# Subarray/Substring vs Subsequence and Programs to Generate them

• Difficulty Level : Medium
• Last Updated : 10 Jan, 2023

Subarray/Substring

A subarray is a contiguous part of 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 starting element and inner loop considers all elements on right of the picked elements as ending element of subarray.

## C++

 `/*  C++ code to generate all possible subarrays/subArrays ` `    ``Complexity- O(n^3) */` `#include ` `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

## Java

 `// 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

## Python3

 `# 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. `

## C#

 `// 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. `

## PHP

 ` `

## Javascript

 ``

Output:

```All 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)

Space Complexity: 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 ` `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<

## Java

 `/*  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); ` `    ``} ` `} `

## Python3

 `# 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``<

## C#

 `// 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`

## PHP

 ` `

## Javascript

 ``

Output:

```All 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))

Space Complexity: 0(1)
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