# Sum triangle from array

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

Explanation :
Here,   
[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)
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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).
4.
Below is implementation of the above approach :

## C++

 `// C++ program to create Special triangle. ` `#include ` `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); ` `         `  `        ``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

 ` `

Output :

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

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