Subarray/Substring vs Subsequence and Programs to Generate them
Last Updated : 26 Mar, 2024
Subarray/Substring
A subarray is a contiguous part of the array. An array that is inside another array. For example, consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. The subarrays are (1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4) and (1,2,3,4). In general, for an array/string of size n, there are n*(n+1)/2 non-empty subarrays/substrings.
How to generate all subarrays?
We can run two nested loops, the outer loop picks the starting element and the inner loop considers all elements on the right of the picked elements as the ending elements of the subarray.
C++ /* C++ code to generate all possible subarrays/subArrays Complexity- O(n^3) */ #include<bits/stdc++.h> using namespace std; // Prints all subarrays in arr[0..n-1] void subArray(int arr[], int n) { // Pick starting point for (int i=0; i <n; i++) { // Pick ending point for (int j=i; j<n; j++) { // Print subarray between current starting // and ending points for (int k=i; k<=j; k++) cout << arr[k] << " "; cout << endl; } } } // Driver program int main() { int arr[] = {1, 2, 3, 4}; int n = sizeof(arr)/sizeof(arr[0]); cout << "All Non-empty Subarrays\n"; subArray(arr, n); return 0; } // Java program to generate all possible subarrays/subArrays // Complexity- O(n^3) */ class Test { static int arr[] = new int[]{1, 2, 3, 4}; // Prints all subarrays in arr[0..n-1] static void subArray( int n) { // Pick starting point for (int i=0; i <n; i++) { // Pick ending point for (int j=i; j<n; j++) { // Print subarray between current starting // and ending points for (int k=i; k<=j; k++) System.out.print(arr[k]+" "); System.out.println(); } } } // Driver method to test the above function public static void main(String[] args) { System.out.println("All Non-empty Subarrays"); subArray(arr.length); } } // C# program to generate all // possible subarrays/subArrays // Complexity- O(n^3) using System; class GFG { static int []arr = new int[]{1, 2, 3, 4}; // Prints all subarrays in arr[0..n-1] static void subArray( int n) { // Pick starting point for (int i = 0; i < n; i++) { // Pick ending point for (int j = i; j < n; j++) { // Print subarray between current // starting and ending points for (int k = i; k <= j; k++) Console.Write(arr[k]+" "); Console.WriteLine(""); } } } // Driver Code public static void Main() { Console.WriteLine("All Non-empty Subarrays"); subArray(arr.Length); } } // This code is contributed by Sam007. //Function that returns all subarrays let getSubArr = (arr) => { //Empty array to store subarrays let arr1 = []; for(let i=0;i<arr.length;i++) { //Empty array to store one subarray let subArr = []; for(let j=i;j<arr.length;j++) { //To get elements to the right of selected i th element till j subArr.push(arr.slice(i,j+1)); } //Storing individual subarrays into main array arr1.push(subArr); } //Return the array of subarrays return arr1; } //Example Array let arr = [1,2,3,4]; let arr1 = getSubArr(arr); console.log(arr1); <?php // PHP code to generate all possible // subarrays/subArrays Complexity- O(n^3) // Prints all subarrays // in arr[0..n-1] function subArray($arr, $n) { // Pick starting point for ($i = 0; $i < $n; $i++) { // Pick ending point for ($j = $i; $j < $n; $j++) { // Print subarray between // current starting // and ending points for ($k = $i; $k <= $j; $k++) echo $arr[$k] , " "; echo "\n"; } } } // Driver Code $arr= array(1, 2, 3, 4); $n = sizeof($arr); echo "All Non-empty Subarrays\n"; subArray($arr, $n); // This code is contributed by m_kit ?> # Python3 code to generate all possible # subarrays/subArrays # Complexity- O(n^3) # Prints all subarrays in arr[0..n-1] def subArray(arr, n): # Pick starting point for i in range(0,n): # Pick ending point for j in range(i,n): # Print subarray between # current starting # and ending points for k in range(i,j+1): print (arr[k],end=" ") print ("\n",end="") # Driver program arr = [1, 2, 3, 4] n = len(arr) print ("All Non-empty Subarrays") subArray(arr, n); # This code is contributed by Shreyanshi. OutputAll Non-empty Subarrays 1 1 2 1 2 3 1 2 3 4 2 2 3 2 3 4 3 3 4 4
Time Complexity: 0(n^3)
Auxiliary Space: 0(1)
Subsequence: A subsequence is a sequence that can be derived from another sequence by removing zero or more elements, without changing the order of the remaining elements.
For the same example, there are 15 sub-sequences. They are (1), (2), (3), (4), (1,2), (1,3),(1,4), (2,3), (2,4), (3,4), (1,2,3), (1,2,4), (1,3,4), (2,3,4), (1,2,3,4). More generally, we can say that for a sequence of size n, we can have (2n-1) non-empty sub-sequences in total.
A string example to differentiate: Consider strings "geeksforgeeks" and "gks". "gks" is a subsequence of "geeksforgeeks" but not a substring. "geeks" is both a subsequence and subarray. Every subarray is a subsequence. More specifically, Subsequence is a generalization of substring.
A subarray or substring will always be contiguous, but a subsequence need not be contiguous. That is, subsequences are not required to occupy consecutive positions within the original sequences. But we can say that both contiguous subsequence and subarray are the same.
How to generate all Subsequences?
We can use algorithm to generate power set for generation of all subsequences.
C++ /* C++ code to generate all possible subsequences. Time Complexity O(n * 2^n) */ #include<bits/stdc++.h> using namespace std; void printSubsequences(int arr[], int n) { /* Number of subsequences is (2**n -1)*/ unsigned int opsize = pow(2, n); /* Run from counter 000..1 to 111..1*/ for (int counter = 1; counter < opsize; counter++) { for (int j = 0; j < n; j++) { /* Check if jth bit in the counter is set If set then print jth element from arr[] */ if (counter & (1<<j)) cout << arr[j] << " "; } cout << endl; } } // Driver program int main() { int arr[] = {1, 2, 3, 4}; int n = sizeof(arr)/sizeof(arr[0]); cout << "All Non-empty Subsequences\n"; printSubsequences(arr, n); return 0; } /* Java code to generate all possible subsequences. Time Complexity O(n * 2^n) */ import java.math.BigInteger; class Test { static int arr[] = new int[]{1, 2, 3, 4}; static void printSubsequences(int n) { /* Number of subsequences is (2**n -1)*/ int opsize = (int)Math.pow(2, n); /* Run from counter 000..1 to 111..1*/ for (int counter = 1; counter < opsize; counter++) { for (int j = 0; j < n; j++) { /* Check if jth bit in the counter is set If set then print jth element from arr[] */ if (BigInteger.valueOf(counter).testBit(j)) System.out.print(arr[j]+" "); } System.out.println(); } } // Driver method to test the above function public static void main(String[] args) { System.out.println("All Non-empty Subsequences"); printSubsequences(arr.length); } } // C# code to generate all possible subsequences. // Time Complexity O(n * 2^n) using System; class GFG{ static void printSubsequences(int[] arr, int n) { // Number of subsequences is (2**n -1) int opsize = (int)Math.Pow(2, n); // Run from counter 000..1 to 111..1 for(int counter = 1; counter < opsize; counter++) { for(int j = 0; j < n; j++) { // Check if jth bit in the counter is set // If set then print jth element from arr[] if ((counter & (1 << j)) != 0) Console.Write(arr[j] + " "); } Console.WriteLine(); } } // Driver Code static void Main() { int[] arr = { 1, 2, 3, 4 }; int n = arr.Length; Console.WriteLine("All Non-empty Subsequences"); printSubsequences(arr, n); } } // This code is contributed by divyesh072019 <script> // Javascript code to generate all possible subsequences. // Time Complexity O(n * 2^n) function printSubsequences(arr, n) { // Number of subsequences is (2**n -1) let opsize = parseInt(Math.pow(2, n), 10); // Run from counter 000..1 to 111..1 for(let counter = 1; counter < opsize; counter++) { for(let j = 0; j < n; j++) { // Check if jth bit in the counter is set // If set then print jth element from arr[] if ((counter & (1 << j)) != 0) document.write(arr[j] + " "); } document.write("</br>"); } } let arr = [ 1, 2, 3, 4 ]; let n = arr.length; document.write("All Non-empty Subsequences" + "</br>"); printSubsequences(arr, n); // This code is contributed by divyeshrabadiya07. </script> <?php // PHP code to generate all // possible subsequences. // Time Complexity O(n * 2^n) function printSubsequences($arr, $n) { // Number of subsequences // is (2**n -1) $opsize = pow(2, $n); /* Run from counter 000..1 to 111..1*/ for ($counter = 1; $counter < $opsize; $counter++) { for ( $j = 0; $j < $n; $j++) { /* Check if jth bit in the counter is set If set then print jth element from arr[] */ if ($counter & (1 << $j)) echo $arr[$j], " "; } echo "\n"; } } // Driver Code $arr = array (1, 2, 3, 4); $n = sizeof($arr); echo "All Non-empty Subsequences\n"; printSubsequences($arr, $n); // This code is contributed by ajit ?> # Python3 code to generate all # possible subsequences. # Time Complexity O(n * 2 ^ n) import math def printSubsequences(arr, n) : # Number of subsequences is (2**n -1) opsize = math.pow(2, n) # Run from counter 000..1 to 111..1 for counter in range( 1, (int)(opsize)) : for j in range(0, n) : # Check if jth bit in the counter # is set If set then print jth # element from arr[] if (counter & (1<<j)) : print( arr[j], end =" ") print() # Driver program arr = [1, 2, 3, 4] n = len(arr) print( "All Non-empty Subsequences") printSubsequences(arr, n) # This code is contributed by Nikita Tiwari.
OutputAll Non-empty Subsequences 1 2 1 2 3 1 3 2 3 1 2 3 4 1 4 2 4 1 2 4 3 4 1 3 4 2 3 4 1 2 3 4
Time Complexity: 0(n*(2^n))
Auxiliary Space: 0(1)
Similar Reads
Subarray, Subsequence and Subsets in Python Algorithms and data manipulation are areas where it is important to grasp the ideas behind subarrays, subsequences as well as subsets. This article introduces the concepts of subarrays, subsequences along with subsets in Python. You will find out what these terms actually mean and how they differ fr
7 min read
Subarrays, Subsequences, and Subsets in Array What is a Subarray?A subarray is a contiguous part of array, i.e., Subarray is an array that is inside another array. In general, for an array of size n, there are n*(n+1)/2 non-empty subarrays. For example, Consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. The subarrays are: (1),
10 min read
Count of possible subarrays and subsequences using given length of Array Given an integer N which denotes the length of an array, the task is to count the number of subarray and subsequence possible with the given length of the array.Examples: Input: N = 5 Output: Count of subarray = 15 Count of subsequence = 32Input: N = 3 Output: Count of subarray = 6 Count of subseque
3 min read
Find the longest subsequence of a string that is a substring of another string Given two strings X and Y consisting of N and M characters, the task is to find the longest subsequence of a string X which is a substring of the string Y. Examples: Input: X = "ABCD", Y = "ACDBDCD"Output: ACDExplanation:"ACD" is longest subsequence of X which is substring of Y. Input: X = A, Y = AO
10 min read
What are Subsequences in an Array? Subsequences are a fundamental concept in computer science and programming when working with arrays. A subsequence of an array is a sequence of elements from the array that appear in the same order, but not necessarily consecutively. In this blog post, we'll discuss subsequences, covering their defi
6 min read