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 
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 string of one group, the difference between consecutive characters for all character of string are equal. As in 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 same, we can use this to identify strings that belong to same group. The idea is to form a string of differences as key. If a string with same difference string is found, then this string also belongs to same group. For example, above three strings have same difference string, that is “21”.

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

/* 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]);
    // iterating through map to print group
    for (auto it=groupMap.begin(); it!=groupMap.end();
        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;


a x
acd dfg wyz yab mop
bdfh moqs

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

This article is attributed to GeeksforGeeks.org

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