Group Shifted String

Given an array of strings (all lowercase letters), the task is to group them in such a way that all strings in a group are shifted versions of each other. Two string S and T are called shifted if, 

S.length = T.length 
and
S[i] = T[i] + K for 
1 <= i <= S.length  for a constant integer K

For example strings, {acd, dfg, wyz, yab, mop} are shifted versions of each other.

Input  : str[] = {"acd", "dfg", "wyz", "yab", "mop",
                 "bdfh", "a", "x", "moqs"};

Output : a x
         acd dfg wyz yab mop
         bdfh moqs
All shifted strings are grouped together.

We can see a pattern among the string of one group, the difference between consecutive characters for all character of the string are equal. As in the above example take acd, dfg and mop
a c d -> 2 1 
d f g -> 2 1 
m o p -> 2 1
Since the differences are the same, we can use this to identify strings that belong to the same group. The idea is to form a string of differences as key. If a string with the same difference string is found, then this string also belongs to the same group. For example, the above three strings have the same difference string, which is “21”. 

In the below implementation, we add ‘a’ to every difference and store 21 as “ba”.

C++

/* C/C++ program to print groups of shifted strings
   together. */
#include <bits/stdc++.h>
using namespace std;
const int ALPHA = 26;   // Total lowercase letter

// Method to a difference string for a given string.
// If string is "adf" then difference string will be
// "cb" (first difference 3 then difference 2)
string getDiffString(string str)
{
    string shift = "";
    for (int i = 1; i < str.length(); i++)
    {
        int dif = str[i] - str[i-1];
        if (dif < 0)
            dif += ALPHA;

        // Representing the difference as char
        shift += (dif + 'a');
    }

    // This string will be 1 less length than str
    return shift;
}

// Method for grouping shifted string
void groupShiftedString(string str[], int n)
{
    // map for storing indices of string which are
    // in same group
    map< string, vector<int> > groupMap;
    for (int i = 0; i < n; i++)
    {
        string diffStr = getDiffString(str[i]);
        groupMap[diffStr].push_back(i);
    }

    // iterating through map to print group
    for (auto it=groupMap.begin(); it!=groupMap.end();
                                                it++)
    {
        vector<int> v = it->second;
        for (int i = 0; i < v.size(); i++)
            cout << str[v[i]] << " ";
        cout << endl;
    }
}

// Driver method to test above methods
int main()
{
    string str[] = {"acd", "dfg", "wyz", "yab", "mop",
                    "bdfh", "a", "x", "moqs"
                   };
    int n = sizeof(str)/sizeof(str[0]);
    groupShiftedString(str, n);
    return 0;
}

Java

//Java code for above approach
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class ShiftedStrings {

    public static final int ALPHA = 26;

    // Method to a difference string for a given string.
    // If string is "adf" then difference string will be
    // "cb" (first difference 3 then difference 2)
    public static String getDiffString(String str) {
        String shift = "";
        for (int i = 1; i < str.length(); i++) {
            int dif = str.charAt(i) - str.charAt(i - 1);
            if (dif < 0)
                dif += ALPHA;

            // Representing the difference as char
            shift += (char)(dif + 'a');
        }
        // This string will be 1 less length than str
        return shift;
    }

    // Method for grouping shifted string
    public static void groupShiftedString(String[] str) {
        // map for storing indices of string which are
        // in same group
        Map< String, List<Integer> > groupMap = new HashMap<>();
        for (int i = 0; i < str.length; i++) {
            String diffStr = getDiffString(str[i]);
            List<Integer> indices = groupMap.getOrDefault(diffStr, new ArrayList<>());
            indices.add(i);
            groupMap.put(diffStr, indices);
        }

        // iterating through map to print group
        for (Map.Entry<String, List<Integer>> entry : groupMap.entrySet()) {
            List<Integer> v = entry.getValue();
            for (int i = 0; i < v.size(); i++)
                System.out.print(str[v.get(i)] + " ");
            System.out.println();
        }
    }

    // Driver method to test above methods
    public static void main(String[] args) {
        String[] str = { "acd", "dfg", "wyz", "yab", "mop", "bdfh", "a", "x", "moqs" };
        groupShiftedString(str);
    }
}

// This code is contributed by adityamaharshi21

Python3

# Python3 program to print groups
# of shifted strings together.

# Total lowercase letter
ALPHA = 26

# Method to a difference string
# for a given string. If string
# is "adf" then difference string
# will be "cb" (first difference
# 3 then difference 2)
def getDiffString(str):

    shift=""

    for i in range(1, len(str)):
        dif = (ord(str[i]) -
              ord(str[i - 1]))

        if(dif < 0):
            dif += ALPHA

        # Representing the difference
        # as char
        shift += chr(dif + ord('a'))

    # This string will be 1 less
    # length than str
    return shift

# Method for grouping
# shifted string
def groupShiftedString(str,n):

    # map for storing indices
    # of string which are
    # in same group
    groupMap = {}

    for i in range(n):
        diffStr = getDiffString(str[i])
        if diffStr not in groupMap:
            groupMap[diffStr] = [i]
        else:
            groupMap[diffStr].append(i)

    # Iterating through map
    # to print group
    for it in groupMap:
        v = groupMap[it]
        for i in range(len(v)):
            print(str[v[i]], end = " ")
        print()

# Driver code
str = ["acd", "dfg", "wyz",
       "yab", "mop","bdfh",
       "a", "x", "moqs"]
n = len(str)
groupShiftedString(str, n)

# This code is contributed by avanitrachhadiya2155

C#

using System;
using System.Collections.Generic;

public class ShiftedStrings {
  public static readonly int ALPHA = 26;

  // Method to a difference string for a given string.
  // If string is "adf" then difference string will be
  // "cb" (first difference 3 then difference 2)
  public static string GetDiffString(string str)
  {
    string shift = "";
    for (int i = 1; i < str.Length; i++) {
      int dif = str[i] - str[i - 1];
      if (dif < 0)
        dif += ALPHA;

      // Representing the difference as char
      shift += (char)(dif + 'a');
    }
    // This string will be 1 less length than str
    return shift;
  }

  // Method for grouping shifted string
  public static void GroupShiftedString(string[] str)
  {
    // map for storing indices of string which are
    // in same group
    Dictionary<string, List<int> > groupMap
      = new Dictionary<string, List<int> >();
    for (int i = 0; i < str.Length; i++) {
      string diffStr = GetDiffString(str[i]);
      List<int> indices;
      if (!groupMap.ContainsKey(diffStr)) {
        indices = new List<int>();
      }
      else {
        indices = groupMap[diffStr];
      }
      indices.Add(i);
      groupMap[diffStr] = indices;
    }

    // iterating through map to print group
    foreach(KeyValuePair<string, List<int> > entry in
            groupMap)
    {
      List<int> v = entry.Value;
      for (int i = 0; i < v.Count; i++)
        Console.Write(str[v[i]] + " ");
      Console.WriteLine();
    }
  }

  // Driver method to test above methods
  public static void Main(string[] args)
  {
    string[] str = { "acd",  "dfg", "wyz", "yab", "mop",
                    "bdfh", "a",   "x",   "moqs" };
    GroupShiftedString(str);
  }
}

// This code is contributed by aadityamaharshi21.

Javascript

<script>

/* Javascript program to print groups of shifted strings
   together. */
let ALPHA = 26;

// Method to a difference string for a given string.
// If string is "adf" then difference string will be
// "cb" (first difference 3 then difference 2)
function getDiffString(str)
{
    let shift = "";
    for (let i = 1; i < str.length; i++)
    {
        let dif = str[i] - str[i-1];
        if (dif < 0)
            dif += ALPHA;

        // Representing the difference as char
        shift += (dif + 'a');
    }

    // This string will be 1 less length than str
    return shift;
}

// Method for grouping shifted string
function groupShiftedString(str, n)
{

    // map for storing indices of string which are
    // in same group
    let groupMap = new Map();
    for (let i = 0; i < n; i++)
    {
        let diffStr = getDiffString(str[i]);
        if(!groupMap.has(diffStr))
            groupMap.set(diffStr,[]);
        groupMap.get(diffStr).push(i);
    }

    // iterating through map to print group
    for (let [key, value] of groupMap.entries())
    {
        let v = value;
        for (let i = 0; i < v.length; i++)
            document.write(str[v[i]]+" ");
        document.write("<br>")
    }
}

// Driver method to test above methods
let str=["acd", "dfg", "wyz", "yab", "mop",
                    "bdfh", "a", "x", "moqs"];
let n = str.length;
groupShiftedString(str, n);

// This code is contributed by ab2127
</script>

Output

a x 
acd dfg wyz yab mop 
bdfh moqs 

Time Complexity: O(N*K), where N=length of string array and K is maximum length of string in string array
Auxiliary Space: O(N)

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