Check if a string is a shuffle of two other given strings - string

Question

This is a question from The Algorithm Design Manual:
Suppose you are given three strings of characters: X, Y, and Z, where |X| = n,
|Y| = m, and |Z| = n+m. Z is said to be a shuffle of X and Y if and only if Z can be formed by interleaving the characters from X and Y in a way that maintains the left-to ­right ordering of the characters from each string.
Give an efficient dynamic ­programming algorithm that determines whether Z is a shuffle of X and Y.
Hint: the values of the dynamic programming matrix you construct should be Boolean, not numeric
This is what I tried:
Initially, I made a 1-D char array and pointers to the starting characters of X,Y,Z respectively. If Z-pointer with matches X-pointer store X in the char array else check the same with Y-pointer.If each entry in the char array is not different from its last entry, Z is not interleaved.
Can someone help me with this problem?

Answer 1

First, let's start with some definitions. I write X[i] for the ith element of X and X[i) for the substring of X starting at index i.
For example, if X = abcde, then X[2] = c and X[2) = cde.
Similar definitions hold for Y and Z.
To solve the problem by dynamic programming, you should keep a 2D boolean array A of size (n+1) x (m+1). In this array, A[i, j] = true if and only if X[i) and Y[j) can be interleaved to form Z[i+j).
For an arbitrary (i, j), somewhere in the middle of the 2D array, the recurrence relation is very simple:
A[i, j] := X[i] = Z[i+j] and A[i+1, j]
or Y[j] = Z[i+j] and A[i, j+1]
On the edges of the 2D array you have the case that either X or Y is already at its end, which means the suffix of the other should be equal to the suffix of Z:
A[m, j] := Y[j) = Z[m+j)
A[i, n] := X[i) = Z[i+n)
A[m, n] := true
If you first fill the border of the array (A[m, j] and A[i, n], for all i, j), you can then simply loop back towards A[0, 0] and set the entries appropriately. In the end A[0, 0] is your answer.

Answer 2

Following approach should give you an idea.
Define the condition d(s1,s2,s3) = (s1 + s2 == s3) { s3 is a shuffle of s1 and s2 }
We have to find d( X, Y, Z ).
if lengths of s1 and s2 are 1 each and length of s3 = 2,
d( s1,s2,s3 ) = { (s1[0] == s3[0] && s2[0] == s3[1]) || (s1[0] == s3[1] && s2[0] == s3[0])
Similarly d can be obtained for empty strings.
For strings of arbitrary length, following relation holds.
d( s1,s2,s3 ) = { ( d( s1-s1[last],s2,s3 - s3[last]) && s1[last] == s3[last] )
|| ( d( s1,s2 - s2[last],s3 - s3[last]) && s2[last] == s3[last] )
}
You can compute the d() entries starting from zero length strings and keep checking.

Answer 3

It is defined by following recurrence relation:-
S(i,j,k) = false
if(Z(i)==Y(k))
S(i,j,k) = S(i,j,k)||S(i+1,j,k+1)
if(Z(i)==X(j))
S(i,j,k) = S(i,j,k)||S(i+1,j+1,k)
Where S(i,j,k) corresponds to Z[i to end] formed by shuffle of X[j to end] and Y[K to end]
You should try to code this into DP on your own.

Answer 4

I think this is quite easy if you are solving this problem by using this approach with java
Java Based Solution
public class ValidShuffle {
public static void main(String[] args) {
String s1 = "XY";
String s2 = "12";
String results = "Y21XX";
validShuffle(s1, s2, results);
}
private static void validShuffle(String s1, String s2, String result) {
String s3 = s1 + s2;
StringBuffer s = new StringBuffer(s3);
boolean flag = false;
char[] ch = result.toCharArray();
if (s.length() != result.length()) {
flag = false;
} else {
for (int i = 0; i < ch.length; i++) {
String temp = Character.toString(ch[i]);
if (s3.contains(temp)) {
s = s.deleteCharAt(s.indexOf(temp));
s3 = new String(s);
flag = true;
} else {
flag = false;
break;
}
}
}
if (flag) {
System.out.println("Yes");
} else {
System.out.println("No");
}
}
}
If any problem in my code then comment me please. thank you

Answer 5

function checkShuffle(str1, str2, str3) {
var merge=str1+str2;
var charArr1= merge.split("").sort();
var charArr2= str3.split("").sort();
for(i=0;i<str3.length;i++){
if(charArr1[i] == charArr2[i]){
return true;
}
}
return false;
}
checkShuffle("abc", "def", "dfabce"); //output is true

Answer 6

JAVASCRIPT BASED SOLUTION
const first = "bac";
const second = "def"
const third = "dabecf";
function createDict(seq,str){
let strObj = {};
str = str.split("");
str.forEach((letter,index)=>{
strObj[letter] = {
wordSeq: seq,
index : index
} ;
})
return strObj;
}
function checkShuffleValidity(thirdWord,firstWord,secondWord){
let firstWordDict = createDict('first',firstWord);
let secondWordDict = createDict('second',secondWord);
let wordDict = {...firstWordDict,...secondWordDict};
let firstCount=0,secondCount = 0;
thirdWord = thirdWord.split("");
for(let i=0; i<thirdWord.length; i++){
let letter = thirdWord[i];
if(wordDict[letter].wordSeq == "first"){
if(wordDict[letter].index === firstCount){
firstCount++;
}else{
return false
}
}else{
if(wordDict[letter].index === secondCount){
secondCount++;
}else{
return false;
}
}
}
return true;
}
console.log(checkShuffleValidity(third,first,second));

Answer 7

Key points:
All strings shouldn't be null or empty.
The sum of the 2 strings length should be equal to the third string.
The third string should not contain the substrings of the 2 strings.
Else create arrays of characters , sort and compare.
Code:
public static boolean validShuffle(String first, String second, String third){
boolean status=false;
if((first==null || second==null || third==null) || (first.isEmpty()|| second.isEmpty() || third.isEmpty())){
status = false;
} else if((first.length()+second.length()) !=third.length()){
//check if the sum of 2 lengths equals to the third string length
status = false;
} else if(third.indexOf(first,0)!=-1 || third.indexOf(second,0)!=-1){
//check if the third string contains substrings
status = false;
} else {
char [] c1_2=(first+second).toCharArray();
char [] c3 =third.toCharArray();
Arrays.sort(c1_2);
Arrays.sort(c3);
status=Arrays.equals(c1_2, c3);
}
return status;
}