# Length of smallest substring of a given string which contains another string as subsequence

• Difficulty Level : Medium
• Last Updated : 20 May, 2021

Given two strings A and B, the task is to find the smallest substring of A having B as a subsequence.

Examples:

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Input: A = “abcdefababaef”, B = “abf”
Output: 5
Explanation:
Smallest substring of A having B as subsequence is abcdef.
Therefore, the required length is 5.

Input: A = “abcdefababaef”, B = “aef”
Output: 3

Approach: Follow the steps below to solve the problem:

• Store all the indices of the characters of A which are also present in B in a Map CharacterIndex.
• Traverse over all the characters of string B.
• Check if the first character of string B is present in the string A or not:
1. If found to be true, then initialize two variables firstVar and lastVar with the index of the first occurrence of B in the string A.
2. After updating the values, remove that character from the Map CharacterIndex.
3. Otherwise, no further substring is possible.
• For the remaining characters of B, check if the character is present in the string A or not. If found to be true, traverse through all the occurrences of that character in the string A and if the index of that character in the string A exceeds lastVar, then update the lastVar with that index. Otherwise, no further substring is possible.
• If B is completely traversed, update answer with the difference between firstVar and the lastVar.
• Print the final minimized answer.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement``// the above approach``#include ``using` `namespace` `std;` `// Function to find the length of``// smallest substring of a having``// string b as a subsequence``int` `minLength(string a, string b)``{` `    ``// Stores the characters present``    ``// in string b``    ``map<``char``, ``int``> Char;``    ``for` `(``int` `i = 0; i < b.length(); i++) {` `        ``Char[b[i]]++;``    ``}` `    ``// Find index of characters of a``    ``// that are also present in string b``    ``map<``char``, vector<``int``> > CharacterIndex;` `    ``for` `(``int` `i = 0; i < a.length(); i++) {` `        ``char` `x = a[i];` `        ``// If character is present in string b``        ``if` `(Char.find(x) != Char.end()) {` `            ``// Store the index of character``            ``CharacterIndex[x].push_back(i);``        ``}``    ``}` `    ``int` `len = INT_MAX;` `    ``// Flag is used to check if``    ``// substring is possible``    ``int` `flag;` `    ``while` `(``true``) {` `        ``// Assume that substring is``        ``// possible``        ``flag = 1;` `        ``// Stores first and last``        ``// indices of the substring``        ``// respectively``        ``int` `firstVar, lastVar;` `        ``for` `(``int` `i = 0; i < b.length(); i++) {` `            ``// For first character of string b``            ``if` `(i == 0) {` `                ``// If the first character of``                ``// b is not present in a``                ``if` `(CharacterIndex.find(b[i])``                    ``== CharacterIndex.end()) {` `                    ``flag = 0;``                    ``break``;``                ``}` `                ``// If the first character of b``                ``// is present in a``                ``else` `{` `                    ``int` `x = *(``                        ``CharacterIndex[b[i]].begin());` `                    ``// Remove the index from map``                    ``CharacterIndex[b[i]].erase(``                        ``CharacterIndex[b[i]].begin());` `                    ``// Update indices of``                    ``// the substring``                    ``firstVar = x;``                    ``lastVar = x;``                ``}``            ``}` `            ``// For the remaining characters of b``            ``else` `{` `                ``int` `elementFound = 0;``                ``for` `(``auto` `e : CharacterIndex[b[i]]) {` `                    ``if` `(e > lastVar) {` `                        ``// If index possible for``                        ``// current character``                        ``elementFound = 1;``                        ``lastVar = e;``                        ``break``;``                    ``}``                ``}``                ``if` `(elementFound == 0) {` `                    ``// If no index is possible``                    ``flag = 0;``                    ``break``;``                ``}``            ``}``        ``}` `        ``if` `(flag == 0) {` `            ``// If no more substring``            ``// is possible``            ``break``;``        ``}` `        ``// Update the minimum length``        ``// of substring``        ``len = min(len,``                  ``abs``(lastVar - firstVar) + 1);``    ``}` `    ``// Return the result``    ``return` `len;``}` `// Driver Code``int` `main()``{` `    ``// Given two string``    ``string a = ``"abcdefababaef"``;``    ``string b = ``"abf"``;` `    ``int` `len = minLength(a, b);``    ``if` `(len != INT_MAX) {` `        ``cout << len << endl;``    ``}``    ``else` `{` `        ``cout << ``"Impossible"` `<< endl;``    ``}``}`

## Java

 `// Java program to implement``// the above approach``import` `java.util.ArrayList;``import` `java.util.HashMap;` `class` `GFG{` `// Function to find the length of``// smallest substring of a having``// string b as a subsequence``static` `int` `minLength(String a, String b)``{``    ` `    ``// Stores the characters present``    ``// in string b``    ``HashMap Char = ``new` `HashMap<>();` `    ``for``(``int` `i = ``0``; i < b.length(); i++)``    ``{``        ``Char.put(b.charAt(i),``                 ``Char.getOrDefault(b.charAt(i), ``0``) + ``1``);``    ``}` `    ``// Find index of characters of a``    ``// that are also present in string b``    ``HashMap>``        ``CharacterIndex = ``new` `HashMap<>();` `    ``for``(``int` `i = ``0``; i < a.length(); i++)``    ``{``        ``char` `x = a.charAt(i);` `        ``// If character is present in string b``        ``if` `(Char.containsKey(x))``        ``{``            ``if` `(CharacterIndex.get(x) == ``null``)``            ``{``                ``CharacterIndex.put(``                    ``x, ``new` `ArrayList());``            ``}``            ` `            ``// Store the index of character``            ``CharacterIndex.get(x).add(i);``        ``}``    ``}` `    ``int` `len = Integer.MAX_VALUE;` `    ``// Flag is used to check if``    ``// substring is possible``    ``int` `flag;` `    ``while` `(``true``)``    ``{` `        ``// Assume that substring is``        ``// possible``        ``flag = ``1``;` `        ``// Stores first and last``        ``// indices of the substring``        ``// respectively``        ``int` `firstVar = ``0``, lastVar = ``0``;` `        ``for``(``int` `i = ``0``; i < b.length(); i++)``        ``{``            ` `            ``// For first character of string b``            ``if` `(i == ``0``)``            ``{` `                ``// If the first character of``                ``// b is not present in a``                ``if` `(CharacterIndex.containsKey(i))``                ``{``                    ``flag = ``0``;``                    ``break``;``                ``}` `                ``// If the first character of b``                ``// is present in a``                ``else``                ``{``                    ``int` `x = CharacterIndex.get(b.charAt(i)).get(``0``);` `                    ``// Remove the index from map``                    ``CharacterIndex.get(b.charAt(i)).remove(``                        ``CharacterIndex.get(b.charAt(i)).get(``0``));` `                    ``// Update indices of``                    ``// the substring``                    ``firstVar = x;``                    ``lastVar = x;``                ``}``            ``}` `            ``// For the remaining characters of b``            ``else``            ``{``                ``int` `elementFound = ``0``;``                ``for``(var e :``                    ``CharacterIndex.get(b.charAt(i)))``                ``{``                    ``if` `(e > lastVar)``                    ``{``                        ` `                        ``// If index possible for``                        ``// current character``                        ``elementFound = ``1``;``                        ``lastVar = e;``                        ``break``;``                    ``}``                ``}``                ``if` `(elementFound == ``0``)``                ``{``                    ` `                    ``// If no index is possible``                    ``flag = ``0``;``                    ``break``;``                ``}``            ``}``        ``}` `        ``if` `(flag == ``0``)``        ``{` `            ``// If no more substring``            ``// is possible``            ``break``;``        ``}` `        ``// Update the minimum length``        ``// of substring``        ``len = Math.min(``            ``len, Math.abs(lastVar - firstVar) + ``1``);``    ``}` `    ``// Return the result``    ``return` `len;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ` `    ``// Given two string``    ``String a = ``"abcdefababaef"``;``    ``String b = ``"abf"``;` `    ``int` `len = minLength(a, b);``    ``if` `(len != Integer.MAX_VALUE)``    ``{``        ``System.out.println(len);``    ``}``    ``else``    ``{``        ``System.out.println(``"Impossible"``);``    ``}``}``}` `// This code is contributed by sk944795`

## Python3

 `# Python3 program to implement``# the above approach``import` `sys` `# Function to find the length of``# smallest substring of a having``# string b as a subsequence``def` `minLength(a, b):``    ` `    ``# Stores the characters present``    ``# in string b``    ``Char ``=` `{}``    ``for` `i ``in` `range``(``len``(b)):``        ``Char[b[i]] ``=` `Char.get(b[i], ``0``) ``+` `1` `    ``# Find index of characters of a``    ``# that are also present in string b``    ``CharacterIndex ``=` `{}` `    ``for` `i ``in` `range``(``len``(a)):``        ``x ``=` `a[i]` `        ``# If character is present in string b``        ``if` `(x ``in` `Char):``            ` `            ``# Store the index of character``            ``CharacterIndex[x] ``=` `CharacterIndex.get(x, [])``            ``CharacterIndex[x].append(i)` `    ``l ``=` `sys.maxsize` `    ``# Flag is used to check if``    ``# substring is possible``    ``while``(``True``):``        ` `        ``# Assume that substring is``        ``# possible``        ``flag ``=` `1` `        ``firstVar ``=` `0``        ``lastVar ``=` `0``        ` `        ``# Stores first and last``        ``# indices of the substring``        ``# respectively``        ``for` `i ``in` `range``(``len``(b)):``            ` `            ``# For first character of string b``            ``if` `(i ``=``=` `0``):``                ` `                ``# If the first character of``                ``# b is not present in a``                ``if` `(b[i] ``not` `in` `CharacterIndex):``                    ``flag ``=` `0``                    ``break` `                ``# If the first character of b``                ``# is present in a``                ``else``:``                    ``x ``=` `CharacterIndex[b[i]][``0``]` `                    ``# Remove the index from map``                    ``CharacterIndex[b[i]].remove(``                    ``CharacterIndex[b[i]][``0``])` `                    ``# Update indices of``                    ``# the substring``                    ``firstVar ``=` `x``                    ``lastVar ``=` `x` `            ``# For the remaining characters of b``            ``else``:``                ``elementFound ``=` `0``                ``for` `e ``in` `CharacterIndex[b[i]]:``                    ``if` `(e > lastVar):``                        ` `                        ``# If index possible for``                        ``# current character``                        ``elementFound ``=` `1``                        ``lastVar ``=` `e``                        ``break``                    ` `                ``if` `(elementFound ``=``=` `0``):``                    ` `                    ``# If no index is possible``                    ``flag ``=` `0``                    ``break``                ` `        ``if` `(flag ``=``=` `0``):``            ` `            ``# If no more substring``            ``# is possible``            ``break` `        ``# Update the minimum length``        ``# of substring``        ``l ``=` `min``(l, ``abs``(lastVar ``-` `firstVar) ``+` `1``)` `    ``# Return the result``    ``return` `l` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``# Given two string``    ``a ``=` `"abcdefababaef"``    ``b ``=` `"abf"` `    ``l ``=` `minLength(a, b)``    ``if` `(l !``=` `sys.maxsize):``        ``print``(l)``    ``else``:``        ``print``(``"Impossible"``)``        ` `# This code is contributed by SURENDRA_GANGWAR`
Output:
`5`

Time Complexity: O(N2)
Auxiliary Space: O(N)

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