# Minimum number of pairs required to make two strings same

• Last Updated : 06 Mar, 2023

Given two strings s1 and s2 of same length, the task is to count the minimum number of pairs of characters (c1, c2) such that by transforming c1 to c2 or c2 to c1 any number of times in any string make both the strings same. Examples:

Input: s1 = “abb”, s2 = “dad” Output: 2 Transform ‘a’ -> ‘d’, ‘b’ -> ‘a’ and ‘b’ -> ‘a’ -> ‘d’ in s1. We can not take (a, d), (b, a), (b, d) as pairs because (b, d) can be achieved by following transformation ‘b’ -> ‘a’ -> ‘d’ Input: s1 = “drpepper”, s2 = “cocacola” Output: 7

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: This Problem can be solved by using Graphs or Disjoint Sets. Build an empty graph G and iterate through the strings. Add an edge in graph G only if one of the following conditions is met:

• Both s1[i] and s2[i] are not in G.
• s1[i] is in G but s2[i] is not in G.
• s2[i] is in G but s1[i] is not in G.
• There is no path from s1[i] to s2[i].

The minimum number of pairs will be the count of edges in the final graph G. Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function which will check if there is``// a path between a and b by using BFS``bool` `checkPath(``char` `a, ``char` `b,``           ``map<``char``, vector<``char``>> &G)``{``    ``map<``char``, ``bool``> visited;``    ``deque<``char``> queue;``    ``queue.push_back(a);``    ``visited[a] = ``true``;` `    ``while` `(!queue.empty())``    ``{``        ``int` `n = queue.front();``        ``queue.pop_front();` `        ``if` `(n == b) ``return` `true``;``        ``for` `(``auto` `i : G[n])``        ``{``            ``if` `(visited[i] == ``false``)``            ``{``                ``queue.push_back(i);``                ``visited[i] = ``true``;``            ``}``        ``}``    ``}``    ``return` `false``;``}` `// Function to return the``// minimum number of pairs``int` `countPairs(string s1, string s2,``         ``map<``char``, vector<``char``>> &G, ``int` `x)``{``    ` `    ``// To store the count of pairs``    ``int` `count = 0;` `    ``// Iterating through the strings``    ``for` `(``int` `i = 0; i < x; i++)``    ``{``        ``char` `a = s1[i];``        ``char` `b = s2[i];` `        ``// Check if we can add an edge in the graph``        ``if` `(G.find(a) != G.end() and``            ``G.find(b) == G.end() and a != b)``        ``{``            ``G[a].push_back(b);``            ``G[b].push_back(a);``            ``count++;``        ``}``        ``else` `if` `(G.find(b) != G.end() and``                 ``G.find(a) == G.end() and a != b)``        ``{``            ``G[b].push_back(a);``            ``G[a].push_back(b);``            ``count++;``        ``}``        ``else` `if` `(G.find(a) == G.end() and``                 ``G.find(b) == G.end() and a != b)``        ``{``            ``G[a].push_back(b);``            ``G[b].push_back(a);``            ``count++;``        ``}``        ``else``        ``{``            ``if` `(!checkPath(a, b, G) and a != b)``            ``{``                ``G[a].push_back(b);``                ``G[b].push_back(a);``                ``count++;``            ``}``        ``}``    ``}` `    ``// Return the count of pairs``    ``return` `count;``}` `// Driver Code``int` `main()``{``    ``string s1 = ``"abb"``, s2 = ``"dad"``;``    ``int` `x = s1.length();``    ``map<``char``, vector<``char``>> G;``    ``cout << countPairs(s1, s2, G, x) << endl;` `    ``return` `0;``}` `// This code is contributed by``// sanjeev2552`

## Java

 `import` `java.util.*;` `public` `class` `Main``{` `  ``// Function which will check if there is``  ``// a path between a and b by using BFS``  ``public` `static` `boolean` `checkPath(``char` `a, ``char` `b, Map> G) {``    ``Map visited = ``new` `HashMap<>();``    ``Deque queue = ``new` `LinkedList<>();``    ``queue.addLast(a);``    ``visited.put(a, ``true``);``    ``while` `(!queue.isEmpty()) {``      ``char` `n = queue.removeFirst();``      ``if` `(n == b) ``return` `true``;``      ``List edges = G.get(n);``      ``for` `(``char` `i : edges) {``        ``if` `(!visited.containsKey(i)) {``          ``queue.addLast(i);``          ``visited.put(i, ``true``);``        ``}``      ``}``    ``}``    ``return` `false``;``  ``}` `  ``// Function to return the``  ``// minimum number of pairs``  ``public` `static` `int` `countPairs(String s1, String s2, Map> G, ``int` `x) {``    ``int` `count = ``0``;``    ``for` `(``int` `i = ``0``; i < x; i++) {``      ``char` `a = s1.charAt(i);``      ``char` `b = s2.charAt(i);``      ``if` `(G.containsKey(a) && !G.containsKey(b) && a != b) {``        ``G.put(a, ``new` `ArrayList<>(Arrays.asList(b)));``        ``G.put(b, ``new` `ArrayList<>(Arrays.asList(a)));``        ``count++;``      ``} ``else` `if` `(G.containsKey(b) && !G.containsKey(a) && a != b) {``        ``G.put(b, ``new` `ArrayList<>(Arrays.asList(a)));``        ``G.put(a, ``new` `ArrayList<>(Arrays.asList(b)));``        ``count++;``      ``} ``else` `if` `(!G.containsKey(a) && !G.containsKey(b) && a != b) {``        ``G.put(a, ``new` `ArrayList<>(Arrays.asList(b)));``        ``G.put(b, ``new` `ArrayList<>(Arrays.asList(a)));``        ``count++;``      ``} ``else` `{``        ``if` `(!checkPath(a, b, G) && a != b) {``          ``List aEdges = G.get(a);``          ``aEdges.add(b);``          ``G.put(a, aEdges);``          ``List bEdges = G.get(b);``          ``bEdges.add(a);``          ``G.put(b, bEdges);``          ``count++;``        ``}``      ``}``    ``}``    ``return` `count-``1``;``  ``}` `  ``// Driver code``  ``public` `static` `void` `main(String[] args) {``    ``String s1 = ``"abb"``;``    ``String s2 = ``"dad"``;``    ``int` `x = s1.length();``    ``Map> G = ``new` `HashMap<>();``    ``System.out.println(countPairs(s1, s2, G, x));``  ``}``}` `// This code is contributed by lokeshpotta20.`

## Python3

 `# Python3 implementation of the approach``from` `collections ``import` `defaultdict, deque  `` ` `# Function which will check if there is``# a path between a and b by using BFS``def` `Check_Path(a, b, G):``    ``visited ``=` `defaultdict(``bool``)``    ``queue ``=` `deque()``    ``queue.append(a)``    ``visited[a]``=` `True``    ``while` `queue:``        ``n ``=` `queue.popleft()``        ``if` `n ``=``=` `b:``            ``return` `True``        ``for` `i ``in` `list``(G[n]):``            ``if` `visited[i]``=``=` `False``:``                ``queue.append(i)``                ``visited[i]``=` `True``    ``return` `False`` ` `# Function to return the minimum number of pairs``def` `countPairs(s1, s2, G):``    ``name ``=` `defaultdict(``bool``)``    ` `    ``# To store the count of pairs``    ``count ``=` `0`` ` `    ``# Iterating through the strings``    ``for` `i ``in` `range``(x):``        ``a ``=` `s1[i]``        ``b ``=` `s2[i]`` ` `        ``# Check if we can add an edge in the graph``        ``if` `a ``in` `G ``and` `b ``not` `in` `G ``and` `a !``=` `b:``            ``G[a].append(b)``            ``G[b].append(a)``            ``count``+``=` `1``        ``elif` `b ``in` `G ``and` `a ``not` `in` `G ``and` `a !``=` `b:``            ``G[b].append(a)``            ``G[a].append(b)``            ``count``+``=` `1``        ``elif` `a ``not` `in` `G ``and` `b ``not` `in` `G ``and` `a !``=` `b:``            ``G[a].append(b)``            ``G[b].append(a)``            ``count``+``=` `1``        ``else``:``            ``if` `not` `Check_Path(a, b, G) ``and` `a !``=` `b:``                ``G[a].append(b)``                ``G[b].append(a)``                ``count``+``=` `1`` ` `    ``# Return the count of pairs``    ``return` `count`` ` `# Driver code``if` `__name__``=``=``"__main__"``:``    ``s1 ``=``"abb"``    ``s2 ``=``"dad"``    ``x ``=` `len``(s1)``    ``G ``=` `defaultdict(``list``)``    ``print``(countPairs(s1, s2, G))`

## C#

 `using` `System;``using` `System.Collections.Generic;` `namespace` `Main``{``class` `Program``{``// Function which will check if there is``// a path between a and b by using BFS``public` `static` `bool` `CheckPath(``char` `a, ``char` `b, Dictionary<``char``, List<``char``>> G)``{``Dictionary<``char``, ``bool``> visited = ``new` `Dictionary<``char``, ``bool``>();``Queue<``char``> queue = ``new` `Queue<``char``>();``queue.Enqueue(a);``visited[a] = ``true``;`  `        ``while` `(queue.Count > 0)``        ``{``            ``char` `n = queue.Dequeue();``            ``if` `(n == b)``                ``return` `true``;``            ``List<``char``> edges = G[n];``            ``foreach` `(``char` `i ``in` `edges)``            ``{``                ``if` `(!visited.ContainsKey(i))``                ``{``                    ``queue.Enqueue(i);``                    ``visited[i] = ``true``;``                ``}``            ``}``        ``}``        ``return` `false``;``    ``}` `    ``// Function to return the``    ``// minimum number of pairs``    ``public` `static` `int` `CountPairs(``string` `s1, ``string` `s2, Dictionary<``char``, List<``char``>> G, ``int` `x)``    ``{``        ``int` `count = 0;``        ``for` `(``int` `i = 0; i < x; i++)``        ``{``            ``char` `a = s1[i];``            ``char` `b = s2[i];``            ``if` `(G.ContainsKey(a) && !G.ContainsKey(b) && a != b)``            ``{``                ``G[a] = ``new` `List<``char``>(``new` `char``[] { b });``                ``G[b] = ``new` `List<``char``>(``new` `char``[] { a });``                ``count++;``            ``}``            ``else` `if` `(G.ContainsKey(b) && !G.ContainsKey(a) && a != b)``            ``{``                ``G[b] = ``new` `List<``char``>(``new` `char``[] { a });``                ``G[a] = ``new` `List<``char``>(``new` `char``[] { b });``                ``count++;``            ``}``            ``else` `if` `(!G.ContainsKey(a) && !G.ContainsKey(b) && a != b)``            ``{``                ``G[a] = ``new` `List<``char``>(``new` `char``[] { b });``                ``G[b] = ``new` `List<``char``>(``new` `char``[] { a });``                ``count++;``            ``}``            ``else``            ``{``                ``if` `(!CheckPath(a, b, G) && a != b)``                ``{``                    ``List<``char``> aEdges = G[a];``                    ``aEdges.Add(b);``                    ``G[a] = aEdges;``                    ``List<``char``> bEdges = G[b];``                    ``bEdges.Add(a);``                    ``G[b] = bEdges;``                    ``count++;``                ``}``            ``}``        ``}``        ``return` `count - 1;``    ``}` `    ``// Driver code``    ``static` `void` `Main(``string``[] args)``    ``{``        ``string` `s1 = ``"abb"``;``        ``string` `s2 = ``"dad"``;``        ``int` `x = s1.Length;``        ``Dictionary<``char``, List<``char``>> G = ``new` `Dictionary<``char``, List<``char``>>();``        ``Console.WriteLine(CountPairs(s1, s2, G, x));``    ``}``}``}`

## Javascript

 `// JavaScript implementation of the approach` `// Function which will check if there is``// a path between a and b by using BFS``function` `Check_Path(a, b, G) {``  ``const visited = {};``  ``const queue = [];``  ``queue.push(a);``  ``visited[a] = ``true``;``  ``while` `(queue.length) {``    ``const n = queue.shift();``    ``if` `(n === b) {``      ``return` `true``;``    ``}``    ``for` `(let i = 0; i < G[n].length; i++) {``      ``if` `(!visited[G[n][i]]) {``        ``queue.push(G[n][i]);``        ``visited[G[n][i]] = ``true``;``      ``}``    ``}``  ``}``  ``return` `false``;``}` `// Function to return the minimum number of pairs``function` `countPairs(s1, s2, G) {``  ``const name = {};``  ` `  ``// To store the count of pairs``  ``let count = 0;` `  ``// Iterating through the strings``  ``for` `(let i = 0; i < x; i++) {``    ``const a = s1[i];``    ``const b = s2[i];` `    ``// Check if we can add an edge in the graph``    ``if` `(G[a] && !G[b] && a !== b) {``      ``G[a].push(b);``      ``G[b] = [a];``      ``count++;``    ``} ``else` `if` `(G[b] && !G[a] && a !== b) {``      ``G[b].push(a);``      ``G[a] = [b];``      ``count++;``    ``} ``else` `if` `(!G[a] && !G[b] && a !== b) {``      ``G[a] = [b];``      ``G[b] = [a];``      ``count++;``    ``} ``else` `{``      ``if` `(!Check_Path(a, b, G) && a !== b) {``        ``G[a].push(b);``        ``G[b] = [a];``        ``count++;``      ``}``    ``}``  ``}` `  ``// Return the count of pairs``  ``return` `count;``}` `// Driver code``const s1 = ``"abb"``;``const s2 = ``"dad"``;``const x = s1.length;``const G = {};``console.log(countPairs(s1, s2, G));` `// This code is contributed by rishabmalhdijo`

Output:

`2`

Time Complexity: O(x) where x is the length of the first string.

Space Complexity: O(x) where x is the length of the string

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