Program to print Sum Triangle for a given array

Given a array, write a program to construct a triangle where last row contains elements of given array, every element of second last row contains sum of below two elements and so on.

Example:

Input: arr[] = {4, 7, 3, 6, 7};
Output:
81
40 41
21 19 22
11 10 9 13
4 7 3 6 7 

Input: {10, 40, 50}
Output:
140
50 90
10 40 50

An important observation about output is final value is at the top and top element needs to printed first. Therefore, we use a 2D auxiliary array to construct the triangle in bottom up manner and then print the triangle. An element tri[i][j] of 2D array can be calculated as sum of tri[i+1][j] and tri[i+1][j+1].

Below is the implementation of above idea : 

C++

// C++ program to print sum triangle for a given array
#include <bits/stdc++.h>
using namespace std;

// prints sum triangle for arr[0..n-1]
void printTriangle(int arr[], int n)
{
    // Initialize a 2D array to store triangle
    int tri[n][n];
    memset(tri, 0, sizeof(tri));

    // Initialize last row of triangle
    for (int i = 0; i < n ; i++)
        tri[n-1][i] = arr[i];

    // Fill other rows
    for (int i = n-2; i >=0; i--)
      for (int j = 0; j <= i; j++)
        tri[i][j] = tri[i+1][j] + tri[i+1][j+1];

    // Print the triangle
    for (int i = 0; i < n; i++)
    {
        for(int j = 0; j <= i ; j++)
            cout << tri[i][j]<<" ";
        cout << endl;
    }
}

// Driver Program
int main()
{
    int arr[] = {4, 7, 3, 6, 7};
    int n = sizeof(arr)/sizeof(arr[0]);
    printTriangle(arr, n);
    return 0;
}

Java

// Java program to print sum triangle for a given array
class Test{

     static int arr[] = new int[]{4, 7, 3, 6, 7};

     // prints sum triangle for arr[0..n-1]
     public static void printTriangle(int n)
     {
        // Initialize a 2D array to store triangle
        int tri[][] = new int[n][n];

        // Initialize last row of triangle
        for (int i = 0; i < n ; i++)
            tri[n-1][i] = arr[i];

        // Fill other rows
        for (int i = n-2; i >=0; i--)
            for (int j = 0; j <= i; j++)
               tri[i][j] = tri[i+1][j] + tri[i+1][j+1];

        // Print the triangle
        for (int i = 0; i < n; i++)
        {
            for(int j = 0; j <= i ; j++)
                System.out.print(tri[i][j] + " ");
            System.out.println();
        }
     }

     public static void main(String[] args)
     {
         printTriangle(arr.length);
        }
 }

Python3

# Python 3 program to print sum triangle
# for a given array

# prints sum triangle for arr[0..n-1]
def printTriangle(arr, n):

    # Initialize a 2D array to store triangle
    tri = [[0 for i in range(n)]
              for i in range(n)]

    # Initialize last row of triangle
    for i in range(n):
        tri[n - 1][i] = arr[i]

    # Fill other rows
    i = n - 2
    while(i >= 0):
        for j in range(0, i + 1, 1):
            tri[i][j] = (tri[i + 1][j] +
                         tri[i + 1][j + 1])

        i -= 1

    # Print the triangle
    for i in range(0, n, 1):
        for j in range(0, i + 1, 1):
            print(tri[i][j], end = " ")
        print("\n", end = "")

# Driver Code
if __name__ == '__main__':
    arr = [4, 7, 3, 6, 7]
    n = len(arr)
    printTriangle(arr, n)

# This code is contributed by
# Shashank_Sharma

C#

// C# program to print sum triangle
// for a given array
using System;

class GFG {

    static int []arr = new int[]{4, 7, 3, 6, 7};

    // prints sum triangle for arr[0..n-1]
    public static void printTriangle(int n)
    {
        // Initialize a 2D array to store triangle
        int [,]tri = new int[n, n];

        // Initialize last row of triangle
        for (int i = 0; i < n ; i++)
            tri[n - 1, i] = arr[i];

        // Fill other rows
        for (int i = n - 2; i >= 0; i--)
            for (int j = 0; j <= i; j++)
            tri[i, j] = tri[i + 1, j] +
                        tri[i + 1, j + 1];

        // Print the triangle
        for (int i = 0; i < n; i++)
        {
            for(int j = 0; j <= i ; j++)
                Console.Write(tri[i, j] + " ");
                Console.WriteLine();
        }
    }

    // Driver Code
    public static void Main()
    {
        printTriangle(arr.Length);
    }
}

// This code is contributed by Sam007.

PHP

<?php
// PHP program to print sum
// triangle for a given array

// prints sum triangle for arr[0..n-1]
function printTriangle($arr, $n)
{
    // Initialize a 2D array to store triangle
    $tri[$n][$n] = array(array());
    array_fill(0, count($tri), 0);

    // Initialize last row of triangle
    for ($i = 0; $i < $n ; $i++)
        $tri[$n - 1][$i] = $arr[$i];

    // Fill other rows
    for ($i = $n - 2; $i >= 0; $i--)
    for ($j = 0; $j <= $i; $j++)
        $tri[$i][$j] = $tri[$i + 1][$j] +
                       $tri[$i + 1][$j + 1];

    // Print the triangle
    for ($i = 0; $i < $n; $i++)
    {
        for( $j = 0; $j <= $i ; $j++)
            echo $tri[$i][$j] . " ";
        echo "\n";
    }
}

// Driver Code
$arr = array(4, 7, 3, 6, 7);
$n = count($arr);
printTriangle($arr, $n);

// This code is contributed by Rajput-Ji
?>

Javascript

<script>
      // JavaScript program to print sum triangle for a given array

      // prints sum triangle for arr[0..n-1]
      function printTriangle(arr, n)
      {

        // Initialize a 2D array to store triangle
        var tri = new Array(n).fill(0).map((item) => new Array(n).fill(0));

        // Initialize last row of triangle
        for (var i = 0; i < n; i++) tri[n - 1][i] = arr[i];

        // Fill other rows
        for (var i = n - 2; i >= 0; i--)
          for (var j = 0; j <= i; j++)
            tri[i][j] = tri[i + 1][j] + tri[i + 1][j + 1];

        // Print the triangle
        for (var i = 0; i < n; i++) {
          for (var j = 0; j <= i; j++)
            document.write(tri[i][j] + "  ");
          document.write("<br>");
        }
      }

      // Driver Program
      var arr = [4, 7, 3, 6, 7];
      var n = arr.length;
      printTriangle(arr, n);

      // This code is contributed by rdtank.
    </script>

Output:

81
40 41
21 19 22
11 10 9 13
4 7 3 6 7

Time Complexity: O(n²)

Auxiliary Space: O(n²) because using array “tr”

Thanks to nish for suggesting this solution.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above