Minimum move to end operations to make all strings equal
Given n strings that are permutations of each other. We need to make all strings same with an operation that takes front character of any string and moves it to the end.
Examples:
Input: n = 2, arr[] = {“molzv”, “lzvmo”}
Output: 2
Explanation: In first string, we remove first element(“m”) from first string and append it end. Then we move second character of first string and move it to end. So after 2 operations, both strings become same.Input: n = 3, arr[] = {“kc”, “kc”, “kc”}
Output: 0
Explanation: already all strings are equal.
Approach:
The move to end operation is basically left rotation. We use the approach discussed in check if strings are rotations of each other or not to count a number of move to front operations required to make two strings the same. We one by one consider every string as the target string. We count rotations required to make all other strings the same as the current target and finally return a minimum of all counts.
Below is the implementation of the above approach.
// CPP program to make all strings same using
// move to end operations.
#include <bits/stdc++.h>
using namespace std;
// Returns minimum number of moves to end
// operations to make all strings same.
int minimunMoves(string arr[], int n)
{
int ans = INT_MAX;
for (int i = 0; i < n; i++)
{
int curr_count = 0;
// Consider s[i] as target string and
// count rotations required to make
// all other strings same as str[i].
for (int j = 0; j < n; j++) {
string tmp = arr[j] + arr[j];
// find function returns the index where we
// found arr[i] which is actually count of
// move-to-front operations.
int index = tmp.find(arr[i]);
// If any two strings are not rotations of
// each other, we can't make them same.
if (index == string::npos)
return -1;
curr_count += index;
}
ans = min(curr_count, ans);
}
return ans;
}
// driver code for above function.
int main()
{
string arr[] = {"xzzwo", "zwoxz", "zzwox", "xzzwo"};
int n = sizeof(arr)/sizeof(arr[0]);
cout << minimunMoves(arr, n);
return 0;
}
// Java program to make all
// strings same using move
// to end operations.
import java.util.*;
class GFG
{
// Returns minimum number of
// moves to end operations
// to make all strings same.
static int minimunMoves(String arr[], int n)
{
int ans = Integer.MAX_VALUE;
for (int i = 0; i < n; i++)
{
int curr_count = 0;
// Consider s[i] as target
// string and count rotations
// required to make all other
// strings same as str[i].
String tmp = "";
for (int j = 0; j < n; j++)
{
tmp = arr[j] + arr[j];
// find function returns the
// index where we found arr[i]
// which is actually count of
// move-to-front operations.
int index = tmp.indexOf(arr[i]);
// If any two strings are not
// rotations of each other,
// we can't make them same.
if (index != -1)
curr_count += index;
else
curr_count = -1;
}
ans = Math.min(curr_count, ans);
}
return ans;
}
// Driver code
public static void main(String args[])
{
String arr[] = {"xzzwo", "zwoxz",
"zzwox", "xzzwo"};
int n = arr.length;
System.out.println(minimunMoves(arr, n));
}
}
// This code is contributed
// by Kirti_Mangal
# Python 3 program to make all strings
# same using move to end operations.
import sys
# Returns minimum number of moves to end
# operations to make all strings same.
def minimunMoves(arr, n):
ans = sys.maxsize
for i in range(n):
curr_count = 0
# Consider s[i] as target string and
# count rotations required to make
# all other strings same as str[i].
for j in range(n):
tmp = arr[j] + arr[j]
# find function returns the index where
# we found arr[i] which is actually
# count of move-to-front operations.
index = tmp.find(arr[i])
# If any two strings are not rotations of
# each other, we can't make them same.
if (index == len(arr[i])):
return -1
curr_count += index
ans = min(curr_count, ans)
return ans
# Driver Code
if __name__ == "__main__":
arr = ["xzzwo", "zwoxz", "zzwox", "xzzwo"]
n = len(arr)
print( minimunMoves(arr, n))
# This code is contributed by ita_c
using System;
// C# program to make all
// strings same using move
// to end operations.
public class GFG
{
// Returns minimum number of
// moves to end operations
// to make all strings same.
public static int minimunMoves(string[] arr, int n)
{
int ans = int.MaxValue;
for (int i = 0; i < n; i++)
{
int curr_count = 0;
// Consider s[i] as target
// string and count rotations
// required to make all other
// strings same as str[i].
string tmp = "";
for (int j = 0; j < n; j++)
{
tmp = arr[j] + arr[j];
// find function returns the
// index where we found arr[i]
// which is actually count of
// move-to-front operations.
int index = tmp.IndexOf(arr[i], StringComparison.Ordinal);
// If any two strings are not
// rotations of each other,
// we can't make them same.
if (index == arr[i].Length)
{
return -1;
}
curr_count += index;
}
ans = Math.Min(curr_count, ans);
}
return ans;
}
// Driver code
public static void Main(string[] args)
{
string[] arr = new string[] {"xzzwo", "zwoxz", "zzwox", "xzzwo"};
int n = arr.Length;
Console.WriteLine(minimunMoves(arr, n));
}
}
// This code is contributed by Shrikant13
<script>
// Javascript program to make all
// strings same using move
// to end operations.
// Returns minimum number of
// moves to end operations
// to make all strings same.
function minimunMoves(arr,n)
{
let ans = Number.MAX_VALUE;
for (let i = 0; i < n; i++)
{
let curr_count = 0;
// Consider s[i] as target
// string and count rotations
// required to make all other
// strings same as str[i].
let tmp = "";
for (let j = 0; j < n; j++)
{
tmp = arr[j] + arr[j];
// find function returns the
// index where we found arr[i]
// which is actually count of
// move-to-front operations.
let index = tmp.indexOf(arr[i]);
// If any two strings are not
// rotations of each other,
// we can't make them same.
if (index == arr[i].length)
return -1;
curr_count += index;
}
ans = Math.min(curr_count, ans);
}
return ans;
}
// Driver code
let arr=["xzzwo", "zwoxz",
"zzwox", "xzzwo"];
let n = arr.length;
document.write(minimunMoves(arr, n));
// This code is contributed by avanitrachhadiya2155
</script>
Output
5
Time Complexity : O(n3), Where n is the size of given string (n2 for the two nested for loops and n is for the function used as find())
Auxiliary Space: O(n)
Minimum move to end operations to make all strings equal using KMP (Knuth-Morris-Pratt) Algorithm
To efficiently determine the minimum number of moves required to make all strings in an array identical by rotating characters, we can use the KMP algorithm. This approach leverages the ability of the KMP algorithm to find substring matches efficiently, which helps in quickly determining how many rotations are needed to transform one string into another.
This method revolves around using KMP for pattern searching, which allows us to detect the smallest shift needed for one string to become another. Instead of performing a find operation on concatenated strings (which is computationally expensive), we preprocess the target string to create a partial match table (or pi table). Using this table, we can efficiently determine how many rotations are needed to align one string to another. This reduces the number of operations significantly compared to the naive method.
- Preprocess all Strings: Compute the KMP tables for all strings in advance. This allows us to quickly compare any string against another using the KMP search method.
- Compute Rotations for Each Target: For each string considered as the potential final form, compute how many rotations are required for all other strings to match this target.
- Select Minimum Rotations: Track and return the minimum number of rotations across all potential target strings.
Below is the implementation of the above approach:
#include <algorithm>
#include <bits/stdc++.h>
#include <iostream>
#include <string>
#include <vector>
// Function to compute the KMP table for a given pattern
std::vector<int> computeKMPTable(const std::string& s)
{
std::vector<int> pi(s.size(), 0);
int j = 0;
for (int i = 1; i < s.size(); ++i) {
while (j > 0 && s[i] != s[j]) {
j = pi[j - 1];
}
if (s[i] == s[j]) {
j++;
pi[i] = j;
}
}
return pi;
}
// Function to perform KMP search for a pattern in a text
int KMPsearch(const std::string& text,
const std::string& pattern,
const std::vector<int>& pi)
{
int j = 0;
for (int i = 0; i < text.size(); ++i) {
while (j > 0 && text[i] != pattern[j]) {
j = pi[j - 1];
}
if (text[i] == pattern[j]) {
if (j == pattern.size() - 1) {
return i - j; // Match found at index i - j
j = pi[j];
}
else {
j++;
}
}
}
return -1; // No match found
}
// Function to find the minimum moves to make all strings
// equal by rotating
int minimumMoves(const std::vector<std::string>& arr)
{
int n = arr.size();
int ans = INT_MAX;
std::vector<std::vector<int> > kmpTables(n);
// Compute KMP tables for all strings
for (int i = 0; i < n; ++i) {
kmpTables[i] = computeKMPTable(arr[i]);
}
// Iterate over each string to find the minimum rotation
// count
for (int i = 0; i < n; ++i) {
int currCount = 0;
const std::string& target = arr[i];
const std::vector<int>& pi = kmpTables[i];
for (int j = 0; j < n; ++j) {
if (i == j) {
continue; // Skip self
}
std::string doubleStr = arr[j] + arr[j];
int rotationIndex
= KMPsearch(doubleStr, target, pi);
if (rotationIndex == -1) {
return -1; // Not possible to match
}
currCount += rotationIndex;
}
ans = std::min(ans, currCount);
}
return ans;
}
int main()
{
std::vector<std::string> arr
= { "xzzwo", "zwoxz", "zzwox", "xzzwo" };
std::cout << minimumMoves(arr)
<< std::endl; // Output should be optimized
// rotation count
return 0;
}
import java.util.ArrayList;
import java.util.List;
public class Main {
// Function to compute the KMP table for a given pattern
public static List<Integer> computeKMPTable(String s)
{
List<Integer> pi = new ArrayList<>(s.length());
for (int i = 0; i < s.length(); i++) {
pi.add(0);
}
int j = 0;
for (int i = 1; i < s.length(); ++i) {
while (j > 0 && s.charAt(i) != s.charAt(j)) {
j = pi.get(j - 1);
}
if (s.charAt(i) == s.charAt(j)) {
j++;
pi.set(i, j);
}
}
return pi;
}
// Function to perform KMP search for a pattern in a
// text
public static int KMPsearch(String text, String pattern,
List<Integer> pi)
{
int j = 0;
for (int i = 0; i < text.length(); ++i) {
while (j > 0
&& text.charAt(i) != pattern.charAt(j)) {
j = pi.get(j - 1);
}
if (text.charAt(i) == pattern.charAt(j)) {
if (j == pattern.length() - 1) {
return i
- j; // Match found at index i - j
}
else {
j++;
}
}
}
return -1; // No match found
}
// Function to find the minimum moves to make all
// strings equal by rotating
public static int minimumMoves(List<String> arr)
{
int n = arr.size();
int ans = Integer.MAX_VALUE;
List<List<Integer> > kmpTables = new ArrayList<>(n);
// Compute KMP tables for all strings
for (int i = 0; i < n; ++i) {
kmpTables.add(computeKMPTable(arr.get(i)));
}
// Iterate over each string to find the minimum
// rotation count
for (int i = 0; i < n; ++i) {
int currCount = 0;
String target = arr.get(i);
List<Integer> pi = kmpTables.get(i);
for (int j = 0; j < n; ++j) {
if (i == j) {
continue; // Skip self
}
String doubleStr = arr.get(j) + arr.get(j);
int rotationIndex
= KMPsearch(doubleStr, target, pi);
if (rotationIndex == -1) {
return -1; // Not possible to match
}
currCount += rotationIndex;
}
ans = Math.min(ans, currCount);
}
return ans;
}
public static void main(String[] args)
{
List<String> arr
= List.of("xzzwo", "zwoxz", "zzwox", "xzzwo");
System.out.println(minimumMoves(arr));
}
}
// This code is contributed by shivamgupta0987654321
def computeKMPTable(s):
pi = [0] * len(s)
j = 0
for i in range(1, len(s)):
while j > 0 and s[i] != s[j]:
j = pi[j - 1]
if s[i] == s[j]:
j += 1
pi[i] = j
return pi
def KMPsearch(text, pattern, pi):
j = 0
for i in range(len(text)):
while j > 0 and text[i] != pattern[j]:
j = pi[j - 1]
if text[i] == pattern[j]:
if j == len(pattern) - 1:
return i - j # Match found at index i - j
j = pi[j]
else:
j += 1
return -1 # No match found
def minimumMoves(arr):
n = len(arr)
ans = float('inf')
kmp_tables = [computeKMPTable(s) for s in arr]
for i in range(n):
curr_count = 0
target = arr[i]
pi = kmp_tables[i]
for j in range(n):
if i == j:
continue
double_str = arr[j] + arr[j]
rotation_index = KMPsearch(double_str, target, pi)
if rotation_index == -1:
return -1 # Not possible to match
curr_count += rotation_index
ans = min(ans, curr_count)
return ans
# Example usage:
arr = ["xzzwo", "zwoxz", "zzwox", "xzzwo"]
print(minimumMoves(arr)) # Output should be optimized rotation count
function computeKMPTable(s) {
const pi = new Array(s.length).fill(0);
let j = 0;
for (let i = 1; i < s.length; i++) {
while (j > 0 && s[i] !== s[j]) {
j = pi[j - 1];
}
if (s[i] === s[j]) {
j++;
pi[i] = j;
}
}
return pi;
}
function KMPsearch(text, pattern, pi) {
let j = 0;
for (let i = 0; i < text.length; i++) {
while (j > 0 && text[i] !== pattern[j]) {
j = pi[j - 1];
}
if (text[i] === pattern[j]) {
if (j === pattern.length - 1) {
return i - j; // Match found at index i - j
j = pi[j];
} else {
j++;
}
}
}
return -1; // No match found
}
function minimumMoves(arr) {
const n = arr.length;
let ans = Infinity;
const kmpTables = arr.map(s => computeKMPTable(s));
for (let i = 0; i < n; i++) {
let currCount = 0;
const target = arr[i];
const pi = kmpTables[i];
for (let j = 0; j < n; j++) {
if (i === j) {
continue;
}
const doubleStr = arr[j] + arr[j];
const rotationIndex = KMPsearch(doubleStr, target, pi);
if (rotationIndex === -1) {
return -1; // Not possible to match
}
currCount += rotationIndex;
}
ans = Math.min(ans, currCount);
}
return ans;
}
// Example usage:
const arr = ["xzzwo", "zwoxz", "zzwox", "xzzwo"];
console.log(minimumMoves(arr)); // Output should be optimized rotation count
Output
5
Time Complexity: O(n^2×m), where m is the length of the longest string.
Auxiliary Space: O(m)
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