Longest mutation sequence

Given a list of conversion tuples Arr[], such that string Arr[i][0] gets converted to string Arr[i][1]. A character is considered good if it has one-to-one mapping to some other character throughout all the conversions, for example during conversion of “abb” to “abc”, b->c is considered good. Your task is to find the longest chain of good characters in the form x->y->z… where x,y, and z are good characters.

Examples:

Input: {{‘ab’, ‘ac’}, {‘yz’, ‘xz’},{‘ee’, ‘ee’},{‘aaac’, ‘abag’},{‘g’, ‘h’}}
Output: {a, b, c, g, h}
Explanation:
tuple 1: b -> c.
tuple 2: y -> x.
tuple 3: no mutations occurred
tuple 4: a -> b, and c -> g
tuple 5: g -> h
the longest mutation sequence is [‘a->b->c->g->h’].

Input: { {“term”, “team”},{“drift”, “draft”}}
Output: { i, a }

Approach Using BFS:

The approach involves constructing a directed graph based on observed good conversions in the tuples, performing a modified BFS (Breadth-First Search) to traverse the graph, and updating the longest good chain, resulting in an efficient solution to identify the sequence of good character conversions.

Steps to solve the problem:

• Create a graph and Initialize adj (adjacency list) and ind (in-degree array).
• For each tuple in arr
  • Compare corresponding letters of the first and second words.
  • If different, update adj and ind based on the character changes.
• Initialize a queue qu with nodes having in-degree 0.
• Initialize variables ans (answer) and maxi (maximum chain length).
• While qu is not empty:
  • Pop a node from qu.
  • Traverse the chain of good characters:
  • Add each letter to the ans.
  • Update maxi if the current chain is longer.
  • Push connected nodes with in-degree 0 to qu.
• Print the longest good character chain stored in ans.

Below is the implementation of the approach:

C++

#include <bits/stdc++.h>
#define ll long long
using namespace std;

void longestGoodSequence(vector<pair<string, string> >& arr,
                         vector<int> adj[],
                         vector<int>& ind)
{
    // Initialize a queue with nodes having in-degree 0
    queue<int> q;
    for (int i = 0; i < 26; i++) {
        if (ind[i] == 0) {
            q.push(i);
        }
    }
    // Variables to store the answer
    vector<char> ans;
    ll maxi = 1;
    // Perform topological sort
    while (q.empty() == false) {
        vector<char> ans1;
        int for1 = q.front();
        q.pop();
        ans1.push_back(for1 + 'a');

        // Traverse the chain of mutations
        while (adj[for1].size() > 0) {
            ans1.push_back(adj[for1][0] + 'a');
            for1 = adj[for1][0];
        }

        // Update the answer if the current chain is longer
        if (ans1.size() > maxi) {
            maxi = ans1.size();
            ans = ans1;
        }
    }

    // Output the result
    for (int i = 0; i < ans.size(); i++) {
        cout << ans[i] << " ";
    }
}

int main()
{
    // User-defined input for the tuples of words
    vector<pair<string, string> > arr
        = { { "ab", "ac" },
            { "yz", "xz" },
            { "ee", "ee" },
            { "aaac", "abag" },
            { "g", "h" } };

    // Create adjacency list and in-degree array
    vector<int> adj[26];
    vector<int> ind(26, 0);

    // Build the adjacency list and in-degree array
    for (int i = 0; i < arr.size(); i++) {
        ll len = arr[i].first.size();
        for (int j = 0; j < len; j++) {
            if (arr[i].first[j] != arr[i].second[j]) {
                ll val1 = arr[i].first[j] - 'a';
                ll val2 = arr[i].second[j] - 'a';
                ind[val2]++;
                adj[val1].push_back(val2);
            }
        }
    }
    longestGoodSequence(arr, adj, ind);
    return 0;
}

Java

import java.util.*;

public class GFG {

    public static void longestGoodSequence(List<Pair<String, String>> arr, List<Integer>[] adj, List<Integer> ind) {
        // Initialize a queue with nodes having in-degree 0
        Queue<Integer> q = new LinkedList<>();
        for (int i = 0; i < 26; i++) {
            if (ind.get(i) == 0) {
                q.add(i);
            }
        }

        // Variables to store the answer
        List<Character> ans = new ArrayList<>();
        long maxi = 1;

        // Perform topological sort
        while (!q.isEmpty()) {
            List<Character> ans1 = new ArrayList<>();
            int for1 = q.poll();
            ans1.add((char) (for1 + 'a'));

            // Traverse the chain of mutations
            while (!adj[for1].isEmpty()) {
                ans1.add((char) (adj[for1].get(0) + 'a'));
                for1 = adj[for1].get(0);
            }

            // Update the answer if the current chain is longer
            if (ans1.size() > maxi) {
                maxi = ans1.size();
                ans = new ArrayList<>(ans1);
            }
        }

        // Output the result
        for (char c : ans) {
            System.out.print(c + " ");
        }
    }

    public static void main(String[] args) {
        // User-defined input for the tuples of words
        List<Pair<String, String>> arr = Arrays.asList(
                new Pair<>("ab", "ac"),
                new Pair<>("yz", "xz"),
                new Pair<>("ee", "ee"),
                new Pair<>("aaac", "abag"),
                new Pair<>("g", "h")
        );

        // Create adjacency list and in-degree array
        List<Integer>[] adj = new ArrayList[26];
        for (int i = 0; i < 26; i++) {
            adj[i] = new ArrayList<>();
        }

        List<Integer> ind = new ArrayList<>(Collections.nCopies(26, 0));

        // Build the adjacency list and in-degree array
        for (Pair<String, String> pair : arr) {
            int len = pair.getFirst().length();
            for (int j = 0; j < len; j++) {
                if (pair.getFirst().charAt(j) != pair.getSecond().charAt(j)) {
                    int val1 = pair.getFirst().charAt(j) - 'a';
                    int val2 = pair.getSecond().charAt(j) - 'a';
                    ind.set(val2, ind.get(val2) + 1);
                    adj[val1].add(val2);
                }
            }
        }

        longestGoodSequence(arr, adj, ind);
    }

    static class Pair<K, V> {
        private K first;
        private V second;

        public Pair(K first, V second) {
            this.first = first;
            this.second = second;
        }

        public K getFirst() {
            return first;
        }

        public V getSecond() {
            return second;
        }
    }
}

Python3

from collections import deque

def longest_good_sequence(arr, adj, ind):
    # Initialize a queue with nodes having in-degree 0
    q = deque([i for i in range(26) if ind[i] == 0])

    # Variables to store the answer
    ans = []
    maxi = 1

    # Perform topological sort
    while q:
        ans1 = []
        for1 = q.popleft()
        ans1.append(chr(for1 + ord('a')))

        # Traverse the chain of mutations
        while adj[for1]:
            ans1.append(chr(adj[for1][0] + ord('a')))
            for1 = adj[for1].pop(0)

        # Update the answer if the current chain is longer
        if len(ans1) > maxi:
            maxi = len(ans1)
            ans = ans1

    # Output the result
    print(" ".join(ans))

if __name__ == "__main__":
    # User-defined input for the tuples of words
    arr = [
        ("ab", "ac"),
        ("yz", "xz"),
        ("ee", "ee"),
        ("aaac", "abag"),
        ("g", "h")
    ]

    # Create adjacency list and in-degree array
    adj = [[] for _ in range(26)]
    ind = [0] * 26

    # Build the adjacency list and in-degree array
    for tup in arr:
        for j in range(len(tup[0])):
            if tup[0][j] != tup[1][j]:
                val1 = ord(tup[0][j]) - ord('a')
                val2 = ord(tup[1][j]) - ord('a')
                ind[val2] += 1
                adj[val1].append(val2)

    longest_good_sequence(arr, adj, ind)

C#

using System;
using System.Collections.Generic;

public class GFG
{
    public static void LongestGoodSequence(List<Pair<string, string>> arr, List<int>[] adj, List<int> ind)
    {
        // Initialize a queue with nodes having in-degree 0
        Queue<int> q = new Queue<int>();
        for (int i = 0; i < 26; i++)
        {
            if (ind[i] == 0)
            {
                q.Enqueue(i);
            }
        }

        // Variables to store the answer
        List<char> ans = new List<char>();
        long maxi = 1;

        // Perform topological sort
        while (q.Count > 0)
        {
            List<char> ans1 = new List<char>();
            int for1 = q.Dequeue();
            ans1.Add((char)(for1 + 'a'));

            // Traverse the chain of mutations
            while (adj[for1].Count > 0)
            {
                ans1.Add((char)(adj[for1][0] + 'a'));
                for1 = adj[for1][0];
            }

            // Update the answer if the current chain is longer
            if (ans1.Count > maxi)
            {
                maxi = ans1.Count;
                ans = new List<char>(ans1);
            }
        }

        // Output the result
        foreach (char c in ans)
        {
            Console.Write(c + " ");
        }
    }

    public static void Main()
    {
        // User-defined input for the tuples of words
        List<Pair<string, string>> arr = new List<Pair<string, string>>
        {
            new Pair<string, string>("ab", "ac"),
            new Pair<string, string>("yz", "xz"),
            new Pair<string, string>("ee", "ee"),
            new Pair<string, string>("aaac", "abag"),
            new Pair<string, string>("g", "h")
        };

        // Create adjacency list and in-degree array
        List<int>[] adj = new List<int>[26];
        for (int i = 0; i < 26; i++)
        {
            adj[i] = new List<int>();
        }

        List<int> ind = new List<int>(new int[26]);

        // Build the adjacency list and in-degree array
        foreach (var pair in arr)
        {
            int len = pair.First.Length;
            for (int j = 0; j < len; j++)
            {
                if (pair.First[j] != pair.Second[j])
                {
                    int val1 = pair.First[j] - 'a';
                    int val2 = pair.Second[j] - 'a';
                    ind[val2]++;
                    adj[val1].Add(val2);
                }
            }
        }

        LongestGoodSequence(arr, adj, ind);
    }

    public class Pair<K, V>
    {
        private K first;
        private V second;

        public Pair(K first, V second)
        {
            this.first = first;
            this.second = second;
        }

        public K First { get { return first; } }

        public V Second { get { return second; } }
    }
}

Javascript

<script>

// Function to find the longest good sequence
function longestGoodSequence(arr, adj, ind) {
    let q = []; // Initialize an empty queue for nodes with in-degree 0

    // Loop to add nodes with in-degree 0 to the queue
    for (let i = 0; i < 26; i++) {
        if (ind[i] === 0) {
            q.push(i);
        }
    }

    let ans = []; // Array to store the answer
    let maxi = 1; // Variable to keep track of the maximum length found

    // Loop until the queue is empty
    while (q.length > 0) {
        let ans1 = []; // Temporary array to store the current sequence
        let for1 = q.shift(); // Remove and get the first element of the queue
        ans1.push(String.fromCharCode(for1 + 'a'.charCodeAt(0))); // Convert the number to its corresponding character and add to the sequence

        // Loop to traverse the chain of mutations
        while (adj[for1].length > 0) {
            ans1.push(String.fromCharCode(adj[for1][0] + 'a'.charCodeAt(0)));
            for1 = adj[for1].shift(); // Move to the next mutation in the chain
        }

        // If the current sequence is longer than the maximum found so far, update the answer
        if (ans1.length > maxi) {
            maxi = ans1.length;
            ans = ans1.slice(); // Copy the current sequence to the answer
        }
    }

    // Output the answer
    console.log(ans.join(" "));
}

function main() {
    // User-defined input for the tuples of words
    let arr = [
        ["ab", "ac"],
        ["yz", "xz"],
        ["ee", "ee"],
        ["aaac", "abag"],
        ["g", "h"]
    ];

    // Create adjacency list and in-degree array
    let adj = Array.from({length: 26}, () => []);
    let ind = new Array(26).fill(0);

    // Build the adjacency list and in-degree array based on the input
    arr.forEach(pair => {
        let len = pair[0].length;
        for (let j = 0; j < len; j++) {
            if (pair[0].charAt(j) !== pair[1].charAt(j)) {
                let val1 = pair[0].charCodeAt(j) - 'a'.charCodeAt(0);
                let val2 = pair[1].charCodeAt(j) - 'a'.charCodeAt(0);
                ind[val2]++; // Increment in-degree for the destination node
                adj[val1].push(val2); // Add an edge from the source node to the destination node
            }
        }
    });

    longestGoodSequence(arr, adj, ind); // Call the function to find and print the longest good sequence
}

main(); // Entry point of the program


</script>

Output

a b c g h 

Time Complexity: O(N * M), where N is the number of tuples and M is the maximum length of words in a tuple
Auxiliary Space: O(N + M).