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?
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.
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.
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.
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
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
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));
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;
}
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Definition:
A palindrome is a word, phrase, number or other sequence of units that has the property of reading the same in either direction
How to check if the given string is a palindrome?
This was one of the FAIQ [Frequently Asked Interview Question] a while ago but that mostly using C.
Looking for solutions in any and all languages possible.
PHP sample:
$string = "A man, a plan, a canal, Panama";
function is_palindrome($string)
{
$a = strtolower(preg_replace("/[^A-Za-z0-9]/","",$string));
return $a==strrev($a);
}
Removes any non-alphanumeric characters (spaces, commas, exclamation points, etc.) to allow for full sentences as above, as well as simple words.
Windows XP (might also work on 2000) or later BATCH script:
#echo off
call :is_palindrome %1
if %ERRORLEVEL% == 0 (
echo %1 is a palindrome
) else (
echo %1 is NOT a palindrome
)
exit /B 0
:is_palindrome
set word=%~1
set reverse=
call :reverse_chars "%word%"
set return=1
if "$%word%" == "$%reverse%" (
set return=0
)
exit /B %return%
:reverse_chars
set chars=%~1
set reverse=%chars:~0,1%%reverse%
set chars=%chars:~1%
if "$%chars%" == "$" (
exit /B 0
) else (
call :reverse_chars "%chars%"
)
exit /B 0
Language agnostic meta-code then...
rev = StringReverse(originalString)
return ( rev == originalString );
C# in-place algorithm. Any preprocessing, like case insensitivity or stripping of whitespace and punctuation should be done before passing to this function.
boolean IsPalindrome(string s) {
for (int i = 0; i < s.Length / 2; i++)
{
if (s[i] != s[s.Length - 1 - i]) return false;
}
return true;
}
Edit: removed unnecessary "+1" in loop condition and spent the saved comparison on removing the redundant Length comparison. Thanks to the commenters!
C#: LINQ
var str = "a b a";
var test = Enumerable.SequenceEqual(str.ToCharArray(),
str.ToCharArray().Reverse());
A more Ruby-style rewrite of Hal's Ruby version:
class String
def palindrome?
(test = gsub(/[^A-Za-z]/, '').downcase) == test.reverse
end
end
Now you can call palindrome? on any string.
Unoptimized Python:
>>> def is_palindrome(s):
... return s == s[::-1]
Java solution:
public class QuickTest {
public static void main(String[] args) {
check("AmanaplanacanalPanama".toLowerCase());
check("Hello World".toLowerCase());
}
public static void check(String aString) {
System.out.print(aString + ": ");
char[] chars = aString.toCharArray();
for (int i = 0, j = (chars.length - 1); i < (chars.length / 2); i++, j--) {
if (chars[i] != chars[j]) {
System.out.println("Not a palindrome!");
return;
}
}
System.out.println("Found a palindrome!");
}
}
Using a good data structure usually helps impress the professor:
Push half the chars onto a stack (Length / 2).
Pop and compare each char until the first unmatch.
If the stack has zero elements: palindrome.
*in the case of a string with an odd Length, throw out the middle char.
C in the house. (not sure if you didn't want a C example here)
bool IsPalindrome(char *s)
{
int i,d;
int length = strlen(s);
char cf, cb;
for(i=0, d=length-1 ; i < length && d >= 0 ; i++ , d--)
{
while(cf= toupper(s[i]), (cf < 'A' || cf >'Z') && i < length-1)i++;
while(cb= toupper(s[d]), (cb < 'A' || cb >'Z') && d > 0 )d--;
if(cf != cb && cf >= 'A' && cf <= 'Z' && cb >= 'A' && cb <='Z')
return false;
}
return true;
}
That will return true for "racecar", "Racecar", "race car", "racecar ", and "RaCe cAr". It would be easy to modify to include symbols or spaces as well, but I figure it's more useful to only count letters(and ignore case). This works for all palindromes I've found in the answers here, and I've been unable to trick it into false negatives/positives.
Also, if you don't like bool in a "C" program, it could obviously return int, with return 1 and return 0 for true and false respectively.
Here's a python way. Note: this isn't really that "pythonic" but it demonstrates the algorithm.
def IsPalindromeString(n):
myLen = len(n)
i = 0
while i <= myLen/2:
if n[i] != n[myLen-1-i]:
return False
i += 1
return True
Delphi
function IsPalindrome(const s: string): boolean;
var
i, j: integer;
begin
Result := false;
j := Length(s);
for i := 1 to Length(s) div 2 do begin
if s[i] <> s[j] then
Exit;
Dec(j);
end;
Result := true;
end;
I'm seeing a lot of incorrect answers here. Any correct solution needs to ignore whitespace and punctuation (and any non-alphabetic characters actually) and needs to be case insensitive.
A few good example test cases are:
"A man, a plan, a canal, Panama."
"A Toyota's a Toyota."
"A"
""
As well as some non-palindromes.
Example solution in C# (note: empty and null strings are considered palindromes in this design, if this is not desired it's easy to change):
public static bool IsPalindrome(string palindromeCandidate)
{
if (string.IsNullOrEmpty(palindromeCandidate))
{
return true;
}
Regex nonAlphaChars = new Regex("[^a-z0-9]");
string alphaOnlyCandidate = nonAlphaChars.Replace(palindromeCandidate.ToLower(), "");
if (string.IsNullOrEmpty(alphaOnlyCandidate))
{
return true;
}
int leftIndex = 0;
int rightIndex = alphaOnlyCandidate.Length - 1;
while (rightIndex > leftIndex)
{
if (alphaOnlyCandidate[leftIndex] != alphaOnlyCandidate[rightIndex])
{
return false;
}
leftIndex++;
rightIndex--;
}
return true;
}
EDIT: from the comments:
bool palindrome(std::string const& s)
{
return std::equal(s.begin(), s.end(), s.rbegin());
}
The c++ way.
My naive implementation using the elegant iterators. In reality, you would probably check
and stop once your forward iterator has past the halfway mark to your string.
#include <string>
#include <iostream>
using namespace std;
bool palindrome(string foo)
{
string::iterator front;
string::reverse_iterator back;
bool is_palindrome = true;
for(front = foo.begin(), back = foo.rbegin();
is_palindrome && front!= foo.end() && back != foo.rend();
++front, ++back
)
{
if(*front != *back)
is_palindrome = false;
}
return is_palindrome;
}
int main()
{
string a = "hi there", b = "laval";
cout << "String a: \"" << a << "\" is " << ((palindrome(a))? "" : "not ") << "a palindrome." <<endl;
cout << "String b: \"" << b << "\" is " << ((palindrome(b))? "" : "not ") << "a palindrome." <<endl;
}
boolean isPalindrome(String str1) {
//first strip out punctuation and spaces
String stripped = str1.replaceAll("[^a-zA-Z0-9]", "");
return stripped.equalsIgnoreCase((new StringBuilder(stripped)).reverse().toString());
}
Java version
Here's my solution, without using a strrev. Written in C#, but it will work in any language that has a string length function.
private static bool Pal(string s) {
for (int i = 0; i < s.Length; i++) {
if (s[i] != s[s.Length - 1 - i]) {
return false;
}
}
return true;
}
Here's my solution in c#
static bool isPalindrome(string s)
{
string allowedChars = "abcdefghijklmnopqrstuvwxyz"+
"1234567890ABCDEFGHIJKLMNOPQRSTUVWXYZ";
string compareString = String.Empty;
string rev = string.Empty;
for (int i = 0; i <= s.Length - 1; i++)
{
char c = s[i];
if (allowedChars.IndexOf(c) > -1)
{
compareString += c;
}
}
for (int i = compareString.Length - 1; i >= 0; i--)
{
char c = compareString[i];
rev += c;
}
return rev.Equals(compareString,
StringComparison.CurrentCultureIgnoreCase);
}
Here's a Python version that deals with different cases, punctuation and whitespace.
import string
def is_palindrome(palindrome):
letters = palindrome.translate(string.maketrans("",""),
string.whitespace + string.punctuation).lower()
return letters == letters[::-1]
Edit: Shamelessly stole from Blair Conrad's neater answer to remove the slightly clumsy list processing from my previous version.
C++
std::string a = "god";
std::string b = "lol";
std::cout << (std::string(a.rbegin(), a.rend()) == a) << " "
<< (std::string(b.rbegin(), b.rend()) == b);
Bash
function ispalin { [ "$( echo -n $1 | tac -rs . )" = "$1" ]; }
echo "$(ispalin god && echo yes || echo no), $(ispalin lol && echo yes || echo no)"
Gnu Awk
/* obvious solution */
function ispalin(cand, i) {
for(i=0; i<length(cand)/2; i++)
if(substr(cand, length(cand)-i, 1) != substr(cand, i+1, 1))
return 0;
return 1;
}
/* not so obvious solution. cough cough */
{
orig = $0;
while($0) {
stuff = stuff gensub(/^.*(.)$/, "\\1", 1);
$0 = gensub(/^(.*).$/, "\\1", 1);
}
print (stuff == orig);
}
Haskell
Some brain dead way doing it in Haskell
ispalin :: [Char] -> Bool
ispalin a = a == (let xi (y:my) = (xi my) ++ [y]; xi [] = [] in \x -> xi x) a
Plain English
"Just reverse the string and if it is the same as before, it's a palindrome"
Ruby:
class String
def is_palindrome?
letters_only = gsub(/\W/,'').downcase
letters_only == letters_only.reverse
end
end
puts 'abc'.is_palindrome? # => false
puts 'aba'.is_palindrome? # => true
puts "Madam, I'm Adam.".is_palindrome? # => true
An obfuscated C version:
int IsPalindrome (char *s)
{
char*a,*b,c=0;
for(a=b=s;a<=b;c=(c?c==1?c=(*a&~32)-65>25u?*++a,1:2:c==2?(*--b&~32)-65<26u?3:2:c==3?(*b-65&~32)-(*a-65&~32)?*(b=s=0,a),4:*++a,1:0:*++b?0:1));
return s!=0;
}
This Java code should work inside a boolean method:
Note: You only need to check the first half of the characters with the back half, otherwise you are overlapping and doubling the amount of checks that need to be made.
private static boolean doPal(String test) {
for(int i = 0; i < test.length() / 2; i++) {
if(test.charAt(i) != test.charAt(test.length() - 1 - i)) {
return false;
}
}
return true;
}
Another C++ one. Optimized for speed and size.
bool is_palindrome(const std::string& candidate) {
for(std::string::const_iterator left = candidate.begin(), right = candidate.end(); left < --right ; ++left)
if (*left != *right)
return false;
return true;
}
Lisp:
(defun palindrome(x) (string= x (reverse x)))
Three versions in Smalltalk, from dumbest to correct.
In Smalltalk, = is the comparison operator:
isPalindrome: aString
"Dumbest."
^ aString reverse = aString
The message #translateToLowercase returns the string as lowercase:
isPalindrome: aString
"Case insensitive"
|lowercase|
lowercase := aString translateToLowercase.
^ lowercase reverse = lowercase
And in Smalltalk, strings are part of the Collection framework, you can use the message #select:thenCollect:, so here's the last version:
isPalindrome: aString
"Case insensitive and keeping only alphabetic chars
(blanks & punctuation insensitive)."
|lowercaseLetters|
lowercaseLetters := aString
select: [:char | char isAlphabetic]
thenCollect: [:char | char asLowercase].
^ lowercaseLetters reverse = lowercaseLetters
Note that in the above C++ solutions, there was some problems.
One solution was inefficient because it passed an std::string by copy, and because it iterated over all the chars, instead of comparing only half the chars. Then, even when discovering the string was not a palindrome, it continued the loop, waiting its end before reporting "false".
The other was better, with a very small function, whose problem was that it was not able to test anything else than std::string. In C++, it is easy to extend an algorithm to a whole bunch of similar objects. By templating its std::string into "T", it would have worked on both std::string, std::wstring, std::vector and std::deque. But without major modification because of the use of the operator <, the std::list was out of its scope.
My own solutions try to show that a C++ solution won't stop at working on the exact current type, but will strive to work an anything that behaves the same way, no matter the type. For example, I could apply my palindrome tests on std::string, on vector of int or on list of "Anything" as long as Anything was comparable through its operator = (build in types, as well as classes).
Note that the template can even be extended with an optional type that can be used to compare the data. For example, if you want to compare in a case insensitive way, or even compare similar characters (like è, é, ë, ê and e).
Like king Leonidas would have said: "Templates ? This is C++ !!!"
So, in C++, there are at least 3 major ways to do it, each one leading to the other:
Solution A: In a c-like way
The problem is that until C++0X, we can't consider the std::string array of chars as contiguous, so we must "cheat" and retrieve the c_str() property. As we are using it in a read-only fashion, it should be ok...
bool isPalindromeA(const std::string & p_strText)
{
if(p_strText.length() < 2) return true ;
const char * pStart = p_strText.c_str() ;
const char * pEnd = pStart + p_strText.length() - 1 ;
for(; pStart < pEnd; ++pStart, --pEnd)
{
if(*pStart != *pEnd)
{
return false ;
}
}
return true ;
}
Solution B: A more "C++" version
Now, we'll try to apply the same solution, but to any C++ container with random access to its items through operator []. For example, any std::basic_string, std::vector, std::deque, etc. Operator [] is constant access for those containers, so we won't lose undue speed.
template <typename T>
bool isPalindromeB(const T & p_aText)
{
if(p_aText.empty()) return true ;
typename T::size_type iStart = 0 ;
typename T::size_type iEnd = p_aText.size() - 1 ;
for(; iStart < iEnd; ++iStart, --iEnd)
{
if(p_aText[iStart] != p_aText[iEnd])
{
return false ;
}
}
return true ;
}
Solution C: Template powah !
It will work with almost any unordered STL-like container with bidirectional iterators
For example, any std::basic_string, std::vector, std::deque, std::list, etc.
So, this function can be applied on all STL-like containers with the following conditions:
1 - T is a container with bidirectional iterator
2 - T's iterator points to a comparable type (through operator =)
template <typename T>
bool isPalindromeC(const T & p_aText)
{
if(p_aText.empty()) return true ;
typename T::const_iterator pStart = p_aText.begin() ;
typename T::const_iterator pEnd = p_aText.end() ;
--pEnd ;
while(true)
{
if(*pStart != *pEnd)
{
return false ;
}
if((pStart == pEnd) || (++pStart == pEnd))
{
return true ;
}
--pEnd ;
}
}
A simple Java solution:
public boolean isPalindrome(String testString) {
StringBuffer sb = new StringBuffer(testString);
String reverseString = sb.reverse().toString();
if(testString.equalsIgnoreCase(reverseString)) {
return true;
else {
return false;
}
}
Many ways to do it. I guess the key is to do it in the most efficient way possible (without looping the string). I would do it as a char array which can be reversed easily (using C#).
string mystring = "abracadabra";
char[] str = mystring.ToCharArray();
Array.Reverse(str);
string revstring = new string(str);
if (mystring.equals(revstring))
{
Console.WriteLine("String is a Palindrome");
}
In Ruby, converting to lowercase and stripping everything not alphabetic:
def isPalindrome( string )
( test = string.downcase.gsub( /[^a-z]/, '' ) ) == test.reverse
end
But that feels like cheating, right? No pointers or anything! So here's a C version too, but without the lowercase and character stripping goodness:
#include <stdio.h>
int isPalindrome( char * string )
{
char * i = string;
char * p = string;
while ( *++i ); while ( i > p && *p++ == *--i );
return i <= p && *i++ == *--p;
}
int main( int argc, char **argv )
{
if ( argc != 2 )
{
fprintf( stderr, "Usage: %s <word>\n", argv[0] );
return -1;
}
fprintf( stdout, "%s\n", isPalindrome( argv[1] ) ? "yes" : "no" );
return 0;
}
Well, that was fun - do I get the job ;^)
Using Java, using Apache Commons String Utils:
public boolean isPalindrome(String phrase) {
phrase = phrase.toLowerCase().replaceAll("[^a-z]", "");
return StringUtils.reverse(phrase).equals(phrase);
}