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).
- Programs to print Triangle and Diamond patterns using recursion
- Triangle of numbers arising from Gilbreath's conjecture
- Print Triangle separated pattern
- Find the Nth row in Pascal's Triangle
- Find maximum subset sum formed by partitioning any subset of array into 2 partitions with equal sum
- Maximize sum of remaining elements after every removal of the array half with greater sum
- Sum of series formed by difference between product and sum of N natural numbers
- Given an array A[] and a number x, check for pair in A[] with sum as x
- Equal sum array partition excluding a given element
- Tail recursion to calculate sum of array elements.
- Split the array into equal sum parts according to given conditions
- Maximum sum in an array such that every element has exactly one adjacent element to it
- Maximise array sum after taking non-overlapping sub-arrays of length K
- Flip minimum signs of array elements to get minimum sum of positive elements possible
- Divide the array in K segments such that the sum of minimums is maximized
- Sum of even elements of an Array using Recursion
- Maximum sum of elements divisible by K from the given array
- Sum and Maximum of elements in array from [L, R] before and after updates
- Maximize sum of K elements in Array by taking only corner elements
- Number of times an array can be partitioned repetitively into two subarrays with equal sum
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 |
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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); } } |
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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 |
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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 |
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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. ?> |
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Output :
[48] [20, 28] [8, 12, 16] [3, 5, 7, 9] [1, 2, 3, 4, 5]
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