Generate all possible sorted arrays from alternate elements of two given sorted arrays
Given two sorted arrays A and B, generate all possible arrays such that first element is taken from A then from B then from A and so on in increasing order till the arrays exhausted. The generated arrays should end with an element from B.
For Example
A = {10, 15, 25}
B = {1, 5, 20, 30}
The resulting arrays are:
10 20
10 20 25 30
10 30
15 20
15 20 25 30
15 30
25 30
We strongly recommend you to minimize your browser and try this yourself first.
The idea is to use recursion. In the recursive function, a flag is passed to indicate whether current element in output should be taken from ‘A’ or ‘B’. Below is C++ implementation.
C++
#include<bits/stdc++.h> using namespace std; void printArr(int arr[], int n); /* Function to generates and prints all sorted arrays from alternate elements of 'A[i..m-1]' and 'B[j..n-1]' If 'flag' is true, then current element is to be included from A otherwise from B. 'len' is the index in output array C[]. We print output array each time before including a character from A only if length of output array is greater than 0. We try than all possible combinations */void generateUtil(int A[], int B[], int C[], int i, int j, int m, int n, int len, bool flag) { if (flag) // Include valid element from A { // Print output if there is at least one 'B' in output array 'C' if (len) printArr(C, len+1); // Recur for all elements of A after current index for (int k = i; k < m; k++) { if (!len) { /* this block works for the very first call to include the first element in the output array */ C[len] = A[k]; // don't increment lem as B is included yet generateUtil(A, B, C, k+1, j, m, n, len, !flag); } else /* include valid element from A and recur */ { if (A[k] > C[len]) { C[len+1] = A[k]; generateUtil(A, B, C, k+1, j, m, n, len+1, !flag); } } } } else /* Include valid element from B and recur */ { for (int l = j; l < n; l++) { if (B[l] > C[len]) { C[len+1] = B[l]; generateUtil(A, B, C, i, l+1, m, n, len+1, !flag); } } } } /* Wrapper function */void generate(int A[], int B[], int m, int n) { int C[m+n]; /* output array */ generateUtil(A, B, C, 0, 0, m, n, 0, true); } // A utility function to print an array void printArr(int arr[], int n) { for (int i = 0; i < n; i++) cout << arr[i] << " "; cout << endl; } // Driver program int main() { int A[] = {10, 15, 25}; int B[] = {5, 20, 30}; int n = sizeof(A)/sizeof(A[0]); int m = sizeof(B)/sizeof(B[0]); generate(A, B, n, m); return 0; } |
Java
class GenerateArrays { /* Function to generates and prints all sorted arrays from alternate elements of 'A[i..m-1]' and 'B[j..n-1]' If 'flag' is true, then current element is to be included from A otherwise from B. 'len' is the index in output array C[]. We print output array each time before including a character from A only if length of output array is greater than 0. We try than all possible combinations */ void generateUtil(int A[], int B[], int C[], int i, int j, int m, int n, int len, boolean flag) { if (flag) // Include valid element from A { // Print output if there is at least one 'B' in output array 'C' if (len != 0) printArr(C, len + 1); // Recur for all elements of A after current index for (int k = i; k < m; k++) { if (len == 0) { /* this block works for the very first call to include the first element in the output array */ C[len] = A[k]; // don't increment lem as B is included yet generateUtil(A, B, C, k + 1, j, m, n, len, !flag); } /* include valid element from A and recur */ else if (A[k] > C[len]) { C[len + 1] = A[k]; generateUtil(A, B, C, k + 1, j, m, n, len + 1, !flag); } } } /* Include valid element from B and recur */ else { for (int l = j; l < n; l++) { if (B[l] > C[len]) { C[len + 1] = B[l]; generateUtil(A, B, C, i, l + 1, m, n, len + 1, !flag); } } } } /* Wrapper function */ void generate(int A[], int B[], int m, int n) { int C[] = new int[m + n]; /* output array */ generateUtil(A, B, C, 0, 0, m, n, 0, true); } // A utility function to print an array void printArr(int arr[], int n) { for (int i = 0; i < n; i++) System.out.print(arr[i] + " "); System.out.println(""); } public static void main(String[] args) { GenerateArrays generate = new GenerateArrays(); int A[] = {10, 15, 25}; int B[] = {5, 20, 30}; int n = A.length; int m = B.length; generate.generate(A, B, n, m); } } // This code has been contributed by Mayank Jaiswal |
Python3
# A utility function to print an array def printArr(arr,n): for i in range(n): print(arr[i] , " ",end="") print() ''' Function to generates and prints all sorted arrays from alternate elements of 'A[i..m-1]' and 'B[j..n-1]' If 'flag' is true, then current element is to be included from A otherwise from B. 'len' is the index in output array C[]. We print output array each time before including a character from A only if length of output array is greater than 0. We try than all possible combinations '''def generateUtil(A,B,C,i,j,m,n,len,flag): if (flag): # Include valid element from A # Print output if there is at # least one 'B' in output array 'C' if (len): printArr(C, len+1) # Recur for all elements of # A after current index for k in range(i,m): if ( not len): ''' this block works for the very first call to include the first element in the output array ''' C[len] = A[k] # don't increment lem # as B is included yet generateUtil(A, B, C, k+1, j, m, n, len, not flag) else: # include valid element from A and recur if (A[k] > C[len]): C[len+1] = A[k] generateUtil(A, B, C, k+1, j, m, n, len+1, not flag) else: # Include valid element from B and recur for l in range(j,n): if (B[l] > C[len]): C[len+1] = B[l] generateUtil(A, B, C, i, l+1, m, n, len+1, not flag) # Wrapper function def generate(A,B,m,n): C=[] #output array for i in range(m+n+1): C.append(0) generateUtil(A, B, C, 0, 0, m, n, 0, True) # Driver program A = [10, 15, 25] B = [5, 20, 30] n = len(A) m = len(B) generate(A, B, n, m) # This code is contributed # by Anant Agarwal. |
C#
// C# Program to generate all possible // sorted arrays from alternate elements // of two given sorted arrays using System; class GenerateArrays { /* Function to generates and prints all sorted arrays from alternate elements of 'A[i..m-1]' and 'B[j..n-1]' If 'flag' is true, then current element is to be included from A otherwise from B. 'len' is the index in output array C[]. We print output array each time before including a character from A only if length of output array is greater than 0. We try than all possible combinations */ public virtual void generateUtil(int[] A, int[] B, int[] C, int i, int j, int m, int n, int len, bool flag) { // Include valid // element from A if (flag) { // Print output if there is // at least one 'B' in // output array 'C' if (len != 0) { printArr(C, len + 1); } // Recur for all elements // of A after current index for (int k = i; k < m; k++) { if (len == 0) { /* this block works for the very first call to include the first element in the output array */ C[len] = A[k]; // don't increment lem // as B is included yet generateUtil(A, B, C, k + 1, j, m, n, len, !flag); } // include valid element // from A and recur else if (A[k] > C[len]) { C[len + 1] = A[k]; generateUtil(A, B, C, k + 1, j, m, n, len + 1, !flag); } } } // Include valid element // from B and recur else { for (int l = j; l < n; l++) { if (B[l] > C[len]) { C[len + 1] = B[l]; generateUtil(A, B, C, i, l + 1, m, n, len + 1, !flag); } } } } // Wrapper function public virtual void generate(int[] A, int[] B, int m, int n) { int[] C = new int[m + n]; // output array generateUtil(A, B, C, 0, 0, m, n, 0, true); } // A utility function to print an array public virtual void printArr(int[] arr, int n) { for (int i = 0; i < n; i++) { Console.Write(arr[i] + " "); } Console.WriteLine(""); } // Driver Code public static void Main(string[] args) { GenerateArrays generate = new GenerateArrays(); int[] A = new int[] {10, 15, 25}; int[] B = new int[] {5, 20, 30}; int n = A.Length; int m = B.Length; generate.generate(A, B, n, m); } } // This code is contributed by Shrikant13 |
PHP
<?php /* Function to generates and prints all sorted arrays from alternate elements of 'A[i..m-1]' and 'B[j..n-1]' If 'flag' is true, then current element is to be included from A otherwise from B. 'len' is the index in output array C[]. We print output array each time before including a character from A only if length of output array is greater than 0. We try than all possible combinations */function generateUtil(&$A, &$B, &$C, $i, $j, $m, $n, $len, $flag) { if ($flag) // Include valid element from A { // Print output if there is at least // one 'B' in output array 'C' if ($len) printArr($C, $len + 1); // Recur for all elements of A // after current index for ($k = $i; $k < $m; $k++) { if (!$len) { /* this block works for the very first call to include the first element in the output array */ $C[$len] = $A[$k]; // don't increment lem as B // is included yet generateUtil($A, $B, $C, $k + 1, $j, $m, $n, $len, !$flag); } else /* include valid element from A and recur */ { if ($A[$k] > $C[$len]) { $C[$len + 1] = $A[$k]; generateUtil($A, $B, $C, $k + 1, $j, $m, $n, $len + 1, !$flag); } } } } else /* Include valid element from B and recur */ { for ($l = $j; $l < $n; $l++) { if ($B[$l] > $C[$len]) { $C[$len + 1] = $B[$l]; generateUtil($A, $B, $C, $i, $l + 1, $m, $n, $len + 1, !$flag); } } } } /* Wrapper function */function generate(&$A, &$B, $m, $n) { $C = array_fill(0, ($m + $n), NULL); /* output array */ generateUtil($A, $B, $C, 0, 0, $m, $n, 0, true); } // A utility function to print an array function printArr(&$arr, $n) { for ($i = 0; $i < $n; $i++) echo $arr[$i] . " "; echo "\n"; } // Driver Code $A = array(10, 15, 25); $B = array(5, 20, 30); $n = sizeof($A); $m = sizeof($B); generate($A, $B, $n, $m); // This code is contributed by ChitraNayal ?> |
Output:
10 20 10 20 25 30 10 30 15 20 15 20 25 30 15 30 25 30
This article is contributed by Gaurav Ahirwar. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above\
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