Minimum number of given operations required to make two strings equal

0 0 12 minutes read

Given two strings A and B, both strings contain characters a and b and are of equal lengths. There is one _ (empty space) in both the strings. The task is to convert first string into second string by doing the minimum number of the following operations:

If _ is at position i then _ can be swapped with a character at position i+1 or i-1.
If characters at positions i+1 and i+2 are different then _ can be swapped with a character at position i+1 or i+2.
Similarly, if characters at positions i-1 and i-2 are different then _ can be swapped with a character at position i-1 or i-2.

Examples:

Input: A = “aba_a”, B = “_baaa”
Output: 2
Move 1 : A = “ab_aa” (Swapped A[2] with A[3]) Move 2 : A = “_baaa” (Swapped A[0] with A[2])

Input: A = “a_b”, B = “ab_”
Output: 1

Source: Directi Interview Set 7

Approach:

Apply a simple Breadth First Search over the string and an element of the queue used for BFS will contain the pair str, pos where pos is the position of _ in the string str.
Also maintain a map vis which will store the string as key and the minimum moves to get to the string as value.
For every string str from the queue, generate a new string tmp based on the four conditions given and update the vis map as vis[tmp] = vis[str] + 1.
Repeat the above steps until the queue is empty or the required string is generated i.e. tmp == B
If the required string is generated then return vis[str] + 1 which is the minimum number of operations required to change A to B.

Below is the implementation of the above approach:

C++

// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the minimum number of
// operations to convert string A to B
int minOperations(string s, string f)
{
 
    // If both the strings are equal then
    // no operation needs to be performed
    if (s == f)
        return 0;
 
    unordered_map<string, int> vis;
 
    int n;
 
    n = s.length();
    int pos = 0;
    for (int i = 0; i < s.length(); i++) {
        if (s[i] == '_') {
 
            // store the position of '_'
            pos = i;
            break;
        }
    }
 
    // to store the generated string at every
    // move and the position of '_' within it
    queue<pair<string, int> > q;
 
    q.push({ s, pos });
 
    // vis will store the minimum operations
    // to reach that particular string
    vis[s] = 0;
 
    while (!q.empty()) {
        string ss = q.front().first;
        int pp = q.front().second;
 
        // minimum moves to reach the string ss
        int dist = vis[ss];
        q.pop();
 
        // try all 4 possible operations
 
        // if '_' can be swapped with
        // the character on it's left
        if (pp > 0) {
 
            // swap with the left character
            swap(ss[pp], ss[pp - 1]);
 
            // if the string is generated
            // for the first time
            if (!vis.count(ss)) {
 
                // if generated string is
                // the required string
                if (ss == f) {
                    return dist + 1;
                    break;
                }
 
                // update the distance for the
                // currently generated string
                vis[ss] = dist + 1;
                q.push({ ss, pp - 1 });
            }
 
            // restore the string before it was
            // swapped to check other cases
            swap(ss[pp], ss[pp - 1]);
        }
 
        // swap '_' with the character
        // on it's right this time
        if (pp < n - 1) {
            swap(ss[pp], ss[pp + 1]);
            if (!vis.count(ss)) {
                if (ss == f) {
                    return dist + 1;
                    break;
                }
                vis[ss] = dist + 1;
                q.push({ ss, pp + 1 });
            }
            swap(ss[pp], ss[pp + 1]);
        }
 
        // if '_' can be swapped
        // with the character 'i+2'
        if (pp > 1 && ss[pp - 1] != ss[pp - 2]) {
            swap(ss[pp], ss[pp - 2]);
            if (!vis.count(ss)) {
                if (ss == f) {
                    return dist + 1;
                    break;
                }
                vis[ss] = dist + 1;
                q.push({ ss, pp - 2 });
            }
            swap(ss[pp], ss[pp - 2]);
        }
 
        // if '_' can be swapped
        // with the character at 'i+2'
        if (pp < n - 2 && ss[pp + 1] != ss[pp + 2]) {
            swap(ss[pp], ss[pp + 2]);
            if (!vis.count(ss)) {
                if (ss == f) {
                    return dist + 1;
                    break;
                }
                vis[ss] = dist + 1;
                q.push({ ss, pp + 2 });
            }
            swap(ss[pp], ss[pp + 2]);
        }
    }
}
 
// Driver code
int main()
{
 
    string A = "aba_a";
    string B = "_baaa";
 
    cout << minOperations(A, B);
 
    return 0;
}

Java

// Java implementation of the above approach
import java.util.*;
 
class GFG {
 
  // Function to return the minimum number of
  // operations to convert string A to B
  static int minOperations(String s, String f)
  {
 
    // If both the strings are equal then
    // no operation needs to be performed
    if (s.equals(f))
      return 0;
 
    Map<String, Integer> vis = new HashMap<>();
 
    int n;
 
    n = s.length();
    int pos = 0;
    for (int i = 0; i < s.length(); i++) {
      if (s.charAt(i) == '_') {
 
        // store the position of '_'
        pos = i;
        break;
      }
    }
 
    // to store the generated string at every
    // move and the position of '_' within it
    Queue<Map.Entry<String, Integer>> q
      = new LinkedList<Map.Entry<String, Integer>>();
 
    q.add(new AbstractMap.SimpleEntry<String, Integer>(s, pos));
 
    // vis will store the minimum operations
    // to reach that particular string
    vis.put(s, 0);
 
    while (!q.isEmpty()) {
      String ss = q.peek().getKey();
      int pp = q.peek().getValue();
 
      // minimum moves to reach the string ss
      int dist = vis.get(ss);
      q.remove();
 
      // try all 4 possible operations
 
      // if '_' can be swapped with
      // the character on it's left
      if (pp > 0) {
 
        // swap with the left character
        char[] ch = ss.toCharArray();
        char temp = ch[pp];
        ch[pp] = ch[pp - 1];
        ch[pp - 1] = temp;
        ss = String.valueOf(ch);
 
        // if the string is generated
        // for the first time
        if (!vis.containsKey(ss)) {
 
          // if generated string is
          // the required string
          if (ss.equals(f)) {
            return dist + 1;
          }
 
          // update the distance for the
          // currently generated string
          vis.put(ss, dist + 1);
          q.add(new AbstractMap.SimpleEntry<String, Integer>(ss, pp - 1));
        }
 
        // restore the string before it was
        // swapped to check other cases
        ch = ss.toCharArray();
        temp = ch[pp];
        ch[pp] = ch[pp - 1];
        ch[pp - 1] = temp;
        ss = String.valueOf(ch);
      }
 
      // swap '_' with the character
      // on it's right this time
      if (pp < n - 1) {
        char[] ch = ss.toCharArray();
        char temp = ch[pp];
        ch[pp] = ch[pp + 1];
        ch[pp + 1] = temp;
        ss = String.valueOf(ch);
        if (!vis.containsKey(ss)) {
          if (ss.equals(f)) {
            return dist + 1;
          }
          vis.put(ss, dist + 1);
          q.add(new AbstractMap.SimpleEntry<String, Integer>(ss, pp + 1));
        }
        ch = ss.toCharArray();
        temp = ch[pp];
        ch[pp] = ch[pp + 1];
        ch[pp + 1] = temp;
        ss = String.valueOf(ch);
      }
 
      // if '_' can be swapped
      // with the character 'i+2'
      if (pp > 1 && ss.charAt(pp - 1) != ss.charAt(pp - 2)) {
        char[] ch = ss.toCharArray();
        char temp = ch[pp];
        ch[pp] = ch[pp - 2];
        ch[pp - 2] = temp;
        ss = String.valueOf(ch);
        if (!vis.containsKey(ss)) {
          if (ss.equals(f)) {
            return dist + 1;
          }
          vis.put(ss, dist + 1);
          q.add(new AbstractMap.SimpleEntry<String, Integer>(ss, pp - 2));
        }
        ch = ss.toCharArray();
        temp = ch[pp];
        ch[pp] = ch[pp - 2];
        ch[pp - 2] = temp;
        ss = String.valueOf(ch);
      }
 
      // if '_' can be swapped
      // with the character at 'i+2'
      if (pp < n - 2 && ss.charAt(pp + 1) != ss.charAt(pp + 2)) {
        char[] ch = ss.toCharArray();
        char temp = ch[pp];
        ch[pp] = ch[pp + 2];
        ch[pp + 2] = temp;
        ss = String.valueOf(ch);
        if (!vis.containsKey(ss)) {
          if (ss.equals(f)) {
            return dist + 1;
          }
          vis.put(ss, dist + 1);
          q.add(new AbstractMap.SimpleEntry<String, Integer>(ss, pp + 2));
        }
        ch = ss.toCharArray();
        temp = ch[pp];
        ch[pp] = ch[pp + 2];
        ch[pp + 2] = temp;
        ss = String.valueOf(ch);
      }
    }
    return -1;
  }
 
  // Driver code
  public static void main(String[] args)
  {
 
    String A = "aba_a";
    String B = "_baaa";
 
    System.out.println(minOperations(A, B));
  }
}

Python3

# Python3 implementation of the approach
from collections import deque
 
# Function to return the minimum number of
# operations to convert string A to B
def minOperations(s: str, f: str) -> int:
 
    # If both the strings are equal then
    # no operation needs to be performed
    if s == f:
        return 0
 
    vis = dict()
    n = len(s)
    pos = 0
    for i in range(n):
        if s[i] == '_':
 
            # store the position of '_'
            pos = i
            break
 
    # to store the generated string at every
    # move and the position of '_' within it
    q = deque()
    q.append((s, pos))
 
    # vis will store the minimum operations
    # to reach that particular string
    vis[s] = 0
 
    while q:
        ss = q[0][0]
        pp = q[0][1]
 
        # minimum moves to reach the string ss
        dist = vis[ss]
        q.popleft()
 
        ss = list(ss)
 
        # try all 4 possible operations
 
        # if '_' can be swapped with
        # the character on it's left
        if pp > 0:
 
            # swap with the left character
            ss[pp], ss[pp - 1] = ss[pp - 1], ss[pp]
            ss = ''.join(ss)
 
            # if the string is generated
            # for the first time
            if ss not in vis:
 
                # if generated string is
                # the required string
                if ss == f:
                    return dist + 1
 
                # update the distance for the
                # currently generated string
                vis[ss] = dist + 1
                q.append((ss, pp - 1))
 
            ss = list(ss)
 
            # restore the string before it was
            # swapped to check other cases
            ss[pp], ss[pp - 1] = ss[pp - 1], ss[pp]
            ss = ''.join(ss)
 
        # swap '_' with the character
        # on it's right this time
        if pp < n - 1:
            ss = list(ss)
            ss[pp], ss[pp + 1] = ss[pp + 1], ss[pp]
            ss = ''.join(ss)
 
            if ss not in vis:
                if ss == f:
                    return dist + 1
 
                vis[ss] = dist + 1
                q.append((ss, pp + 1))
 
            ss = list(ss)
            ss[pp], ss[pp + 1] = ss[pp + 1], ss[pp]
            ss = ''.join(ss)
 
        # if '_' can be swapped
        # with the character 'i+2'
        if pp > 1 and ss[pp - 1] != ss[pp - 2]:
            ss = list(ss)
            ss[pp], ss[pp - 2] = ss[pp - 2], ss[pp]
            ss = ''.join(ss)
 
            if ss not in vis:
                if ss == f:
                    return dist + 1
 
                vis[ss] = dist + 1
                q.append((ss, pp - 2))
 
            ss = list(ss)
            ss[pp], ss[pp - 2] = ss[pp - 2], ss[pp]
            ss = ''.join(ss)
 
        # if '_' can be swapped
        # with the character at 'i+2'
        if pp < n - 2 and ss[pp + 1] != ss[pp + 2]:
            ss = list(ss)
            ss[pp], ss[pp + 2] = ss[pp + 2], ss[pp]
            ss = ''.join(ss)
 
            if ss not in vis:
                if ss == f:
                    return dist + 1
 
                vis[ss] = dist + 1
                q.append((ss, pp + 2))
 
            ss = list(ss)
            ss[pp], ss[pp + 2] = ss[pp + 2], ss[pp]
            ss = ''.join(ss)
 
# Driver Code
if __name__ == "__main__":
 
    A = "aba_a"
    B = "_baaa"
 
    print(minOperations(A, B))
 
# This code is contributed by
# sanjeev2552

Javascript

// JavaScript implementation of the approach
 
// Function to return the minimum number of
// operations to convert string A to B
function minOperations(s, f) {
     
    // If both the strings are equal then
    // no operation needs to be performed
    if (s === f) {
        return 0;
    }
 
    let vis = {};
    let n = s.length;
    let pos = 0;
    for (let i = 0; i < n; i++) {
        if (s[i] === '_') {
            // store the position of '_'
            pos = i;
            break;
        }
    }
     
     
    // to store the generated string at every
    // move and the position of '_' within it
    let q = [];
    q.push([s, pos]);
     
     
    // vis will store the minimum operations
    // to reach that particular string
    vis[s] = 0;
 
    while (q.length) {
        let [ss, pp] = q[0];
         
        // minimum moves to reach the string ss
        let dist = vis[ss];
        q.shift();
        ss = ss.split('');
         
         
        // try all 4 possible operations
 
        // if '_' can be swapped with
        // the character on it's left
        if (pp > 0) {
             
            // swap with the left character
            [ss[pp], ss[pp - 1]] = [ss[pp - 1], ss[pp]];
            ss = ss.join('');
             
             
            // if the string is generated
            // for the first time
            if (!(ss in vis)) {
                 
                 
                // if generated string is
                // the required string
                if (ss === f) {
                    return dist + 1;
                }
                 
                 
                // update the distance for the
                // currently generated string
                vis[ss] = dist + 1;
                q.push([ss, pp - 1]);
            }
 
            ss = ss.split('');
             
            // restore the string before it was
            // swapped to check other cases
            [ss[pp], ss[pp - 1]] = [ss[pp - 1], ss[pp]];
            ss = ss.join('');
        }
 
         
        // swap '_' with the character
        // on it's right this time
        if (pp < n - 1) {
            ss = ss.split('');
            [ss[pp], ss[pp + 1]] = [ss[pp + 1], ss[pp]];
            ss = ss.join('');
 
            if (!(ss in vis)) {
                if (ss === f) {
                    return dist + 1;
                }
 
                vis[ss] = dist + 1;
                q.push([ss, pp + 1]);
            }
 
            ss = ss.split('');
            [ss[pp], ss[pp + 1]] = [ss[pp + 1], ss[pp]];
            ss = ss.join('');
        }
 
         
         
        // if '_' can be swapped
        // with the character 'i+2'
        if (pp > 1 && ss[pp - 1] !== ss[pp - 2]) {
            ss = ss.split('');
            [ss[pp], ss[pp - 2]] = [ss[pp - 2], ss[pp]];
            ss = ss.join('');
 
            if (!(ss in vis)) {
                if (ss === f) {
                    return dist + 1;
                }
 
                vis[ss] = dist + 1;
                q.push([ss, pp - 2]);
            }
 
            ss = ss.split('');
            [ss[pp], ss[pp - 2]] = [ss[pp - 2], ss[pp]];
            ss = ss.join('');
        }
         
     
        // if '_' can be swapped
        // with the character at 'i+2'
        if (pp < n - 2 && ss[pp + 1] !== ss[pp + 2]) {
            ss = ss.split('');
            [ss[pp], ss[pp + 2]] = [ss[pp + 2], ss[pp]];
            ss = ss.join('');
 
            if (!(ss in vis)) {
                if (ss === f) {
                    return dist + 1;
                }
 
                vis[ss] = dist + 1;
                q.push([ss, pp + 2]);
            }
 
            ss = ss.split('');
            [ss[pp], ss[pp + 2]] = [ss[pp + 2], ss[pp]];
            ss = ss.join('');
        }
    }
}
 
// Driver Code
let A = "aba_a";
let B = "_baaa";
console.log(minOperations(A, B))
 
// This code is contributed by codebraxnzt

C#

using System;
using System.Collections.Generic;
 
class GFG
{
    // Function to return the minimum number of
    // operations to convert string A to B
    static int minOperations(string s, string f)
    {
        // If both the strings are equal then
        // no operation needs to be performed
        if (s == f)
            return 0;
 
        Dictionary<string, int> vis = new Dictionary<string, int>();
 
        int n = s.Length;
        int pos = 0;
        for (int i = 0; i < s.Length; i++)
        {
            if (s[i] == '_')
            {
                // store the position of '_'
                pos = i;
                break;
            }
        }
 
        // to store the generated string at every
        // move and the position of '_' within it
        Queue<Tuple<string, int>> q = new Queue<Tuple<string, int>>();
 
        q.Enqueue(new Tuple<string, int>(s, pos));
 
        // vis will store the minimum operations
        // to reach that particular string
        vis[s] = 0;
 
        while (q.Count > 0)
        {
            string ss = q.Peek().Item1;
            int pp = q.Peek().Item2;
 
            // minimum moves to reach the string ss
            int dist = vis[ss];
            q.Dequeue();
 
            // try all 4 possible operations
 
            // if '_' can be swapped with
            // the character on it's left
            if (pp > 0)
            {
                // swap with the left character
                char[] arr = ss.ToCharArray();
                char temp = arr[pp];
                arr[pp] = arr[pp - 1];
                arr[pp - 1] = temp;
                ss = new string(arr);
 
                // if the string is generated
                // for the first time
                if (!vis.ContainsKey(ss))
                {
                    // if generated string is
                    // the required string
                    if (ss == f)
                        return dist + 1;
 
                    // update the distance for the
                    // currently generated string
                    vis[ss] = dist + 1;
                    q.Enqueue(new Tuple<string, int>(ss, pp - 1));
                }
 
                // restore the string before it was
                // swapped to check other cases
                arr = ss.ToCharArray();
                temp = arr[pp];
                arr[pp] = arr[pp - 1];
                arr[pp - 1] = temp;
                ss = new string(arr);
            }
 
            // swap '_' with the character
            // on it's right this time
            if (pp < n - 1)
            {
                char[] arr = ss.ToCharArray();
                char temp = arr[pp];
                arr[pp] = arr[pp + 1];
                arr[pp + 1] = temp;
                ss = new string(arr);
                if (!vis.ContainsKey(ss))
                {
                    if (ss == f)
                        return dist + 1;
 
                    vis[ss] = dist + 1;
                    q.Enqueue(new Tuple<string, int>(ss, pp + 1));
                }
                arr = ss.ToCharArray();
                temp = arr[pp];
                arr[pp] = arr[pp + 1];
                arr[pp + 1] = temp;
                ss = new string(arr);
            }
             
            // if '_' can be swapped
            // with the character 'i+2'
            if (pp > 1 && ss[pp - 1] != ss[pp - 2]) {
                char[] arr = ss.ToCharArray();
                char temp = arr[pp];
                arr[pp] = arr[pp - 2];
                arr[pp - 2] = temp;
                ss = new string(arr);
                if (!vis.ContainsKey(ss)) {
                    if (ss == f) {
                        return dist + 1;
                    }
                    vis[ss] = dist + 1;
                    q.Enqueue(new Tuple<string, int>(ss, pp - 2));
 
                }
                arr = ss.ToCharArray();
                temp = arr[pp];
                arr[pp] = arr[pp - 2];
                arr[pp - 2] = temp;
                ss = new string(arr);
            }
     
            // if '_' can be swapped
            // with the character at 'i+2'
            if (pp < n - 2 && ss[pp + 1] != ss[pp + 2]) {
                char[] arr = ss.ToCharArray();
                char temp = arr[pp];
                arr[pp] = arr[pp + 2];
                arr[pp + 2] = temp;
                ss = new string(arr);
                 
                if (!vis.ContainsKey(ss)) {
                    if (ss == f) {
                        return dist + 1;
                    }
                    vis[ss] = dist + 1;
                    q.Enqueue(new Tuple<string, int>(ss, pp + 2));
                }
                arr = ss.ToCharArray();
                temp = arr[pp];
                arr[pp] = arr[pp + 2];
                arr[pp + 2] = temp;
                ss = new string(arr);
                 
            }
        }
        return -1;
    }
     
    // Driver code
    public static void Main()
    {
     
        string A = "aba_a";
        string B = "_baaa";
     
        Console.Write(minOperations(A, B));
     
    }
}

Output

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!