Make all Strings palindrome by swapping characters from adjacent Strings

Given an array of strings S[] of size X where each string has length N. In one move, you can swap the i^th character of two adjacent strings, the task is to find the minimum number of moves to make every string a palindrome. If this is not possible, print -1.

Examples:

Input: S[] = {"13", "21", "32"}
Output: 2
?Explanation: We make all the strings palindromes in two operations:
First, swap the second characters of S1 and S2. 
Now, the strings are {"11", "23", "32"}
Then, swap the first characters of S2 and S3. 
Now, the strings are {"11", "22", "33"}, which are all palindromes.

Input: S1 = "131", S2 = "525" 
?Output: 0

Approach: The problem can be solved based on the following observation: 

• For a string S of length N to be a palindrome, we must have S_i = S_N+1?i for each 1 ? i ? N
• In particular, for X strings to all be palindromes, the following must hold:
  • Let C_i denote the string formed by the i^th characters of all the strings. That is, C_i = S_{1, i}S_{2, i}…S_{X, i} .
  • Then, it must hold that C_i = C_N+1?i for every 1 ? i ? N.
•  Note that the given operation only allows us to move a character within its own column — it cannot be moved to a different column.
• So, we only really need to compute the following:
  • For each 1 ? i ? N, compute the minimum number of adjacent swaps required to make C_i = C_N+1?I , when swaps can be performed on both strings.
  • Then, add this answer up for all pairs of columns.
  • If any pair of columns cannot be made equal, the answer is ?1.

Follow the steps mentioned below to implement the above idea:

• Let S and T be two adjacent strings.
• For each position i, compute the position where S_i should end up. Denote this by pos_i.
• This can be done somewhat easily as follows:
  • Let’s look at each character individually.
  • The first occurrence of the character in S should end up as the first occurrence of the character in T, the second occurrence in S should end up as the second occurrence in T, and so on.
  • This applies to each character.
  • Finding this can be done by simply knowing the positions of the characters in S and T.
• Once we know the positions where each character ends up, the problem asks for the minimum number of swaps to reach this configuration.
• This is simply the number of inversions in the pos array, which is the answer. 

Below is the implementation of the above approach.

// C++ code to implement the approach
#include <bits/stdc++.h>
using namespace std;

vector<char> getCol(vector<string> s, int index)
{
  vector<char> v;
  for (auto it : s) {
    v.push_back(it[index]);
  }
  return v;
}

// func to check if matching possible
bool ispossible(vector<char> row1, vector<char> row2)
{
  map<char, int> hash;
  for (auto it : row1)
    hash[it]++;
  for (auto it : row2)
    hash[it]--;
  for (auto it : hash) {
    if (it.second != 0)
      return 0;
  }
  return 1;
}

//  Function to determine minimum number of swaps
//  to make ith and N-i + 1th column similar
int getSwaps(vector<char> row1, vector<char> row2)
{
  int swaps = 0;
  int i = 0;
  while (i != row1.size()) {
    if (row1[i] != row2[i]) {
      if (i == row1.size() - 1)
        swap(row2[i - 1], row2[i]);
      else
        swap(row2[i], row2[i + 1]);
      swaps += 1;
      i = 0;
    }
    else
      i += 1;
  }
  return swaps;
}

// Function to get total swaps required
int totSwap(vector<string> s)
{
  int ans = 0;
  int N = s[0].size();
  for (int i = 0; i < N / 2; i++) {
    vector<char> row1 = getCol(s, i);
    vector<char> row2 = getCol(s, N - i - 1);
    if (row1 == row2)
      continue;
    if (!ispossible(row1, row2)) {
      ans = -1;
      break;
    }
    else {
      ans += getSwaps(row1, row2);
    }
  }
  return ans;
}

// Driver Code
int main()
{
  vector<string> S{ "13", "21", "32" };
  cout << totSwap(S) << endl;
}

// This code is contributed by garg28harsh.

import java.io.*;
import java.util.*;
public class Main {
  static List<Character> getCol(String[] s, int index)
  {
    List<Character> v = new ArrayList<>();
    for (int i = 0; i < s.length; i++) {
      v.add(s[i].charAt(index));
    }
    return v;
  }
  
  // func to check if matching possible
  static boolean ispossible(List<Character> row1,
                            List<Character> row2)
  {
    Map<Integer, Integer> hash = new HashMap<>();
    for (int it : row1) {
      if (hash.containsKey(it))
        hash.put(it, hash.get(it) + 1);
      else
        hash.put(it, 1);
    }
    for (int it : row1) {
      if (hash.containsKey(it))
        hash.put(it, hash.get(it) - 1);
      else
        hash.put(it, -1);
    }
    for (Map.Entry<Integer, Integer> entry :
         hash.entrySet()) {
      if (entry.getValue() != 0)
        return false;
    }
    return true;
  }
  //  Function to determine minimum number of swaps
  //  to make ith and N-i + 1th column similar
  static int getSwaps(List<Character> row1,
                      List<Character> row2)
  {
    int swaps = 0;
    int i = 0;
    while (i != row1.size()) {
      if (row1.get(i) != row2.get(i)) {
        if (i == row1.size() - 1)
          Collections.swap(row2, i, i - 1);
        else
          Collections.swap(row2, i, i + 1);
        swaps += 1;
        i = 0;
      }
      else
        i += 1;
    }
    return swaps;
  }
  // Function to get total swaps required
  static int totSwap(String[] s)
  {
    int ans = 0;
    int N = s[0].length();
    for (int i = 0; i < N / 2; i++) {
      List<Character> row1 = getCol(s, i);
      List<Character> row2 = getCol(s, N - i - 1);
      if (row1 == row2)
        continue;
      if (!ispossible(row1, row2)) {
        ans = -1;
        break;
      }
      else {
        ans += getSwaps(row1, row2);
      }
    }
    return ans;
  }
  public static void main(String[] args)
  {
    String[] S = { "13", "21", "32" };
    System.out.println(totSwap(S));
  }
}

// This code is contributed by garg28harsh.

# Python3 code to implement the approach
from collections import Counter

def getCol(strings, index):
    return [string[index] for string in strings]


# Function to form hash for a string
def myCounter(row):
    counter = {}
    for character in row:
        if character in counter:
            counter[character] += 1
        else:
            counter[character] = 1
    return Counter(row)


# Function to determine minimum number of swaps 
# to make ith and N-i + 1th column similar
def getSwaps(r1, r2):
    swaps = 0
    row1 = r1
    row2 = r2
    if row1 == row2:
        return 0
    i = 0
    while i != len(row1):
        if row1[i] != row2[i]:
            if i == len(row1) - 1:
                row2[i-1], row2[i] = row2[i], row2[i-1]
            else:
                row2[i], row2[i + 1] = row2[i + 1], row2[i]
            swaps += 1
            i = 0
        else:
            i += 1
    return swaps


# Function to get total swaps required
def totSwap(strings):
    ans = 0
    for i in range(len(strings[0])//2):
        row1 = getCol(strings, i)
        row2 = getCol(strings, -i - 1)
        if row1 == row2:
            continue
        if myCounter(row1) != myCounter(row2):
            ans = -1
            break
        else:
            ans += getSwaps(row1, row2)
    return ans

# Driver Code
if __name__ == '__main__':
    S = ["13", "21", "32"]
    print(totSwap(S))

using System;
using System.Collections.Generic;

public class GFG {

  public static List<char> getCol(String[] s, int index)
  {
    List<char> v = new List<char>();
    for (int i = 0; i < s.Length; i++) {
      v.Add(s[i][index]);
    }
    return v;
  }

  // func to check if matching possible
  public static bool ispossible(List<char> row1,
                                List<char> row2)
  {
    Dictionary<char, int> hash
      = new Dictionary<char, int>();
    for (int i = 48; i <= 57; i += 1) {
      char c = Convert.ToChar(i);
      hash.Add(c, 0);
    }
    for (int i = 0; i < row1.Count; i++) {
      char it = row1[i];
      hash[it] = hash[it] + 1;
    }
    for (int i = 0; i < row2.Count; i++) {
      char it = row2[i];
      hash[it] = hash[it] - 1;
    }

    for (int i = 48; i <= 57; i++) {
      if (hash[Convert.ToChar(i)] != 0)
        return false;
    }
    return true;
  }
  //  Function to determine minimum number of swaps
  //  to make ith and N-i + 1th column similar
  public static int getSwaps(List<char> row1,
                             List<char> row2)
  {
    int swaps = 0;
    int i = 0;
    while (i != row1.Count) {
      if (row1[i] != row2[i]) {
        if (i == row1.Count - 1) {
          char tempswap = row2[i];
          row2[i] = row2[i - 1];
          row2[i - 1] = tempswap;
        }
        else {
          char tempswap = row2[i];
          row2[i] = row2[i + 1];
          row2[i + 1] = tempswap;
        }
        swaps += 1;
        i = 0;
      }
      else
        i += 1;
    }
    return swaps;
  }
  // Function to get total swaps required
  public static int totSwap(String[] s)
  {
    int ans = 0;
    int N = s[0].Length;
    for (int i = 0; i < N / 2; i++) {
      List<char> row1 = getCol(s, i);
      List<char> row2 = getCol(s, N - i - 1);
      if (row1 == row2)
        continue;
      if (!ispossible(row1, row2)) {
        ans = -1;
        break;
      }
      else {
        ans += getSwaps(row1, row2);
      }
    }
    return ans;
  }

  static public void Main()
  {
    String[] S = { "13", "21", "32" };
    Console.WriteLine(totSwap(S));
  }
}

// This code is contributed by akashish__

<script>
// Javascript code to implement the approach
function getCol(s, index)
{
    let v = [];
    for(let i=0;i<s.length;i++)
    {
        v.push(s[i].charAt(index));
    }
    return v;
}

// func to check if matching possible
function ispossible(row1, row2)
{
    let hash = new Map();
    for(let i=0;i<row1.length;i++)
    {
        hash.set(i, 0);
    }
    for(let i=0;i<row2.length;i++)
    {
        hash.set(i, 0);
    }
    for(let i=0;i<row1.length;i++)
        hash.set(i,hash.get(i)+1);
    for(let i=0;i<row2.length;i++)
        hash.set(i,hash.get(i)-1);
    for (let [key, value] of hash) {
        if (value != 0)
        {
            return false;
        }
    }
  return true;
}

//  Function to determine minimum number of swaps
//  to make ith and N-i + 1th column similar
function getSwaps( row1,row2)
{
  let swaps = 0;
  let i = 0;
  while (i != row1.length) {
    if (row1[i] != row2[i]) {
      if (i == row1.length - 1)
      {
        let temp = row2[i - 1];
        row2[i - 1] = row2[i];
        row2[i] = temp;
      }
      else
      {
        let temp = row2[i];
        row2[i] = row2[i+1];
        row2[i+1] = temp;
      }
      swaps += 1;
      i = 0;
    }
    else
      i += 1;
  }
  return swaps;
}

// Function to get total swaps required
function totSwap( s)
{
  let ans = 0;
  let N = s[0].length;
  for (let i = 0; i < N / 2; i++) {
    let row1 = getCol(s, i);
    let row2 = getCol(s, N - i - 1);
    if (row1 == row2)
      continue;
    if (ispossible(row1, row2)!=true) {
      ans = -1;
      break;
    }
    else {
      ans += getSwaps(row1, row2);
    }
  }
  return ans;
}

// Driver Code
let S = ["13", "21", "32" ];
console.log(totSwap(S));

// This code is contributed by akashish__.

</script>

<?php
function getCol($s, $index)
{
    $v = [];
    foreach ($s as $it) {
        array_push($v, $it[$index]);
    }
    return $v;
}

// func to check if matching possible
function ispossible($row1, $row2)
{
    $hash = [];
    foreach ($row1 as $it)
        $hash[$it]++;
    foreach ($row2 as $it)
        $hash[$it]--;
    foreach ($hash as $it) {
        if ($it != 0)
            return false;
    }
    return true;
}

//  Function to determine minimum number of swaps
//  to make ith and N-i + 1th column similar
function getSwaps($row1, $row2)
{
    $swaps = 0;
    $i = 0;
    while ($i != count($row1)) {
        if ($row1[$i] != $row2[$i]) {
            if ($i == count($row1) - 1)
                list($row2[$i - 1], $row2[$i]) = array($row2[$i], $row2[$i - 1]);
            else
                list($row2[$i], $row2[$i + 1]) = array($row2[$i + 1], $row2[$i]);
            $swaps += 1;
            $i = 0;
        } else
            $i += 1;
    }
    return $swaps;
}

// Function to get total swaps required
function totSwap($s)
{
    $ans = 0;
    $N = strlen($s[0]);
    for ($i = 0; $i < $N / 2; $i++) {
        $row1 = getCol($s, $i);
        $row2 = getCol($s, $N - $i - 1);
        if ($row1 == $row2)
            continue;
        if (!ispossible($row1, $row2)) {
            $ans = -1;
            break;
        } else {
            $ans += getSwaps($row1, $row2);
        }
    }
    return $ans;
}

// Driver Code
$S = ["13", "21", "32"];
echo totSwap($S) . "\n";
?>

2

Time Complexity: O(X * N * logN) 
Auxiliary Space: O(N)