Check if a string can be obtained by appending subsequences of another string

Given two strings str1 and str2 of lengths N and M respectively, the task is to check if str2 can be formed by appending subsequences of str1 multiple times. If possible, print the minimum number of append operations required. Otherwise, print -1.

Examples:

Input: str1 = “abb”, str2 = “ababbbbb”
Output: 4
Explanation:
String str2 can be formed by appending subsequences of str1 = “ab” + “abb” + “bb” + “b” = “ababbbbb”. Since at least 4 operations are required, print 4.

Input: str1 = “mt”, str2 = “atttm”
Output: -1
Explanation:
Since ‘a’ is not present in the string str1, str2 cannot be generated from str1. Therefore, print -1.

 

 Approach: The idea is to use the concept of Hashing based on the following observations below: 



  • Consider strings str1 = “abb” and str2 = “aba”. Find the position of character str2[0] in str1 whose index is greater than or equals to 0 i.e., index 0 of str1.
  • Again, find str2[1] in str1 such that its index is greater than or equals to 1 i.e., index 1 of str1.
  • Then, find str2[2] in str1 such that its index is greater than or equals to 2 which does not exist.
  • Therefore, start again from index 0 and find str2[2] in str1 having an index greater than or equals to index 0 i.e., index 0 of str1.
  • Hence, two subsequences “ab” and “a” can be appended to form “aba”.

Follow the below steps to solve the problem:

  • Initialize an array of vectors vec[] of length 26.
  • Push all the indices str1 having character ‘a’ in vec[0]. Similarly, push all indices having character ‘b’ in vec[1]. Do this for every character from ‘a’ to ‘z’.
  • Initialize a variable result with 1 and position with 0 to store the minimum operations and current position of str1.
  • Traverse the string str2 over the range [0, M] and for each character do the following:
    • If vec[str2[i] – ‘a’] is empty then the character str2[i] is not present in str1. Hence, the answer is not possible. Therefore, print -1.
    • Otherwise, find the lower bound of position in vec[str2[i] – ‘a’]. Let it be p. If p is equals the size of the vec[str2[i] – ‘a’] then increment the result by 1 and decrement i by 1 as answer for character str2[i] is not found yet and set position to 0.
    • Otherwise, set position as (vec[p] + 1).
  • After traversing, print the result as the minimum operations required.

Below is the implementation of the above approach:

C++

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// C++ program for the above approach
 
#include <bits/stdc++.h>
 
using namespace std;
 
// Function to find minimum operations
// required to form str2 by adding
// subsequences of str1
void find(string str1, string str2)
{
 
    // Initialize vector of length 26
    vector<int> vec1[26];
 
    // Push indices of characters of str1
    for (int i = 0; i < str1.size(); i++)
        vec1[str1[i] - 'a'].push_back(i);
 
    // Initialize the result & position
    int result = 1, position = 0;
 
    // Traverse the string str2
    for (int i = 0; i < str2.size(); i++)
    {
 
        char c = str2[i];
 
        // Return if no answer exist
        if (vec1.empty())
        {
            result = -1;
            break;
        }
 
        // Pointer of vec1[c-'a']
        vector<int>& vec2 = vec1;
 
        // Lower bound of position
        int p = lower_bound(vec2.begin(),
                            vec2.end(),
                            position)
                - vec2.begin();
 
        // If no index found
        if (p == vec2.size())
        {
            // Increment result
            result++;
            i--;
            position = 0;
            continue;
        }
 
        // Update the position
        else {
            position = vec2[p] + 1;
        }
    }
 
    // Print the result
    cout << result << '\n';
}
 
// Driver Code
int main()
{
    // Given string str1 & str2
    string str1 = "abb", str2 = "ababbbbb";
 
    // Function Call
    find(str1, str2);
 
    return 0;
}

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Java

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// C++ program for the above approach
import java.io.*;
import java.util.*;
 
class GFG {
 
    static void find(String str1, String str2)
    {
 
        List<List<Integer> > vec1
            = new ArrayList<List<Integer> >();
 
        // Initialize vector of length 26
        for (int i = 0; i < 26; i++) {
            vec1.add(new ArrayList<Integer>());
        }
 
        // Push indices of characters of str1
        for (int i = 0; i < str1.length(); i++)
            vec1.get(str1.charAt(i) - 'a').add(i);
 
        // Initialize the result & position
        int result = 1, position = 0;
 
        // Traverse the string str2
        for (int i = 0; i < str2.length(); i++)
        {
            char c = str2.charAt(i);
 
            // Return if no answer exist
            if (vec1.get(c - 'a').size() == 0)
            {
                result = -1;
                break;
            }
 
            List<Integer> vec2 = vec1.get(c - 'a');
 
            // Lower bound of position
            int p = lower_bound(vec2, position);
 
            // If no index found
            if (p == vec2.size())
            {
 
                // Increment result
                result++;
                i--;
                position = 0;
                continue;
            }
 
            // Update the position
            else {
                position = vec2.get(p) + 1;
            }
        }
 
        // Print the result
        System.out.println(result);
    }
 
    // Driver Code
    static int lower_bound(List<Integer> vec2, int position)
    {
        int low = 0, high = vec2.size() - 1;
 
        while (low < high) {
            int mid = (low + high) / 2;
            if (vec2.get(mid) < position)
                low = mid + 1;
            else
                high = mid;
        }
        return (vec2.get(low) < position) ? low + 1 : low;
    }
 
    public static void main(String[] args)
    {
        // Given string str1 & str2
        String str1 = "abb", str2 = "ababbbbb";
 
        // Function Call
        find(str1, str2);
    }
}

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Python3

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# Python3 program for the above approach
from bisect import bisect_left
 
# Function to find minimum operations
# required to form str2 by adding
# subsequences of str1
def find(str1, str2):
   
    # Initialize vector of length 26
    vec1 = [[] for i in range(26)]
 
    # Push indices of characters of str1
    for i in range(len(str1)):
        vec1[ord(str1[i]) - ord('a')].append(i)
 
    # Initialize the result & position
    result = 1
    position = 0
 
    # Traverse the str2
    i = 0
    while i < len(str2):
        c = str2[i]
 
        # Return if no answer exist
        if (len(vec1[ord(c) - ord('a')]) == 0):
            result = -1
            break
 
        # Pointer of vec1[c-'a']
        vec2 = vec1[ord(c) - ord('a')]
 
        # Lower bound of position
        p = bisect_left(vec2, position)
         
        #print(c)
 
        # If no index found
        if (p == len(vec2)):
 
            # Increment result
            result += 1
             
            #i-=1
            position = 0
            continue
             
        # Update the position
        else:
            i += 1
            position = vec2[p] + 1
 
    # Print the result
    print(result)
 
# Driver Code
if __name__ == '__main__':
   
    # Given str1 & str2
    str1 = "abb"
    str2 = "ababbbbb"
 
    # Function Call
    find(str1, str2)
 
# This code is contributed by mohit kumar 29

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Output

4

Time Complexity: O(N + M log N)
Auxiliary Space: O(M + N)

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