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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 check if a string is a floating point number?

In my program I'm going to store user input in an array then going to check each character to see if it's a digit or dot or E or negative sign after that I'll store it in to an array called temps.
Now I have problem in my fleating method () that don't how should I make my condition for the pattern of floating number digit-digit-dot-digit-digit (e.g 12.22)
I have my work here:
public void sorting(String data) {
String[] temps = new String[200];
int cpos = 0;
int tpos = 0;
Arrays.fill(temps, null);
if (str.isEmpty() == false) {
char char1 = str.charAt(cpos);
int i = 0;
while (i < str.length()) {
char1 = str.charAt(cpos);
char1 = str.charAt(tpos);
System.out.println("the current value is " + char1 + " ");
tpos++;
if (Character.isDigit(char1)) {
temps[cpos] = "Digit";
// System.out.println(" this number is digit");
cpos++;
} else if (char1 == 'e' || char1 == 'E') {
temps[cpos] = "s_notaion";
cpos++;
} else if (char1 == '-') {
temps[cpos] = "negative";
cpos++;
} else if (char1 == '.') {
temps[cpos] = ".";
cpos++;
}
i++;
}
}
}
here is the method for floating number
private static boolean floating(String [] data) {
int count =0;
boolean correct = false;
for (int i = 0; i < data.length; i++) {
if (data[i]== "Digit" )
&& data[i]=="." && data[i]"Digit"){
// here is the problem for the condition
}
}
return false;
}

If I understood correctly, the Data array has stuff like ["Digit","Digit",".","Digit"]
So you want the
private static boolean floating(String [] data) {
method to return true if the array only has "Digit" entries and exactly one "." entry? is that it?
If so:
boolean foundLeDigit = false;
for (int i = 0; i < data.length; i++) {
if (data[i].equals("Digit") == false && data[i].equals(".") == false {
//we found something other than a Digit or . it's not a float
return false;
}
if(data[i].equals(".")) {
if(foundLeDigit) { return false; //as we found 2 "." }
foundLeDigit = true
}
}
return foundLeDigit;

The easiest way to test if a String can represent a float is to try to parse it:
String testString = "1.2345";
double result;
try {
result = Double.parseDouble(testString);
System.out.println("Success!")
}
catch (NumberFormatException nfe) {
// wasn't a double, deal with the failure in whatever way you like
}

The questions lacks a bit of context, so for my answer I'm going to presume that this is homework requiring a manual solution, and that all floating point numbers are supposed to be accepted.
Your approach (while over-engineered) is half-right: you are reducing the input string into classes of characters - digit, sign, exponent marker. What is missing is that now you have to make sure that these character classes come in the right order.
Identify the various parts of float numbers (just look at 0, -1.0, 400E30, 42.1E-30) and you'll see that they come in a specific order, even if some are optional, and that each part imposes restrictions on what characters are allowed there. For example, if there is an 'E' in the number, it has to be followed by a number (with optional sign).
So as you step through the characters of the string, think about how you could keep track of where you are in the number, and base your character validation on that (this is the state machine #JonKiparsky was mentioning).
A few small things:
Don't compare strings with '==' - use equalsTo().
Think about what it means if sorting() finds a character which is neither a digit, a sign, or the exponent 'E'?
You allocate the temps array for 200 entries, but the input string could be larger.

using the regular expression is the best way to Handel this problem
private static boolean floating(String [] data) {
int count =0;
boolean correct = false;
for (int i = 0; i < data.length; i++) {
if (str.matches("((-|\\+)?[0-9]+(\\.[0-9]+)?)+")){
System.out.println(" it's a floating number ");
correct= true;
break;
}else
correct = false;
}if (correct ==true){
return true;
}else
return false;
}

Finding number of mismatches between two strings

I am needed find number of mismatching characters between two strings. Currently i m doing it by converting strings into char Arrays and comparing element by element.
Is there any other way to achieve above requirement.
Note: consider string as lower case
Inputs :
input
utput
Output :
2

StringUtils in Apache commons.lang has a method for getting the Levenshtein distance of two strings.

If the two string are of different size the following code you return the total mismatch of alphabets.
You can try this -
String ip1 = "input"; // input1
String ip2 = "utput"; // input2
int count = 0; // difference in string
String ipx2 = ip2;
for (int j = 0; j <= ip2.length(); j++) {
int value = ip1.indexOf(ipx2);
if (value != -1) {
if (("").equals(ipx2)) { // if the second string is blank after continous reducing
count = ip1.length() + ip2.length();
} else {
count = ip1.length() + ip2.length() - 2 * ipx2.length();
}
break;
} else {
count = ip1.length() + ip2.length(); // if there is no match at all
}
ipx2 = ip2.substring(j);
}
System.out.println("" + count);
}
You will have to check whether the inputs have some data or not. I have not done that check.

This is the way you are describing, but it is the simplest way of implementing:
int counter = 0;
for(int i = 0; i < str1.length(); i++) if(str1.charAt(i) != str2.charAt(i)) counter++;
They can be fit on just two lines of code, without explicitly creating a whole new character array.