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 )
- 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_pat[].
- Start matching the characters of pattern with the characters of 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 found, try to minimize it by removing extra characters from the beginning of the current window.
- Update min_length.
- Print the minimum length window.
A diagram to explain the stated algorithm:
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 ?> |
Smallest window is : t stri
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