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Count all possible decoding Combination of the given binary String in Java

Suppose we have a string of binary values in which some portions may correspond to specific letters, for example:
A = 0
B = 00
C = 001
D = 010
E = 0010
F = 0100
G = 0110
H = 0001
For example, if we assume the string "00100", we can have 5 different possibilities:
ADA
AF
CAA
CB
EA
I have to extract the exact number of combinations using Dynamic programming.
But I have difficulty in the formulation of subproblems and in the composition of the corresponding vector of solutions.
I appreciate any indications of the correct algorithm formulation.
class countString {
static int count(String a, String b, int m, int n) {
if ((m == 0 && n == 0) || n == 0)
return 1;
if (m == 0)
return 0;
if (a.charAt(m - 1) == b.charAt(n - 1))
return count(a, b, m - 1, n - 1) +
count(a, b, m - 1, n);
else
return count(a, b, m - 1, n);
}
public static void main(String[] args) {
Locale.setDefault(Locale.US);
ArrayList<String> substrings = new ArrayList<>();
substrings.add("0");
substrings.add("00");
substrings.add("001");
substrings.add("010");
substrings.add("0010");
substrings.add("0100");
substrings.add("0110");
substrings.add("0001");
if (args.length != 1) {
System.err.println("ERROR - execute with: java countString -filename- ");
System.exit(1);
}
try {
Scanner scan = new Scanner(new File(args[0])); // not important
String S = "00100";
int count = 0;
for(int i=0; i<substrings.size(); i++){
count = count + count(S,substrings.get(i),S.length(),substrings.get(i).length());
}
System.out.println(count);
} catch (FileNotFoundException e) {
System.out.println("File not found " + e);
}
}
}

In essence, Dynamic Programming is an enhanced brute-force approach.
Like in the case of brute-force, we need to generate all possible results. But contrary to a plain brute-force the problem should be divided into smaller subproblems, and previously computed result of each subproblem should be stored and reused.
Since you are using recursion you need to apply so-called Memoization technic in order to store and reuse the intermediate results. In this case, HashMap would be a perfect mean of storing results.
But before applying the memoization in order to understand it better, it makes sense to start with a clean and simple recursive solution that works correctly, and only then enhance it with DP.
Plain Recursion
Every recursive implementation should contain two parts:
Base case - that represents a simple edge-case (or a set of edge-cases) for which the outcome is known in advance. For this problem, there are two edge-cases: the length of the given string is 0 and result would be 1 (an empty binary string "" results into an empty string of letters ""), another case is when it's impossible to decode a given binary string and result will be 0 (in the solution below it resolves naturally when the recursive case is being executed).
Recursive case - a part of a solution where recursive calls a made and when the main logic resides. In the recursive case, we need to find each binary "binary letter" at the beginning of the string and then call the method recursively by passing the substring (without the "letter"). Results of these recursive calls need to be accumulated in the total count that will returned from the method.
In order to implement this logic we need only two arguments: the binary string to analyze and a list of binary letters:
public static int count(String str, List<String> letters) {
if (str.isEmpty()) { // base case - a combination was found
return 1;
}
// recursive case
int count = 0;
for (String letter: letters) {
if (str.startsWith(letter)) {
count += count(str.substring(letter.length()), letters);
}
}
return count;
}
This concise solution is already capable of producing the correct result. Now, let's turn this brute-force version into a DP-based solution, by applying the memoization.
Dynamic Programming
As I've told earlier, a HashMap will be a perfect mean to store the intermediate results because allows to associate a count (number of combinations) with a particular string and then retrieve this number almost instantly (in O(1) time).
That how it might look like:
public static int count(String str, List<String> letters, Map<String, Integer> vocab) {
if (str.isEmpty()) { // base case - a combination was found
return 1;
}
if (vocab.containsKey(str)) { // result was already computed and present in the map
return vocab.get(str);
}
int count = 0;
for (String letter: letters) {
if (str.startsWith(letter)) {
count += count(str.substring(letter.length()), letters, vocab);
}
}
vocab.put(str, count); // storing the total `count` into the map
return count;
}
main()
public static void main(String[] args) {
List<String> letters = List.of("0", "00", "001", "010", "0010", "0100", "0110", "0001"); // binary letters
System.out.println(count("00100", letters, new HashMap<>())); // DP
System.out.println(count("00100", letters)); // brute-force recursion
}
Output:
5 // DP
5 // plain recursion
A link to Online Demo

Hope this helps.
Idea is to create every possible string with these values and check whether input starts with the value or not. If not then switch to another index.
If you have test cases ready with you you can verify more.
I have tested only with 2-3 values.
public int getCombo(String[] array, int startingIndex, String val, String input) {
int count = 0;
for (int i = startingIndex; i < array.length; i++) {
String matchValue = val + array[i];
if (matchValue.length() <= input.length()) {
// if value matches then count + 1
if (matchValue.equals(input)) {
count++;
System.out.println("match Found---->" + count); //ommit this sysout , its only for testing.
return count;
} else if (input.startsWith(matchValue)) { // checking whether the input is starting with the new value
// search further combos
count += getCombo(array, 0, matchValue, input);
}
}
}
return count;
}
In main Method
String[] arr = substrings.toArray(new String[0]);
int count = 0;
for (int i = 0; i < arr.length; i++) {
System.out.println("index----?> " + i);
//adding this condition for single inputs i.e "0","010";
if(arr[i].equals(input))
count++;
else
count = count + getCombo(arr, 0, arr[i], input);
}
System.out.println("Final count : " + count);
My test results :
input : 00100
Final count 5
input : 000
Final count 3

How do I find the decomposition of a string?

I need to create an algorithm for String decomposition.
Some examples:
ABCABCDEDEDEF --> ABC*2+DE*3+F
ABCcABCczcz --> ABC*2+cz*2+c
test --> test
Each segment of the string should be seperated by a + and, if repeated, followed up by a * plus the number of times it appears in succession.
This is what I have tried:
private static int[] prefixFunction(String source) {
int n = source.length();
int[] pi = new int[n];
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && source.charAt(i) != source.charAt(j))
j = pi[j - 1];
if (source.charAt(i) == source.charAt(j))
j++;
pi[i] = j;
}
return pi;
}

This solution keeps everything in order, meaning an input like ABCABCDEDEDEF will return ABC*2+DE*3+F or an input like abDEDEab will return ab+DE*2+ab.
If you don't keep the order, it will be impossible to reconstruct the String later with 100 % accuracy.
public static void main(String[] args) {
String input = "ABCABCDEDEDEF";
String output = findDecomposition(input);
System.out.println("Output: " + output);
}
public static String findDecomposition(String input) {
String substring = input;
StringBuilder builder = new StringBuilder();
for (int start = 0, count = 1; start < input.length(); start++, count = 1) {
for (int end = start + 1; end < input.length(); end++) {
substring = input.substring(start, end);
while (true) {
String next = input.substring(start + substring.length(), Math.min(end + substring.length(), input.length()));
if (next.equals(substring)) {
count++;
start += substring.length();
end += substring.length();
} else
break;
}
if (count > 1) {
start += substring.length() - 1;
break;
}
}
if (count > 1) {
if (builder.length() > 0 && builder.charAt(builder.length() - 1) != '+')
builder.append('+');
builder.append(substring + "*" + count + "+");
} else
builder.append(input.charAt(start));
}
String result = builder.toString();
if (result.endsWith("+"))
return result.substring(0, result.length() - 1);
else
return result;
}

THe brute force alghoritm can work as follows.
Prerequisities:
First letter is set as root
Data structure of each possible solution is linked list. Value of each node is text to be written.
When outputting solution, first put to Map all text values together with number of appereances. If it appears more than once, use * as multiplicator
Example: One of the solution looks like this ABC-C-ABC, the output will be ABC*2+C
Solution:
Take next letter from input
New solutions are based on existing solutions. Each new solution is old solution + new letter added in one of the existing nodes or as single letter in new node.
Save new solutions as existing solutions.
Repeat from 1 until you process all letters
Calculate value of all solutions and select one with lowest string characters
I added example, as you can see the number of solutions are increasing quickly so it is not fully finished for all 6 letters. Each step represent the cycle from 1. to 4., you can see that in each step the previous solutions are used as base for new solutions. There are multiple new solutions created for each existing solution.

This code returns the following compositions:
ABCABCDEDEDEF -> ABC*2+DE*3+F
ABCcABCczcz -> ABCc*2+zcz
cefABCcABCczcz -> cef+ABCc*2+zcz
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.stream.Collectors;
public class Decomposition {
public static void main(String[] args) {
Decomposition d = new Decomposition("ABCABCDEDEDEF");
System.out.println(d.getOptimalDecomposition());// Output: ABC*2+DE*3+F
d = new Decomposition("ABCcABCczcz");
System.out.println(d.getOptimalDecomposition());// Output: ABCc*2+zcz
d = new Decomposition("cefABCcABCczcz");
System.out.println(d.getOptimalDecomposition());// Output: cef+ABCc*2+zcz
}
private List> decompositions;
private String toDecompose;
public Decomposition(String toDecompose) {
decompositions = new ArrayList();
this.toDecompose = toDecompose;
}
public String getOptimalDecomposition() {
decompose(0, new ArrayList());
return calculateOptimal(convertToPartsMap());
}
private String calculateOptimal(List> partsCount) {
Collections.sort(partsCount, new SortDecompositions());
StringBuilder optimal = new StringBuilder();
for (int i = 0; i 1) {
optimal.append("*");
optimal.append(pc.count);
}
if (i != partsCount.get(0).size() - 1) {
optimal.append("+");
}
}
return optimal.toString();
}
private List> convertToPartsMap() {
List> partsMap = new ArrayList();
for (List parts : decompositions) {
List partsCount = new ArrayList();
String lastPart = null;
int curCount = 0;
for (int i = 0; i parts) {
if (nextChar == toDecompose.length()) {
decompositions.add(parts);
return;
}
char toAdd = toDecompose.charAt(nextChar);
if (parts.isEmpty()) {
parts.add("" + toAdd);
decompose(nextChar + 1, parts);
} else {
// left
List leftParts = parts.stream().collect(Collectors.toList());// shallow copy
if (!leftParts.isEmpty()) {
int last = leftParts.size() - 1;
leftParts.set(last, leftParts.get(last) + toAdd);
} else {
leftParts.add("" + toAdd);
}
// right
List rightParts = parts.stream().collect(Collectors.toList());// shallow copy
rightParts.add("" + toAdd);
decompose(nextChar + 1, leftParts);
decompose(nextChar + 1, rightParts);
}
}
}
class PartCount {
String part;
int count;
public PartCount(String part, int count) {
this.part = part;
this.count = count;
}
#Override
public String toString() {
return "[" + part + ", " + count + "]";
}
}
class SortDecompositions implements Comparator> {
public int compare(List a, List b) {
// Here you can define what exactly means "taking up least space".
return countChars(a) - countChars(b);
}
private int countChars(List listPc) {
int count = 0;
for (PartCount pc : listPc) {
count += pc.part.length();
}
return count;
}
}

This can be solved by using KMP alogorthm longest prefix which is also suffix
Steps:
iterate the string "ABCABCDEDEDEF" and construct lps array for the string. The values in the array will be
0 0 0 1 2 3 0 0 0 0 0 0 0
This lps array gives the number of times the prefix is repeated in the string.
In the above case it is repeated only one time. Considering the actual prefix number of times will be 2 it becomes ABC*2
Take the substring of the remaining string and repeat the step 1 till the end of the string.
I can provide you the code if needed. The worst time complexity will be O(n2)

Need to encode repetitive pattern in String with * , such that * means "repeat from beginning"

Encoding format: introduce * to indicate "repeat from beginning". Example. Input-{a,b,a,b,c,a,b,a,b,c,d} can be written as {a , b, * ,c, * , d}. Output:5; E.g 2: ABCABCE, output- 5.
Here * means repeat from beginning. For example if given String is ABCABCABCABC , it will return ABC**, another example is if String is ABCABCABC, it will return ABC*ABC.
I have the below code but this code assumes that the string will contain the repetitive pattern only and no other characters, I want to modify it to check :
1. Which pattern is repeating
2. Ignore non repeating patterns
2. encode that pattern according to the problem statement
import java.util.Scanner;
public class Magicpotion {
public static void main(String args[]) {
Scanner sc = new Scanner(System.in);
System.out.println("Enter the string:");
String str = sc.nextLine();
int len = str.length();
if (len != 0) {
int lenby3 = len / 3;
int starcount = ( int).(Math.log(lenby3) / Math.log(2));
int leftstring = (lenby3 - (int) Math.pow(2, starcount));
int resultlen = (1 * 3) + starcount + (leftstring * 3);
System.out.println("ResultLength: " + resultlen);
System.out.print("ABC");
for (int i = 0; i < starcount; i++) {
System.out.print("*");
}
for (int i = 0; i < leftstring; i++) {
System.out.print("ABC");
}
} else
System.out.println("ResultLength: " + 0);
}
}
Here my assumption is that ABC will always be repeating pattern , hence I have divided the length by 3. I want to generalise it such that I find the repeating pattern which can be a AB or BC or ABCD and proceed accordingly.

This looks like homework. So instead of a full solution just some hints:
You can process the input string character by character and encode as you go. If you have at some point already read k characters and the next k characters are exactly the same, output a * and advance to position 2k.
Otherwise, output the next input character and advance position to k+1.
As mentioned by dyukha this algorithm does not always result in the shortest possible encoding. If this is required some more effort has to be put into the search.

This problem can be solved using dynamic programming.
Assume that you processed your stay at some position i. You want to understand what it the minimal length of encoding of str[0..i]. Let's call it ans[i]. You have two options:
Just add i-th character to the encoding. So the length is ans[i-1] + 1.
You may write *, when possible. In this case the length is ans[i / 2] + 1 or something like this.
The final length is in ans[n-1]. You can store how you obtained ans[i] to recover the encoding itself.
Checking whether you can write * can be optimized, using some hashing (to obtain O(n) solution instead of O(n^2)).
The difference with Henry's solution is that he always applies * when it's possible. It's not clear to me that it results into the minimal length (if I understood correctly, aaaaaa is a counterexample), so I'm giving a solution I'm sure about.

/**
* #author mohamed ali
* https://www.linkedin.com/in/oo0shaheen0oo/
*/
public class Magic_potion_encoding
{
private static int minimalSteps( String ingredients )
{
StringBuilder sb = new StringBuilder(ingredients);
for(int i =0;i<sb.length();i++)
{
char startChar = sb.charAt(i);
int walkingIndex1=i;
int startIndex2 =sb.toString().indexOf(startChar,i+1);
int walkingIndex2=startIndex2;
while(walkingIndex2 !=-1 && walkingIndex2<sb.length() && sb.charAt(walkingIndex1) == sb.charAt(walkingIndex2) )
{
if(walkingIndex1+1==startIndex2)
{
String subStringToBeEncoded = sb.substring(i,walkingIndex2+1);//substring the string found and the original "substring does not include the last index hence the +1
int matchStartIndex = sb.indexOf(subStringToBeEncoded,walkingIndex2+1);// look for first match for the whole string matched
int matchEndeIndex= matchStartIndex+subStringToBeEncoded.length();
int origStartIndex=i;
int origEndIndex = i+subStringToBeEncoded.length();
if (matchStartIndex!=-1 )
{
if(origEndIndex==matchStartIndex)
{
sb.replace(matchStartIndex,matchEndeIndex,"*");
}
else
{
while(matchStartIndex!=-1 && matchEndeIndex<sb.length() && sb.charAt(origEndIndex) == sb.charAt(matchEndeIndex) )
{
if(origEndIndex==matchStartIndex-1)// if the index of the 2 strings are right behind one another
{
sb.replace(matchStartIndex,matchEndeIndex+1,"*");
}
else
{
origEndIndex++;
matchEndeIndex++;
}
}
}
}
sb.replace(startIndex2,walkingIndex2+1,"*");
break;
}
walkingIndex1++;
walkingIndex2++;
}
}
System.out.println("orig= " + ingredients + " encoded = " + sb);
return sb.length();
}
public static void main( String[] args )
{
if ( minimalSteps("ABCABCE") == 5 &&
minimalSteps("ABCABCEA") == 6 &&
minimalSteps("abbbbabbbb") == 5 &&
minimalSteps("abcde") == 5 &&
minimalSteps("abcbcbcbcd") == 6 &&
minimalSteps("ababcababce") == 6 &&
minimalSteps("ababababxx") == 6 &&
minimalSteps("aabbccbbccaabbccbbcc") == 8)
{
System.out.println( "Pass" );
}
else
{
System.out.println( "Fail" );
}
}
}

Given that the repetitions are from the beginning, every such repeating substring will have the very first character of the given string. [Every repetition needs to be represented by a "star". (i.e ABCABCABC ans = ABC** ) . If all sequential repetitions are to be represented with one "star". (i.e ABCABCABC and = ABC* ), a slight modification to (2) will do the thing (i.e remove the if case where the just a star is added)]
Divide the given string to substrings based on the first character.
Eg. Given String = "ABABCABD"
Sub Strings = {"AB", "ABC", "AB", "ABD"}
Just traverse through the list of substrings and get the required result. I've used a map here, to make the search easy.
Just a rough write up.
SS = {"AB", "ABC", "AB", "ABD"};
result = SS[0];
Map<string, bool> map;
map.put(SS[0],true);
for (i = 1; i < SS.length; i++){
if (map.hasKey(SS[i])){
result += "*";
}
else {
res = nonRepeatingPart(SS[i], map);
result += "*" + res;
map.put(SS[i], true);
}
}
String nonRepeatingPart(str, map){
for (j = str.length-1; j >= 0; j--){
if (map.hasKey(str.subString(0, j))){
return str.subString(j, str.length-1);
}
}
return throwException("Wrong Input");
}

string getCompressed(string str){
string res;
res += str[0];
int i=1;
while(i<str.size()){
//check if current char is the first char in res
char curr = str[i];
if(res[0]==curr){
if(str.substr(0,i)==str.substr(i,i)){
res += '*';
i+=i; continue;
}else{
res += curr;
i++; continue;
}
}else {
res += curr;
i++; continue;
}
}
return res;
}
int main()
{
string s = "ABCABCABC";
string res = getCompressed(s);
cout<<res.size();
return 0;
}

How can I find all recursive combinations of different size Strings in an ArrayList? - See example

Clearly, that is almost impossible to understand.
So, here is an example:
If I have an ArrayList = ["abc", "def"]
Then the result I desire is:
ad ae af
bd be bf
cd ce cf
And the same can be assumed if I have an ArrayList = ["ab", "cd", "efg"]:
ace acf acg
ade adf adg
bce bcf bcg
bde bdf bdg
Where all the options are shown. The first index String corresponds to the first 'potential' letter of the result. The second corresponds with the second, and so forth. I have been looking into different forms of recursion, but I seem to have run into a hole. Here is what I have so far:
public static void main(String[] args) {
ArrayList<String> param = new ArrayList<String>();
param.add("jkl");
param.add("mno");
param.add("pqrs");
System.out.println(giveFrag(param, 0));
}
static String giveLetter(String s, int indexForString) {
// return the letter given
return s.substring(indexForString, indexForString+1);
}
static String giveFrag(ArrayList<String> strs, int start) {
String output = "";
if (start == strs.size()-1) {
output = giveLetter(strs.get(start),0);
} else {
for (int i = 0; i < strs.get(start).length(); i++) {
String q = strs.get(start).substring(i,i+1);
output += q;
for (int k = strs.size()-1; k < strs.size(); k++) {
output += giveFrag(strs, start+1);
}
output += " ";
}
output += "\n";
}
return output;
}
NOTICE THAT FOR SIMPLICITY'S SAKE, I IGNORE THE LAST ELEMENT OF THE ARRAYLIST. THIS CAN BE SEEN IN THE IF STATEMENT OF giveFrag().
Currently, my result is as follows:
jmp np op
kmp np op
lmp np op
Now, to the actual question! First of all, if anyone spots any glaring errors that would produce this result instead of:
jmp jnp jop
kmp knp kop
lmp lnp lop
Please let me know. If there aren't any obvious ones, and an entire restructure is needed, could you please be very specific for what I should be doing instead?
In addition, if anyone has any additional time on their hands, could they find a way to include the last array element when iterating?
Thanks so much for your help, and sorry for the incredibly vague title.

The current output doesn't match the description of the problem.
The first line of the output should be:
jmp jmq jmr jms
The implementation is not really close to what you need.
Consider this instead:
private void accumulateFrags(List<String> strings, int start, String prefix, List<String> frags) {
if (start == strings.size()) {
frags.add(prefix);
return;
}
String current = strings.get(start);
for (char c : current.toCharArray()) {
accumulateFrags(strings, start + 1, prefix + c, frags);
}
}
This function will accumulate all combinations in a list.
Call it like this:
List<String> frags = new ArrayList<>();
accumulateFrags(Arrays.asList("jkl", "mno", "pqrs"), 0, "", frags);
System.out.println(frags);
This doesn't produce the line by line output you desire.
But that should be fairly straightforward to do,
so I leave that as an exercise for you.

recursive
// arguments are passed using the text field below this editor
public static void main(String[] args)
{
String arr[] = {"jkl", "mno", "pqrs"};
List<String> res = new ArrayList<String>();
constructStr(res, "", 0, arr);
String s = "";
for (int i=0; i<res.size(); i++) {
int mod = arr[arr.length-1].length();
if (i % mod == 0) {
System.out.println(s);
s = res.get(i) + " ";
}
else {
s += res.get(i) + " ";
}
}
System.out.println(s);
}
private static void constructStr(List<String> result, String curStr, int i, String arr[]) {
if (i + 1 < arr.length) {
for (int k=0; k<arr[i].length(); k++) {
constructStr(result, curStr + arr[i].charAt(k), i + 1, arr);
}
}
else {
for (int k=0; k<arr[i].length(); k++) {
result.add(curStr + arr[i].charAt(k));
}
}
}

Generating the lexicographically greatest string

The question is to generate the lexicographically greatest string given some string s.
So the aim is to find lexicographically greatest, unique(no repetitions) substring s1 from s.
We say that some subsequence s1 is greater than another subsequence s2 if s1 has more characters than s2 or s1 is lexicographically greater than s2 if equal length.
I/O are as follows:
Input is: babab
output is: ba
Second input is: nlhthgrfdnnlprjtecpdrthigjoqdejsfkasoctjijaoebqlrgaiakfsbljmpibkidjsrtkgrdnqsknbarpabgokbsrfhmeklrle
Second output is:
tsocrpkijgdqnbafhmle
This is what I wrote for my java code but my code fails on the second test case. Also I'm having a hard time understanding why second output isn't tsrqponmlkjihgfedcba.
Can somebody provide suggestions for a fix or even java code?
I think the algorithm has to be more efficient than generating all possible unique strings, sort them and find lexicographically largest one.
To make the question much clearer, if the input is babab, then all the possible unique combinations would be b, a, ba, ab. And the output will be ba because it's the longest and lexicographically greater than ab.
Note: this is not a homework assignment.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class mostBeautiful {
final static int MAX = 1000000;
static String[] permute;
static void permutation(String prefix, String str, int counter) {
int n = str.length();
//System.out.println("n is: "+ n);
if (n == 0) {
permute[counter] = prefix;
} else {
for (int i = 0; i < n; i++) {
//System.out.println("str is: "+ str);
permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n), counter++);
}
}
}
public static void main(String[] args) throws IOException {
BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
String s = bf.readLine();
char[] unique = new char[26];
int counter = 0;
String answer = "";
//System.out.println("s is: " + s);
int ascii = 0;
final int asciiAVal = 97;
final int asciiZVal = 122;
for (int i = 0; i < s.length(); i++) {
ascii = (int)s.charAt(i);
if (ascii < asciiAVal || ascii > asciiZVal) {
continue;
}
char ch = s.charAt(i);
unique[ch - 'a'] = ch;
}
String result = "";
for (int j = 25; j >= 0; j--) {
result += unique[j];
}
result = result.trim();
System.out.println(result);
int size = result.length() * (result.length() - 1);
permute = new String[size];
permutation("", result, counter);
for (int i = 1; i < size; i++) {
if (permute[i].compareTo(permute[i - 1]) > 0){
answer = permute[i];
} else {
answer = permute[i - 1];
}
}
System.out.println("answer is: " + answer);
}
}

After thinking about this problem in many ways, I have determined a divide-and-conquer algorithm that gets the results right:
Algorithm - Pseudocode
Assuming some input string, S defined as a concatenation of two substrings A + B, we compute the lexicographically greatest string recursively as:
LexMax(S) = Merge(LexMax(A),LexMax(B))
Where
LexMax(S)
{
if Length(S) = 1
return S
else
{
LMA = LexMax(S[0:Length/2])
LMB = LexMax(S[Length/2:end])
return Merge(LMA,LMB)
}
}
Merge(A,B)
{
Sa = A
Sb = B
for n = 0:Length(A)
{
if Sb contains A[n]
{
if A[n+1:end] contains character > A[n]
Remove A[n] from Sa
else
Remove A[n] from Sb
}
}
return Sa + Sb
}
Java Code
Coming soon!
Example
Given an input string
cefcfdabbcfed
Divide it into
cefcfda
bbcfed
Assuming the function works we have:
LexMax("cefcfda") = "efcda"
LexMax("bbcfed") = "bcfed"
Merging works as follows:
e: efcda bcfed
In both substrings, greater value found to right of e in left substring, remove from left
f: fcda bcfed
In both substrings, no greater value in left substring, remove from right
c: fcda bced
In both substrings, greater value found to right of c in left substring, remove from left
d: fda bced
In both substrings, no greater value in left substring, remove from right
a: fda bce
Not in both substrings, do nothing
Final result:
LexMax(cefcfdabbcfed) = fdabce

This is not a direct answer, but doesn't this code meet the requirement as you explained it in the discussion above?
final String x = "saontehusanoethusnaoteusnaoetuh";
final SortedSet<Character> chars =
new TreeSet<Character>(Collections.reverseOrder());
for (char c : x.toCharArray()) chars.add(c);
System.out.println(chars);

Lexicographic order is an order in which words are displayed in alphabetical order using the appearance of letters in the word.It is also know as dictionary order or alphabetical order.For ex:-"Africa" is smaller than "Bangladesh" ,"He" is smaller than "he".
public class LexicographicExample {
public static void main(String a[]) {
Scanner sc = new Scanner(System.in);
System.out.println("Enter the String:-");
String str = sc.nextLine();
System.out.println("Enter the length");
int count = sc.nextInt();
List<String> list = new ArrayList<String>();
for (int i = 0; i < str.length(); i = i + 1) {
if (str.length() - i >= count) {
list.add(str.substring(i, count + i));
}
}
Collections.sort(list);
System.out.println("Smallest subString:-" + list.get(0));
System.out.println("Largest subString:-" + list.get(list.size() - 1));
}
}
For reference ,refer this link http://techno-terminal.blogspot.in/2015/09/java-program-to-find-lexicographically.html

"tsrqponmlkjihgfedcba" is not the answer because it is not a subsequence of the input. The definition of subsequence requires that the characters of the subsequence occur in the original sequence in the same order. For example, "abc" is a subsequence of "apbqcr", while "cba" is not.
As to the solution, I think a simple greedy algorithm would suffice. First, one has to understand that the maximum possible length of the output is the number of unique symbols (say, N) in the input. Since any output shorter than that would not be the greatest one, it has to be exactly N symbols long. The rest of the procedure is simple and at most quadratic in time complexity: one has to go through the input string and at each step pick the lexicographically highest symbol such that the part of the string to the left of it would still contain all the "unused" symbols.
As an example, consider a string "bacb". The first symbol can be 'a' or 'b', since in both cases the remainder contains both of the other letters. 'b' is greater, so we pick it. Now for "acb" we can only pick 'a' and than 'c' according to that condition, so we end up with "bac" for output.

import java.util.ArrayList;
import java.util.HashMap;
import java.util.Scanner;
class aaa {
public static void main(String args[]) throws Exception {
Scanner scan = new Scanner(System.in);
// int n = scan.nextInt();
String s = scan.next();
HashMap<Character, Node5> map = new HashMap<>();
for (int i = 0; i < s.length(); i++) {
if (!map.containsKey(s.charAt(i))) {
Node5 node = new Node5();
node.nl.add(i);
node.li = i;
map.put(s.charAt(i), node);
} else {
Node5 rn = map.get(s.charAt(i));
rn.nl.add(i);
rn.li = i;
map.put(s.charAt(i), rn);
}
}
String s1 = "";
int index = -1;
for (int i = 25; i >= 0; i--) {
if (map.containsKey((char) (97 + i))) {
if (map.get((char) (97 + i)).li > index) {
for (int j = 0; j < map.get((char) (97 + i)).nl.size(); j++) {
if (map.get((char) (97 + i)).nl.get(j) > index) {
s1 += (char) (97 + i);
index = map.get((char) (97 + i)).nl.get(j);
}
}
}
}
}
System.out.println(s1);
scan.close();
}
}
class Node5 {
int li;
ArrayList<Integer> nl;
public Node5() {
this.nl = new ArrayList<>();
}
}