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);
        }
 }

Python

# 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.

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] + "&nbsp;&nbsp;");
          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>

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
?>

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.

Recursive Approach: We can obtain the sum triangle using recursion by following the steps given below,

• Base case: If n is 0, just return.
• Create a new array b and store the elements of the given array in it.
• Update the new array b, an element b[i] can be calculated as the sum of b[i] and b[i+1].
• Call the function recursively for the new array b.
• Finally, print the elements of the given array.

Below is the implementation of above approach : 

C++

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

// recursive funtion to prints
// sum triangle for arr[0..n-1]
void printTriangle(int arr[], int n)
{
    // Base case: if n is 0, just return
    if (n == 0)
        return;
    
      // Initialize a new array to store 
      // the given array
    int b[n];
    for (int i = 0; i < n; i++)
        b[i] = arr[i];
    
    // modify the array
    for (int i = 0; i < n-1; i++) {
        b[i] = b[i] + b[i+1];
    }
    
    // recursively calling the function
      // for new elements of the array
    printTriangle(b,n-1);
    
      // print the given array
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
    cout << "\n";
}

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

// This code is contributed by abhishekmaran_.

Java

import java.util.Arrays;

public class Main {

    // recursive function to print
    // sum triangle for arr[0..n-1]
    static void printTriangle(int arr[], int n) {
        // Base case: if n is 0, just return
        if (n == 0)
            return;

        // Initialize a new array to store
        // the given array
        int[] b = Arrays.copyOf(arr, n);

        // modify the array
        for (int i = 0; i < n - 1; i++) {
            b[i] = b[i] + b[i + 1];
        }

        // recursively calling the function
        // for new elements of the array
        printTriangle(b, n - 1);

        // print the given array
        for (int i = 0; i < n; i++) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }

    // Driver Program
    public static void main(String[] args) {
        int[] arr = {4, 7, 3, 6, 7};
        int n = arr.length;
        printTriangle(arr, n);
    }
}

JavaScript

// Function to print sum triangle for a given array
function printTriangle(arr, n) {
    // Base case: if n is 0, just return
    if (n === 0)
        return;

    // Initialize a new array to store the given array
    let b = arr.slice(0, n);

    // Modify the array to calculate the sum triangle
    for (let i = 0; i < n - 1; i++) {
        b[i] = b[i] + b[i + 1];
    }

    // Recursively call the function for new elements of the array
    printTriangle(b, n - 1);

    // Print the given array
    console.log(arr.slice(0, n).join(" "));
}

// Driver Program
function main() {
    let arr = [4, 7, 3, 6, 7];
    let n = arr.length;
    printTriangle(arr, n);
}

// Call the main function
main();

Python3

# Recursive function to print sum triangle for arr[0..n-1]
def print_triangle(arr, n):
    # Base case: if n is 0, just return
    if n == 0:
        return
    
    # Initialize a new list to store the given array
    b = arr[:]
    
    # Modify the array
    for i in range(n-1):
        b[i] = b[i] + b[i+1]
    
    # Recursively call the function for new elements of the array
    print_triangle(b, n-1)
    
    # Print the given array
    for i in range(n):
        print(arr[i], end=" ")
    print()

# Driver Program
if __name__ == "__main__":
    arr = [4, 7, 3, 6, 7]
    n = len(arr)
    print_triangle(arr, n)

Output

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

Time Complexity: O(n²)

Auxiliary Space: O(n²), there are n recursive calls and for each call we are creating a new array of size n.

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