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 : [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).
- Program to print Sum Triangle for a given array
- Possible to form a triangle from array values
- Maximum Perimeter Triangle from array
- Pascal's Triangle
- Triangle of numbers arising from Gilbreath's conjecture
- Programs to print Triangle and Diamond patterns using recursion
- Minimum increment in the sides required to get non-negative area of a triangle
- Find original array from encrypted array (An array of sums of other elements)
- Find an element in array such that sum of left array is equal to sum of right array
- Minimum cost to reach end of array array when a maximum jump of K index is allowed
- Find minimum value to assign all array elements so that array product becomes greater
- Generate original array from an array that store the counts of greater elements on right
- Minimum number greater than the maximum of array which cannot be formed using the numbers in the array
- Maximize the size of array by deleting exactly k sub-arrays to make array prime
- Count number of permutation of an Array having no SubArray of size two or more from original Array
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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