Smallest window in a String containing all characters of other String

Given two strings, string, and pattern, the task is to find the smallest substring in string containing all characters of pattern. 

Examples:

Input: string = “this is a test string”, pattern = “tist” 
Output: “t stri” 
Explanation: “t stri” contains all the characters of pattern.

Input: string = “geeksforgeeks”, pattern = “ork” 
Output: “ksfor”

Smallest window in a String containing all characters of other String by generating all substrings:

• Generate all substrings of string.
• For each substring, check whether the substring contains all characters of pattern (“tist”) 
• Finally, print the smallest substring containing all characters of pattern.

Below is the implementation of the above approach.

C++

#include <bits/stdc++.h>

using namespace std;

// Function to check if the substring contains all
// characters of the pattern
bool containsAllCharacters(string& substr, string& pattern)
{
    int count[256] = { 0 };

    // Count the frequency of each character in the pattern
    for (char ch : pattern)
        count[ch]++;

    // For each character in the substring, decrement its
    // count
    for (char ch : substr) {
        if (count[ch] > 0)
            count[ch]--;
    }

    // If all counts in the count array are zero, the
    // substring contains all characters of the pattern
    for (int i = 0; i < 256; i++) {
        if (count[i] > 0)
            return false;
    }

    return true;
}

// Function to find the smallest substring containing all
// characters of the pattern
string findSmallestSubstring(string& str, string& pattern)
{
    int len_str = str.length();
    int len_pattern = pattern.length();
    string smallestSubstring = "";

    int minLength = INT_MAX;

    // Generate all substrings of the given string
    for (int i = 0; i < len_str; i++) {
        for (int j = i; j < len_str; j++) {
            string substr = str.substr(i, j - i + 1);

            // Check if the substring contains all
            // characters of the pattern
            if (containsAllCharacters(substr, pattern)) {
                int currentLength = substr.length();

                // Update the smallestSubstring if the
                // current substring is smaller
                if (currentLength < minLength) {
                    minLength = currentLength;
                    smallestSubstring = substr;
                }
            }
        }
    }

    return smallestSubstring;
}

int main()
{
    string str1 = "this is a test string";
    string pattern1 = "tist";
    cout << "Input: string = \"" << str1
         << "\", pattern = \"" << pattern1 << "\"" << endl;
    cout << "Output: \""
         << findSmallestSubstring(str1, pattern1) << "\""
         << endl;

    string str2 = "geeksforgeeks";
    string pattern2 = "ork";
    cout << "Input: string = \"" << str2
         << "\", pattern = \"" << pattern2 << "\"" << endl;
    cout << "Output: \""
         << findSmallestSubstring(str2, pattern2) << "\""
         << endl;

    return 0;
}

Java

import java.util.Arrays;

public class SubstringContainingPattern {
    // Function to check if the substring contains all
    // characters of the pattern
    static boolean containsAllCharacters(String substr, String pattern) {
        int[] count = new int[256];

        // Count the frequency of each character in the pattern
        for (char ch : pattern.toCharArray())
            count[ch]++;

        // For each character in the substring, decrement its
        // count
        for (char ch : substr.toCharArray()) {
            if (count[ch] > 0)
                count[ch]--;
        }

        // If all counts in the count array are zero, the
        // substring contains all characters of the pattern
        for (int i = 0; i < 256; i++) {
            if (count[i] > 0)
                return false;
        }

        return true;
    }

    // Function to find the smallest substring containing all
    // characters of the pattern
    static String findSmallestSubstring(String str, String pattern) {
        int lenStr = str.length();
        int lenPattern = pattern.length();
        String smallestSubstring = "";

        int minLength = Integer.MAX_VALUE;

        // Generate all substrings of the given string
        for (int i = 0; i < lenStr; i++) {
            for (int j = i; j < lenStr; j++) {
                String substr = str.substring(i, j + 1);

                // Check if the substring contains all
                // characters of the pattern
                if (containsAllCharacters(substr, pattern)) {
                    int currentLength = substr.length();

                    // Update the smallestSubstring if the
                    // current substring is smaller
                    if (currentLength < minLength) {
                        minLength = currentLength;
                        smallestSubstring = substr;
                    }
                }
            }
        }

        return smallestSubstring;
    }

    public static void main(String[] args) {
        String str1 = "this is a test string";
        String pattern1 = "tist";
        System.out.println("Input: string = \"" + str1
                + "\", pattern = \"" + pattern1 + "\"");
        System.out.println("Output: \""
                + findSmallestSubstring(str1, pattern1) + "\"");

        String str2 = "geeksforgeeks";
        String pattern2 = "ork";
        System.out.println("Input: string = \"" + str2
                + "\", pattern = \"" + pattern2 + "\"");
        System.out.println("Output: \""
                + findSmallestSubstring(str2, pattern2) + "\"");
    }
}

// This code is contributed by shivamgupta0987654321

C#

using System;

class Program
{
    // Function to check if the substring contains all
    // characters of the pattern
    static bool ContainsAllCharacters(string substr, string pattern)
    {
        int[] count = new int[256];

        // Count the frequency of each character in the pattern
        foreach (char ch in pattern)
            count[ch]++;

        // For each character in the substring, decrement its
        // count
        foreach (char ch in substr)
        {
            if (count[ch] > 0)
                count[ch]--;
        }

        // If all counts in the count array are zero, the
        // substring contains all characters of the pattern
        foreach (int val in count)
        {
            if (val > 0)
                return false;
        }

        return true;
    }

    // Function to find the smallest substring containing all
    // characters of the pattern
    static string FindSmallestSubstring(string str, string pattern)
    {
        int lenStr = str.Length;
        int lenPattern = pattern.Length;
        string smallestSubstring = "";

        int minLength = int.MaxValue;

        // Generate all substrings of the given string
        for (int i = 0; i < lenStr; i++)
        {
            for (int j = i; j < lenStr; j++)
            {
                string substr = str.Substring(i, j - i + 1);

                // Check if the substring contains all
                // characters of the pattern
                if (ContainsAllCharacters(substr, pattern))
                {
                    int currentLength = substr.Length;

                    // Update the smallestSubstring if the
                    // current substring is smaller
                    if (currentLength < minLength)
                    {
                        minLength = currentLength;
                        smallestSubstring = substr;
                    }
                }
            }
        }

        return smallestSubstring;
    }

    static void Main(string[] args)
    {
        string str1 = "this is a test string";
        string pattern1 = "tist";
        Console.WriteLine("Input: string = \"" + str1 +
                          "\", pattern = \"" + pattern1 + "\"");
        Console.WriteLine("Output: \"" +
                          FindSmallestSubstring(str1, pattern1) + "\"");

        string str2 = "geeksforgeeks";
        string pattern2 = "ork";
        Console.WriteLine("Input: string = \"" + str2 +
                          "\", pattern = \"" + pattern2 + "\"");
        Console.WriteLine("Output: \"" +
                          FindSmallestSubstring(str2, pattern2) + "\"");
    }
}

Javascript

// Function to check if the substring contains all
// characters of the pattern
function containsAllCharacters(substr, pattern) {
    let count = Array(256).fill(0);

    // Count the frequency of each character in the pattern
    for (let c of pattern) {
        count++;
    }

    // For each character in the substring, decrement its count
    for (let c of substr) {
        if (count > 0) {
            count--;
        }
    }

    // If all counts in the count array are zero, the
    // substring contains all characters of the pattern
    for (let i = 0; i < 256; i++) {
        if (count[i] > 0) {
            return false;
        }
    }

    return true;
}

// Function to find the smallest substring containing all
// characters of the pattern
function findSmallestSubstring(str, pattern) {
    let len_str = str.length;
    let len_pattern = pattern.length;
    let smallestSubstring = "";

    let minLength = Number.MAX_VALUE;

    // Generate all substrings of the given string
    for (let i = 0; i < len_str; i++) {
        for (let j = i; j < len_str; j++) {
            let substr = str.substring(i, j + 1);

            // Check if the substring contains all characters of the pattern
            if (containsAllCharacters(substr, pattern)) {
                let currentLength = substr.length;

                // Update the smallestSubstring if the current substring is smaller
                if (currentLength < minLength) {
                    minLength = currentLength;
                    smallestSubstring = substr;
                }
            }
        }
    }

    return smallestSubstring;
}

// Driver code
let str1 = "this is a test string";
let pattern1 = "tist";
console.log(`Input: string = "${str1}", pattern = "${pattern1}"`);
console.log(`Output: "${findSmallestSubstring(str1, pattern1)}"`);

let str2 = "geeksforgeeks";
let pattern2 = "ork";
console.log(`Input: string = "${str2}", pattern = "${pattern2}"`);
console.log(`Output: "${findSmallestSubstring(str2, pattern2)}"`);

Output

Input: string = "this is a test string", pattern = "tist"
Output: "t stri"
Input: string = "geeksforgeeks", pattern = "ork"
Output: "ksfor"

Time Complexity: O(N³)
Auxiliary Space: O(N) to create substrings.

Smallest window in a String containing all characters of other String using Binary Search on Answer:

The idea is to check if a window of a certain size “mid” is valid (contains all characters of the “pattern” string), then all windows of size greater than “mid” will also be valid. Similarly, if a window of size “mid” is not valid, then all windows of size smaller than “mid” will also not be valid. This property allows us to apply binary search effectively.

Follow the steps below to solve the problem:

• Initialize low and high as 1 and string length respectively denoting the minimum and maximum possible answer.
• For any value mid check if there is any substring of length mid in the string that contains all the characters of the pattern.
• If any such substring of length exists then store the starting index of that substring and update high to mid-1 and, check for substrings having lengths smaller than mid.
• Otherwise, if any such substring does not exist then update low to mid+1 and, check for substrings having lengths larger than mid.

Below is the implementation of the above approach.

C++

#include <bits/stdc++.h>
using namespace std;


// Function to check if any substring of length mid contains
// all characters of the pattern
bool isValid(string& str, string& pattern, int mid,
             int& start)
{
    // Count the frequency of each character in the pattern
    int count[256] = { 0 };

    // Stores number of distinct characters in pattern
    int distinct = 0;

    bool found = false;

    // Count the frequency of each character in the pattern
    for (char c : pattern) {
        count++;
        if (count == 1)
            distinct++;
    }

    // Stores the number of charcters in a substring of size
    // mid in str whose frequency is same as frequency in
    // pattern
    int curr_count = 0;
    for (int i = 0; i < str.size(); i++) {
        count[str[i]]--;
        if (count[str[i]] == 0) {
            curr_count++;
        }
        if (i >= mid) {
            count[str[i - mid]]++;
            if (count[str[i - mid]] == 1) {
                curr_count--;
            }
        }
        if (i >= mid - 1) {

            // Substring of length mid found which contains
            // all the characters of pattern
            if (curr_count == distinct) {

                found = true;

                // Stores starting index of that substring
                start = (i - mid) + 1;
                break;
            }
        }
    }

    return found;
}

// Function to find the smallest substring containing all
// characters of the pattern
string findSmallestSubstring(string& str, string& pattern)
{
    int len_str = str.length();
    int len_pattern = pattern.length();
    string smallestSubstring = "";

    int minLength = INT_MAX;

    // Lower bound and Upper Bound for Binary Serach
    int low_bound = 1, high_bound = len_str;

    // Stores starting index of min length substring
    int idx;

    // Applying Binary Search on answer
    while (low_bound <= high_bound) {
        int mid = (low_bound + high_bound) / 2;
        int start;

        // If a substring of length mid is found which
        // contains all teh characters of pattern then
        // update minLenght and high_bound otherwise update
        // low_bound
        if (isValid(str, pattern, mid, start)) {
            if (mid < minLength) {
                minLength = mid;
                idx = start;
            }
            high_bound = mid - 1;
        }

        else {
            low_bound = mid + 1;
        }
    }

    return smallestSubstring = str.substr(idx, minLength);
}

int main()
{
    string str1 = "this is a test string";
    string pattern1 = "tist";
    cout << "Input: string = \"" << str1
         << "\", pattern = \"" << pattern1 << "\"" << endl;
    cout << "Output: \""
         << findSmallestSubstring(str1, pattern1) << "\""
         << endl;

    string str2 = "geeksforgeeks";
    string pattern2 = "ork";
    cout << "Input: string = \"" << str2
         << "\", pattern = \"" << pattern2 << "\"" << endl;
    cout << "Output: \""
         << findSmallestSubstring(str2, pattern2) << "\""
         << endl;

    return 0;
}

Output

Input: string = "this is a test string", pattern = "tist"
Output: "t stri"
Input: string = "geeksforgeeks", pattern = "ork"
Output: "ksfor"

Time Complexity:  O(N*logN), where N is the length of string. 
Auxiliary Space: O(1)

Smallest window in a String containing all characters of other String using Two Pointers and Hashing:

The idea is to use the two pointer approach on the hash array of pattern string and then find the minimum window by eliminating characters from the start of the window.

Follow the steps below to solve the problem:

• First check if the length of the string is less than the length of the given pattern, if yes then “no such window can exist “.
• Store the occurrence of characters of the given pattern in a hash array (say, hash_pat[]).
• We will be using two pointer technique here
• Start matching the characters of the pattern with the characters of the string i.e. increment count if a character matches.
  • Check if (count == length of pattern ) this means a window is found.
  • If such a window is found, try to minimize it by removing extra characters from the beginning of the current window.
  • Delete one character from the first and again find this deleted key at right.
  • If found, then again check if the count and pattern length are the same and repeat the process.
  • Update min_length.
• Print the minimum length window.

Illustration:

Smallest Window in a String Containing all characters of other String Using Two Pointers

Below is the implementation of the above approach.

C++

// C++ program to find
// smallest window containing
// all characters of a pattern.
#include <bits/stdc++.h>
using namespace std;

const int no_of_chars = 256;

// Function to find smallest
// window containing
// all characters of 'pat'
string findSubString(string str, string pat)
{
    int len1 = str.length();
    int len2 = pat.length();

    // Check if string's length
    // is less than pattern's
    // length. If yes then no such
    // window can exist
    if (len1 < len2) {
        cout << "No such window exists";
        return "";
    }

    int hash_pat[no_of_chars] = { 0 };
    int hash_str[no_of_chars] = { 0 };

    // Store occurrence ofs characters
    // of pattern
    for (int i = 0; i < len2; i++)
        hash_pat[pat[i]]++;

    int start = 0, start_index = -1, min_len = INT_MAX;

    // Start traversing the string
    // Count of characters
    int count = 0;
    for (int j = 0; j < len1; j++) {

        // Count occurrence of characters
        // of string
        hash_str[str[j]]++;

        // If string's char matches with
        // pattern's char
        // then increment count
        if (hash_str[str[j]] <= hash_pat[str[j]])
            count++;

        // if all the characters are matched
        if (count == len2) {

            // Try to minimize the window
            while (hash_str[str[start]]
                       > hash_pat[str[start]]
                   || hash_pat[str[start]] == 0) {

                if (hash_str[str[start]]
                    > hash_pat[str[start]])
                    hash_str[str[start]]--;
                start++;
            }

            // update window size
            int len_window = j - start + 1;
            if (min_len > len_window) {
                min_len = len_window;
                start_index = start;
            }
        }
    }

    // If no window found
    if (start_index == -1) {
        cout << "No such window exists";
        return "";
    }

    // Return substring starting from start_index
    // and length min_len
    return str.substr(start_index, min_len);
}

// Driver code
int main()
{
   string str1 = "this is a test string";
    string pattern1 = "tist";
    cout << "Input: string = \"" << str1
         << "\", pattern = \"" << pattern1 << "\"" << endl;
    cout << "Output: \""
         << findSubString(str1, pattern1) << "\""
         << endl;

    string str2 = "geeksforgeeks";
    string pattern2 = "ork";
    cout << "Input: string = \"" << str2
         << "\", pattern = \"" << pattern2 << "\"" << endl;
    cout << "Output: \""
         << findSubString(str2, pattern2) << "\""
         << endl;
      return 0;
}

Java

// Java program to find smallest
// window containing
// all characters of a pattern.

public class GFG {
    static final int no_of_chars = 256;

    // Function to find smallest
    // window containing
    // all characters of 'pat'
    static String findSubString(String str, String pat)
    {
        int len1 = str.length();
        int len2 = pat.length();

        // Check if string's length is
        // less than pattern's
        // length. If yes then no such
        // window can exist
        if (len1 < len2) {
            System.out.println("No such window exists");
            return "";
        }

        int hash_pat[] = new int[no_of_chars];
        int hash_str[] = new int[no_of_chars];

        // Store occurrence ofs
        // characters of pattern
        for (int i = 0; i < len2; i++)
            hash_pat[pat.charAt(i)]++;

        int start = 0, start_index = -1,
            min_len = Integer.MAX_VALUE;

        // Start traversing the string
        // Count of characters
        int count = 0;
        for (int j = 0; j < len1; j++) {

            // Count occurrence of characters
            // of string
            hash_str[str.charAt(j)]++;

            // If string's char matches
            // with pattern's char
            // then increment count
            if (hash_str[str.charAt(j)]
                <= hash_pat[str.charAt(j)])
                count++;

            // If all the characters are matched
            if (count == len2) {

                // Try to minimize the window
                while (hash_str[str.charAt(start)]
                           > hash_pat[str.charAt(start)]
                       || hash_pat[str.charAt(start)]
                              == 0) {

                    if (hash_str[str.charAt(start)]
                        > hash_pat[str.charAt(start)])
                        hash_str[str.charAt(start)]--;
                    start++;
                }

                // update window size
                int len_window = j - start + 1;
                if (min_len > len_window) {
                    min_len = len_window;
                    start_index = start;
                }
            }
        }

        // If no window found
        if (start_index == -1) {
            System.out.println("No such window exists");
            return "";
        }

        // Return substring starting
        // from start_index
        // and length min_len
        return str.substring(start_index,
                             start_index + min_len);
    }

    // Driver Method
    public static void main(String[] args)
    {
        String str = "this is a test string";
        String pat = "tist";

        System.out.print(findSubString(str, pat));
    }
}

Python3

# Python3 program to find the smallest window
# containing all characters of a pattern.
no_of_chars = 256

# Function to find smallest window
# containing all characters of 'pat'
def findSubString(string, pat):

    len1 = len(string)
    len2 = len(pat)

    # Check if string's length is
    # less than pattern's
    # length. If yes then no such
    # window can exist
    if len1 < len2:

        print("No such window exists")
        return ""

    hash_pat = [0] * no_of_chars
    hash_str = [0] * no_of_chars

    # Store occurrence ofs characters of pattern
    for i in range(0, len2):
        hash_pat[ord(pat[i])] += 1

    start, start_index, min_len = 0, -1, float('inf')

    # Start traversing the string
    count = 0  # count of characters
    for j in range(0, len1):

        # count occurrence of characters of string
        hash_str[ord(string[j])] += 1

        # If string's char matches with
        # pattern's char then increment count
        if (hash_str[ord(string[j])] <=
                hash_pat[ord(string[j])]):
            count += 1

        # if all the characters are matched
        if count == len2:

            # Try to minimize the window
            while (hash_str[ord(string[start])] >
                   hash_pat[ord(string[start])] or
                   hash_pat[ord(string[start])] == 0):

                if (hash_str[ord(string[start])] >
                        hash_pat[ord(string[start])]):
                    hash_str[ord(string[start])] -= 1
                start += 1

            # update window size
            len_window = j - start + 1
            if min_len > len_window:

                min_len = len_window
                start_index = start

    # If no window found
    if start_index == -1:
        print("No such window exists")
        return ""

    # Return substring starting from
    # start_index and length min_len
    return string[start_index: start_index + min_len]


# Driver code
if __name__ == "__main__":

    string = "this is a test string"
    pat = "tist"

    print(findSubString(string, pat))

# This code is contributed by Rituraj Jain

C#

// C# program to find smallest
// window containing
// all characters of a pattern.
using System;

class GFG {
    static int no_of_chars = 256;

    // Function to find smallest
    // window containing
    // all characters of 'pat'
    static String findSubString(String str,
                                String pat)
    {
        int len1 = str.Length;
        int len2 = pat.Length;

        // Check if string's length is
        // less than pattern's
        // length. If yes then no such
        // window can exist
        if (len1 < len2) {
            Console.WriteLine("No such window exists");
            return "";
        }

        int[] hash_pat = new int[no_of_chars];
        int[] hash_str = new int[no_of_chars];

        // Store occurrence ofs characters
        // of pattern
        for (int i = 0; i < len2; i++)
            hash_pat[pat[i]]++;

        int start = 0, start_index = -1,
            min_len = int.MaxValue;

        // Start traversing the string
        // Count of characters
        int count = 0;
        for (int j = 0; j < len1; j++) {

            // Count occurrence of characters
            // of string
            hash_str[str[j]]++;

            // If string's char matches
            // with pattern's char
            // then increment count
            if (hash_str[str[j]] <= hash_pat[str[j]])
                count++;

            // if all the characters are matched
            if (count == len2) {

                // Try to minimize the window
                while (hash_str[str[start]]
                           > hash_pat[str[start]]
                       || hash_pat[str[start]] == 0) {

                    if (hash_str[str[start]]
                        > hash_pat[str[start]])
                        hash_str[str[start]]--;
                    start++;
                }

                // update window size
                int len_window = j - start + 1;
                if (min_len > len_window) {
                    min_len = len_window;
                    start_index = start;
                }
            }
        }

        // If no window found
        if (start_index == -1) {
            Console.WriteLine("No such window exists");
            return "";
        }

        // Return substring starting from start_index
        // and length min_len
        return str.Substring(start_index, min_len);
    }

    // Driver Method
    public static void Main(String[] args)
    {
        String str = "this is a test string";
        String pat = "tist";

        Console.WriteLine(findSubString(str, pat));
    }
}

/* This code contributed by PrinciRaj1992 */

Javascript

<script>
// javascript program to find smallest
// window containing
// all characters of a pattern.

var no_of_chars = 256;

// Function to find smallest
// window containing
// all characters of 'pat'
function findSubString(str, pat)
{
    var len1 = str.length;
    var len2 = pat.length;

    // Check if string's length is
    // less than pattern's
    // length. If yes then no such
    // window can exist
    if (len1 < len2) {
        document.write("No such window exists");
        return "";
    }

    var hash_pat = Array.from({length: no_of_chars}, (_, i) => 0);
    var hash_str = Array.from({length: no_of_chars}, (_, i) => 0);

    // Store occurrence ofs
    // characters of pattern
    for (var i = 0; i < len2; i++)
        hash_pat[pat.charAt(i).charCodeAt(0)]++;

    var start = 0, start_index = -1,
        min_len = Number.MAX_VALUE;

    // Start traversing the string
    // Count of characters
    var count = 0;
    for (var j = 0; j < len1; j++) {

        // Count occurrence of characters
        // of string
        hash_str[str.charAt(j).charCodeAt(0)]++;

        // If string's char matches
        // with pattern's char
        // then increment count
        if (hash_str[str.charAt(j).charCodeAt(0)]
            <= hash_pat[str.charAt(j).charCodeAt(0)])
            count++;

        // If all the characters are matched
        if (count == len2) {

            // Try to minimize the window
            while (hash_str[str.charAt(start).charCodeAt(0)]
                       > hash_pat[str.charAt(start).charCodeAt(0)]
                   || hash_pat[str.charAt(start).charCodeAt(0)]
                          == 0) {

                if (hash_str[str.charAt(start).charCodeAt(0)]
                    > hash_pat[str.charAt(start).charCodeAt(0)])
                    hash_str[str.charAt(start).charCodeAt(0)]--;
                start++;
            }

            // update window size
            var len_window = j - start + 1;
            if (min_len > len_window) {
                min_len = len_window;
                start_index = start;
            }
        }
    }

    // If no window found
    if (start_index == -1) {
        document.write("No such window exists");
        return "";
    }

    // Return substring starting
    // from start_index
    // and length min_len
    return str.substring(start_index,
                         start_index + min_len);
}

// Driver Method
var str = "this is a test string";
var pat = "tist";

document.write(findSubString(str, pat));
// This code is contributed by 29AjayKumar
</script>

PHP

<?php
// PHP program to find smallest window
// containing all characters of a pattern.

define("no_of_chars", 256);

// Function to find smallest window
// containing all characters of 'pat'
function findSubString(&$str, &$pat)
{
    $len1 = strlen($str);
    $len2 = strlen($pat);

    // check if string's length is less
    // than pattern's length. If yes
    // then no such window can exist
    if ($len1 < $len2)
    {
        echo "No such window exists";
        return "";
    }

    $hash_pat = array_fill(0, no_of_chars, 0);
    $hash_str = array_fill(0, no_of_chars, 0);

    // store occurrence ofs characters
    // of pattern
    for ($i = 0; $i < $len2; $i++)
        $hash_pat[ord($pat[$i])]++;

    $start = 0;
    $start_index = -1;
    $min_len = PHP_INT_MAX;

    // start traversing the string
    $count = 0; // count of characters
    for ($j = 0; $j < $len1 ; $j++)
    {
        // count occurrence of characters
        // of string
        $hash_str[ord($str[$j])]++;

        // If string's char matches with
        // pattern's char then increment count
        if ($hash_str[ord($str[$j])] <=
            $hash_pat[ord($str[$j])])
            $count++;

        // if all the characters are matched
        if ($count == $len2)
        {
            // Try to minimize the window i.e.,
            // check if any character is occurring
            // more no. of times than its occurrence
            // in pattern, if yes then remove it from
            // starting and also remove the useless
            // characters.
            while ($hash_str[ord($str[$start])] >
                   $hash_pat[ord($str[$start])] ||
                   $hash_pat[ord($str[$start])] == 0)
            {

                if ($hash_str[ord($str[$start])] >
                    $hash_pat[ord($str[$start])])
                    $hash_str[ord($str[$start])]--;
                $start++;
            }

            // update window size
            $len_window = $j - $start + 1;
            if ($min_len > $len_window)
            {
                $min_len = $len_window;
                $start_index = $start;
            }
        }
    }

    // If no window found
    if ($start_index == -1)
    {
        echo "No such window exists";
        return "";
    }

    // Return substring starting from
    // start_index and length min_len
    return substr($str, $start_index, $min_len);
}

// Driver code
$str = "this is a test string";
$pat = "tist";

echo findSubString($str, $pat);

// This code is contributed by
// rathbhupendra
?>

Output

Input: string = "this is a test string", pattern = "tist"
Output: "t stri"
Input: string = "geeksforgeeks", pattern = "ork"
Output: "ksfor"

Time Complexity:  O(N), where N is the length of string. 
Auxiliary Space: O(1)

This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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