Find minimum number of Substrings with unique characters

Last Updated : 19 Apr, 2023

Given string 's', the task is to divide a given string s into multiple substrings, with each substring containing only unique characters. This means that no character should be repeated within a single substring. The goal is to find the minimum number of such substrings required to satisfy this condition.

Examples:

Input: s = "abacaba"
Output: 4
Explanation: Two possible partitions are ("a", "ba", "cab", "a") and ("ab", "a", "ca", "ba"). It can be shown that 4 is the minimum number of substrings needed.

Input: s = "ssssss"
Output: 6
Explanation: The only valid partition is ("s", "s", "s", "s", "s", "s").

Naive Approach: The basic way to solve the problem follows the below idea:

We initialize an empty set and iterate through the given string. For each character encountered, we check if it is already present in the set.
If it is, this means that we need to start a new substring since the current substring has a repeated character. We increase our answer variable and clear the set to start a new substring. We then add the current character to the set.
After iterating through the entire string, the value of the answer variable gives us the minimum number of substrings required to partition the given string such that each substring has unique characters.

Below is the implementation for the above approach:

C++

// C++ program to Finding minimum number // of Substrings with unique Characters #include <bits/stdc++.h> using namespace std;  // Function to Find Minimum Number of // Substrings with Unique Characters int partitionString(string s) {      // Create an unordered set to     // store unique characters     unordered_set<char> st;      // Initialize the answer     // variable to 1     int ans = 1;      // Iterate through the given string     for (int i = 0; i < s.size(); i++) {          // Check if the current character         // is already present in the set         if (st.find(s[i]) != st.end()) {              // If it is, increment the             // answer variable and clear             // the set to start a             // new substring             ans++;             st.clear();         }          // Add the current character         // to the set         st.insert(s[i]);     }      // Return the answer variable, which     // gives the minimum number     // of substrings required     return ans; }  // Drivers code int main() {     string S = "abacaba";      // Function Call     cout << "Minimum Number of Substrings with Unique "             "Characters: "          << partitionString(S);      return 0; }

Java

// Java program to Finding Minimum Number of Substrings with // Unique Characters import java.util.*;  // Function to Find Minimum Number of Substrings with Unique // Characters class GFG {     static int partitionString(String s)     {         // Create a HashSet to store unique characters         Set<Character> set = new HashSet<>();         // Initialize the answer variable to 1         int ans = 1;         // Iterate through the given string         for (int i = 0; i < s.length(); i++) {             // Check if the current character is already             // present in the set             if (set.contains(s.charAt(i))) {                 // If it is, increment the answer variable                 // and clear the set to start a new                 // substring                 ans++;                 set.clear();             }             // Add the current character to the set             set.add(s.charAt(i));         }         // Return the answer variable, which gives the         // minimum number of substrings required         return ans;     }      public static void main(String[] args)     {         String S = "abacaba";          System.out.print(partitionString(S));     } } // This code is contributed by Ravi Singh

Python3

# Function to Find Minimum Number of # Substrings with Unique Characters def partitionString(s):     # Create an unordered set to     # store unique characters     st = set()      # Initialize the answer     # variable to 1     ans = 1      # Iterate through the given string     for i in range(len(s)):         # Check if the current character         # is already present in the set         if s[i] in st:             # If it is, increment the             # answer variable and clear             # the set to start a             # new substring             ans += 1             st.clear()          # Add the current character         # to the set         st.add(s[i])      # Return the answer variable, which     # gives the minimum number     # of substrings required     return ans   # Drivers code S = "abacaba"  # Function Call print("Minimum Number of Substrings with Unique Characters:", partitionString(S))

// C# program to Finding Minimum Number of Substrings with // Unique Characters  using System; using System.Collections.Generic;  public class GFG {      static int partitionString(string s)     {         // Create a HashSet to store unique characters         HashSet<char> set = new HashSet<char>();         // Initialize the answer variable to 1         int ans = 1;         // Iterate through the given string         for (int i = 0; i < s.Length; i++) {             // Check if the current character is already             // present in the set             if (set.Contains(s[i])) {                 // If it is, increment the answer variable                 // and clear the set to start a new                 // substring                 ans++;                 set.Clear();             }             // Add the current character to the set             set.Add(s[i]);         }         // Return the answer variable, which gives the         // minimum number of substrings required         return ans;     }      static public void Main()     {          // Code         String S = "abacaba";          Console.Write("Minimum Number of Substrings with Unique Characters: " + partitionString(S));     } }  // THis code is contributed by karthik

JavaScript

// JavaScript program to Finding minimum number // of Substrings with unique Characters  // Function to Find Minimum Number of Substrings with Unique // Characters function partitionString(s) {     // Create a set to store unique characters     let st = new Set();      // Initialize the answer     // variable to 1     let ans = 1;      // Iterate through the given string     for (let i = 0; i < s.length; i++) {          // Check if the current character         // is already present in the set         if (st.has(s[i])) {              // If it is, increment the             // answer variable and clear             // the set to start a             // new substring             ans++;             st.clear();         }          // Add the current character         // to the set         st.add(s[i]);     }      // Return the answer variable, which     // gives the minimum number     // of substrings required     return ans; }  // Driver code let S = "abacaba";  // Function Call console.log(     "Minimum Number of Substrings with Unique Characters: "     + partitionString(S));

Output

Minimum Number of Substrings with Unique Characters: 4

Time Complexity: O(n) where n is the length of the input string.
Auxiliary Space: O(n) in the worst case This is because we store each character of the input string in the hash set, and in the worst case, all characters of the string are unique.

Efficient Approach: To solve the problem using a Greedy approach follow the below idea:

To solve this problem, we need to keep track of the last occurrence of each character in the string s. Whenever we encounter a repeated character, we know that the current substring contains a character that is repeated, so we need to start a new substring. We can determine the start of the new substring by setting the value of start to the index of the repeated character. We also increased the value of ans to indicate that we have started a new substring.

Below are the steps for the above approach:

Create an array list of size 26 to store the last index of each character (initially set to -1).
Initialize the starting index of the current substring to 0.
Initialize the answer variable ans to 1.
Iterate through the given string s:
- Get the index of the current character in the array by subtracting 'a' from it.
- Check if the current character is already present in the current substring by comparing its last index with the starting index of the current substring.
- If it is, increment the answer variable ans and update the starting index of the new substring to the current index.
Update the last index of the current character in the array with the current index.
Return the answer variable ans, which gives the minimum number of substrings required.

Below is the implementation for the above approach:

C++

// C++ program to Finding Minimum // Number of Substrings with // Unique Characters  #include <bits/stdc++.h> using namespace std;  // Function to Find Minimum Number of // Substrings with Unique characters int partitionString(string s) {      // Create an array to store the     // last index of each character     vector<int> last(26, -1);      // Initialize the starting index     // of the current substring to 0     int start = 0;      // Initialize the answer variable to 1     int ans = 1;      // Iterate through the given string     for (int i = 0; i < s.length(); i++) {          // Get the index of the current         // character in the array         int index = s[i] - 'a';          // Check if the current character         // is already present in the         // current substring         if (last[index] >= start) {              // If it is, increment the answer             // variable and update the             // starting index of the             // new substring             ans++;             start = i;         }          // Update the last index         // of the current character         last[index] = i;     }      // Return the answer variable, which     // gives the minimum number of     // substrings required     return ans; }  // Drivers code int main() {      string S = "abacaba";      // Function Call     cout << "Minimum Number of Substrings with Unique "             "Characters: "          << partitionString(S);      return 0; }

Java

// Java program to Finding Minimum Number of Substrings with // Unique Characters import java.util.*;  // Function to Find Minimum Number of Substrings with Unique // Characters  class GFG {     static int partitionString(String s)     {         // Create an array to store the last index of each         // character         int[] last = new int[26];         Arrays.fill(last, -1);          // Initialize the starting index of the current         // substring to 0         int start = 0;          // Initialize the answer variable to 1         int ans = 1;          // Iterate through the given string         for (int i = 0; i < s.length(); i++) {             // Get the index of the current character in the             // array             int index = s.charAt(i) - 'a';              // Check if the current character is already             // present in the current substring             if (last[index] >= start) {                 // If it is, increment the answer variable                 // and update the starting index of the new                 // substring                 ans++;                 start = i;             }              // Update the last index of the current             // character             last[index] = i;         }          // Return the answer variable, which gives the         // minimum number of substrings required         return ans;     }      public static void main(String[] args)     {          String S = "ssssss";          System.out.print(partitionString(S));     } } // This code is contributed by Ravi Singh

Python3

# Function to Find Minimum Number of # Substrings with Unique characters def partitionString(s):     # Create an array to store the     # last index of each character     last = [-1] * 26      # Initialize the starting index     # of the current substring to 0     start = 0      # Initialize the answer variable to 1     ans = 1      # Iterate through the given string     for i in range(len(s)):         # Get the index of the current         # character in the array         index = ord(s[i]) - ord('a')          # Check if the current character         # is already present in the         # current substring         if last[index] >= start:             # If it is, increment the answer             # variable and update the             # starting index of the             # new substring             ans += 1             start = i          # Update the last index         # of the current character         last[index] = i      # Return the answer variable, which     # gives the minimum number of     # substrings required     return ans   # Drivers code if __name__ == '__main__':     S = "abacaba"      # Function Call     print("Minimum Number of Substrings with Unique Characters: ", partitionString(S))

using System; using System.Collections.Generic;  public class Program {   // Function to find minimum number of substrings with unique characters   public static int PartitionString(string s)   {     // Create a dictionary to store the last index of each character     Dictionary<char, int> last = new Dictionary<char, int>();      // Initialize the starting index of the current substring to 0     int start = 0;      // Initialize the answer variable to 1     int ans = 1;      // Iterate through the given string     for (int i = 0; i < s.Length; i++)     {       char c = s[i];        // Check if the current character is       // already present in the current substring       if (last.ContainsKey(c) && last[c] >= start)       {         // If it is, increment the answer variable and         // update the starting index of the new substring         ans++;         start = i;       }        // Update the last index of the current character       last[c] = i;     }      // Return the answer variable, which gives      // the minimum number of substrings required     return ans;   }    // Driver's code   public static void Main()   {     string S = "abacaba";      // Function call     Console.WriteLine("Minimum Number of Substrings with Unique Characters: " + PartitionString(S));   } } // This code is contributed by Prajwal Kandekar

JavaScript

// JavaScript program to Finding Minimum // Number of Substrings with // Unique Characters  function partitionString(s) {    // Create an array to store the   // last index of each character   const last = new Array(26).fill(-1);    // Initialize the starting index   // of the current substring to 0   let start = 0;    // Initialize the answer variable to 1   let ans = 1;    // Iterate through the given string   for (let i = 0; i < s.length; i++) {      // Get the index of the current     // character in the array     const index = s.charCodeAt(i) - 97;      // Check if the current character     // is already present in the     // current substring     if (last[index] >= start) {        // If it is, increment the answer       // variable and update the       // starting index of the       // new substring       ans++;       start = i;     }      // Update the last index     // of the current character     last[index] = i;   }    // Return the answer variable, which   // gives the minimum number of   // substrings required   return ans; }  // Example usage const S = "abacaba"; console.log(`Minimum Number of Substrings with Unique Characters: ${partitionString(S)}`);

Output

Minimum Number of Substrings with Unique Characters: 4

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

Find the number of Substrings with even number of K

the_ravisingh

Improve

Article Tags :

Practice Tags :

Find minimum number of Substrings with unique characters

Similar Reads