Jun, 2021
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 :  
Recursion is the key. At each iteration create a new array which contains the Sum of consecutive elements in the array passes as parameter.Make a recursive call and pass the newly created array in the previous step.While back tracking print the array (for printing in reverse order).
Recursion is the key. At each iteration create a new array which contains the Sum of consecutive elements in the array passes as parameter.
Make a recursive call and pass the newly created array in the previous step.
While back tracking print the array (for printing in reverse order).
Below is the implementation of the above approach :
C++
Java
Python3
C#
PHP
Javascript
// C++ program to create Special triangle.#include<bits/stdc++.h>using namespace std;   // Function to generate Special Trianglevoid 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 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 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 functionA = [ 1, 2, 3, 4, 5 ]printTriangle(A)   # This code is contributed by Smitha Dinesh Semwal
// C# program to create Special triangle.    using System;                       public class ConstructTriangle{// Function to generate Special Trianglestatic 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 program to create// Special triangle.   // Function to generate// Special Trianglefunction 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.?>
<script> // JavaScript 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.        var temp = new Array(n - 1);        for (var i = 0; i < n - 1; i++)        {            var 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 (var i = 0; i < n ; i++)        {            if(i == n - 1)                document.write( A[i]  + " ");            else            document.write( A[i]  + ", ");        }                            document.write("<br>");    }        // Driver function          var A = [ 1, 2, 3, 4, 5 ];        var n = A.length;        printTriangle(A,n); </script>
Output:
48
20, 28
8, 12, 16
3, 5, 7, 9
1, 2, 3, 4, 5
nitin mittal
29AjayKumar
bunnyram19
Arrays
Recursion
Arrays
Recursion
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