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Find the smallest window in a string containing all characters of another string
  • Difficulty Level : Hard
  • Last Updated : 09 Mar, 2021
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Given two strings string1 and string2, the task is to find the smallest substring in string1 containing all characters of string2 efficiently. 
Examples: 

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

Method 1 ( Brute force solution ) 
1- Generate all substrings of string1 (“this is a test string”) 
2- For each substring, check whether the substring contains all characters of string2 (“tist”) 
3- Finally, print the smallest substring containing all characters of string2.
  
Method 2 ( Efficient Solution ) 

  1. 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 “.
  2. Store the occurrence of characters of the given pattern in a hash_pat[].
  3. we will be using two pointer technique basically
  4. Start matching the characters of pattern with the characters of string i.e. increment count if a character matches.
  5. Check if (count == length of pattern ) this means a window is found.
  6. If such a window found, try to minimize it by removing extra characters from the beginning of the current window.
  7. delete one character from first and again find this deleted key at right, once found apply step 5 .
  8. Update min_length.
  9. Print the minimum length window.

A diagram to explain the stated algorithm:  

smallest-window

after the second image(array) our left pointer should be at s and then find I at right and then apply step5 (basically one step has not been shown)

Below is the program to implement the above algorithm:
 



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 str = "this is a test string";
    string pat = "tist";
 
    cout << "Smallest window is : \n"
         << findSubString(str, pat);
    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("Smallest window is :\n "
                         + 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("Smallest window is : ")
    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("Smallest window is :\n "
                          + findSubString(str, pat));
    }
}
 
/* This code contributed by PrinciRaj1992 */

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 "Smallest window is : \n" .
      findSubString($str, $pat);
       
// This code is contributed by
// rathbhupendra
?>
Output
Smallest window is : 
t stri

This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 

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