Find the smallest window in a string containing all characters of another string
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[].
- we will be using two pointer technique basically
- 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.
- delete one character from first and again find this deleted key at right, once found apply step 5 .
- Update min_length.
- Print the minimum length window.
A diagram to explain the stated algorithm:
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 codeint 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 codeif __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?> |
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 Methodvar str = "this is a test string";var pat = "tist";document.write("Smallest window is :\n " + findSubString(str, pat));// This code is contributed by 29AjayKumar</script> |
Output
Smallest window is : t stri
Method 3 (Efficient Solution)
(Using sliding window Technique )
C++14
#include <bits/stdc++.h>using namespace std;// Functionstring Minimum_Window(string s, string t){ int m[256] = { 0 }; // Answer int ans = INT_MAX; // length of ans int start = 0; // starting index of ans int count = 0; // creating map for (int i = 0; i < t.length(); i++) { if (m[t[i]] == 0) count++; m[t[i]]++; } // References of Window int i = 0; int j = 0; // Traversing the window while (j < s.length()) { // Calculations m[s[j]]--; if (m[s[j]] == 0) count--; // Condition matching if (count == 0) { while (count == 0) { // Sorting ans if (ans > j - i + 1) { ans = min(ans, j - i + 1); start = i; } // Sliding I // Calculation for removing I m[s[i]]++; if (m[s[i]] > 0) count++; i++; } } j++; } if (ans != INT_MAX) return s.substr(start, ans); else return "-1";}main(){ string s = "ADOBECODEBANC"; string t = "ABC"; cout<<"-->Smallest window that contain all character : "<<endl; cout << Minimum_Window(s, t);} |
Java
import java.util.*;class GFG{// Functionstatic String Minimum_Window(char []s, char []t){ int m[] = new int[256]; // Answer int ans = Integer.MAX_VALUE; // length of ans int start = 0; // starting index of ans int count = 0; // creating map for (int i = 0; i < t.length; i++) { if (m[t[i]] == 0) count++; m[t[i]]++; } // References of Window int i = 0; int j = 0; // Traversing the window while (j < s.length) { // Calculations m[s[j]]--; if (m[s[j]] == 0) count--; // Condition matching if (count == 0) { while (count == 0) { // Sorting ans if (ans > j - i + 1) { ans = Math.min(ans, j - i + 1); start = i; } // Sliding I // Calculation for removing I m[s[i]]++; if (m[s[i]] > 0) count++; i++; } } j++; } if (ans != Integer.MAX_VALUE) return String.valueOf(s).substring(start, ans+start); else return "-1";}public static void main(String[] args){ String s = "ADOBECODEBANC"; String t = "ABC"; System.out.print("-->Smallest window that contain all character : "); System.out.print(Minimum_Window(s.toCharArray(), t.toCharArray()));}}// This code is contributed by 29AjayKumar |
C#
using System;class GFG{// Functionstatic String Minimum_Window(char []s, char []t){ int []m = new int[256]; // Answer // Length of ans int ans = int.MaxValue; // Starting index of ans int start = 0; int count = 0, i = 0; // Creating map for(i = 0; i < t.Length; i++) { if (m[t[i]] == 0) count++; m[t[i]]++; } // References of Window i = 0; int j = 0; // Traversing the window while (j < s.Length) { // Calculations m[s[j]]--; if (m[s[j]] == 0) count--; // Condition matching if (count == 0) { while (count == 0) { // Sorting ans if (ans > j - i + 1) { ans = Math.Min(ans, j - i + 1); start = i; } // Sliding I // Calculation for removing I m[s[i]]++; if (m[s[i]] > 0) count++; i++; } } j++; } if (ans != int.MaxValue) return String.Join("", s).Substring(start, ans); else return "-1";}// Driver codepublic static void Main(String[] args){ String s = "ADOBECODEBANC"; String t = "ABC"; Console.Write( "-->Smallest window that contain all character : "); Console.Write(Minimum_Window(s.ToCharArray(), t.ToCharArray()));}}// This code is contributed by 29AjayKumar |
Javascript
<script>// Functionfunction Minimum_Window(s,t){ let m = new Array(256); for(let i = 0; i < 256; i++) { m[i] = 0; } // Length of ans let ans = Number.MAX_VALUE; // Starting index of ans let start = 0; let count = 0; // Creating map for(let i = 0; i < t.length; i++) { if (m[t[i].charCodeAt(0)] == 0) count++; m[t[i].charCodeAt(0)]++; } // References of Window let i = 0; let j = 0; // Traversing the window while (j < s.length) { // Calculations m[s[j].charCodeAt(0)]--; if (m[s[j].charCodeAt(0)] == 0) count--; // Condition matching if (count == 0) { while (count == 0) { // Sorting ans if (ans > j - i + 1) { ans = Math.min(ans, j - i + 1); start = i; } // Sliding I // Calculation for removing I m[s[i].charCodeAt(0)]++; if (m[s[i].charCodeAt(0)] > 0) count++; i++; } } j++; } if (ans != Number.MAX_VALUE) return (s).join("").substring( start, (start + ans)); else return "-1";}// Driver codelet s = "ADOBECODEBANC";let t = "ABC";document.write("-->Smallest window that " + "contain all character : <br>");document.write(Minimum_Window( s.split(""), t.split("")));// This code is contributed by rag2127</script> |
Output:
-->Smallest window that contain all character : BANC
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