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m_aakash
Junior Member

Posts: 96
 interesting string problems   « on: Mar 22nd, 2008, 12:18pm » Quote Modify

1) Given s string, rearrange characters to form a longest palindrome. If multiple palindromes are possible, return first one in lexicographic order. If no palindrome can be formed then return NULL.

2) Describe an efficient algorithm to find the length of the longest substring that appears both forward and backward in an input string T[1 . n]. The forward and backward  must not overlap.
Ex: redivide
output: 3 (edi)
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Grimbal
wu::riddles Moderator
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Posts: 7527
 Re: interesting string problems   « Reply #1 on: Mar 22nd, 2008, 4:09pm » Quote Modify

1) Order all characters in ascending order.  You have a sequence of characters, some repeated.
Build the palindrome from the ends while scanning the sorted string from left to right.  I.e. start with strings S and E, both empty.
For every repeated character, add half of them at the end of S and another half to the front of S.  Round the halves down.  If any character is left (for an odd number) store the first one you meet as F.
When done with the sorted string, your palindrome is S+F+E.
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m_aakash
Junior Member

Posts: 96
 Re: interesting string problems   « Reply #2 on: Mar 22nd, 2008, 8:36pm » Quote Modify

on Mar 22nd, 2008, 4:09pm, Grimbal wrote:
 1) Order all characters in ascending order.  You have a sequence of characters, some repeated. Build the palindrome from the ends while scanning the sorted string from left to right.  I.e. start with strings S and E, both empty. For every repeated character, add half of them at the end of S and another half to the front of S.  Round the halves down.  If any character is left (for an odd number) store the first one you meet as F. When done with the sorted string, your palindrome is S+F+E.

well done grimbal...

can you think of O(n^2) algo for second problem...
i think we have to use dp for second one.
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Leo
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 Re: interesting string problems   « Reply #3 on: Mar 22nd, 2008, 8:48pm » Quote Modify

(b) How about finding the longest common substring of the string and its reverse with an extra condition to check for overlap ... something like
If S is the String and S' is its reverse. Then the LCS that comes up should be tested for
length(S) - start_index(S') - start_index(S) - (2 * lendth(LCS)) > 0

would this work?
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m_aakash
Junior Member

Posts: 96
 Re: interesting string problems   « Reply #4 on: Mar 22nd, 2008, 9:48pm » Quote Modify

on Mar 22nd, 2008, 8:48pm, Leo wrote:
 (b) How about finding the longest common substring of the string and its reverse with an extra condition to check for overlap ... something like If S is the String and S' is its reverse. Then the LCS that comes up should be tested for length(S) - start_index(S') - start_index(S) - (2 * lendth(LCS)) > 0   would this work?

ex: fghqaaaaphgf
Longest common substring is aaaa
say your test detects overlap even then how do you find the actual result which is fgh
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pscoe2
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Posts: 77
 Re: interesting string problems   « Reply #5 on: Mar 22nd, 2008, 10:23pm » Quote Modify

we can do as Leo suggested just keeping an array with tags which increment if they are counted for LCS

Ex:
fghqaaaaphgr
000022220000

bcoz this part has been considered for LCS twice for both S and S'

in such a situation LCS can be either equal to half (or as the case might be...see the first starting 1 n the ending 1 and take mean)

In the above case LCS=4/2=2

but as there are repetitions we hv to run the algo again just this time forbidding the LCS to come out to be the same

do this till u get an LCS with all 0's and 1's and the find the longest of them

Ex(contd.)
in second iteration the array become
111000000111
which gives the value of LCS=3

and we see tht in the second case the LCS is higher and also there are only 0's and 1's in the final array so no more iterations are req. to get the optimal soln.s
 « Last Edit: Mar 22nd, 2008, 10:28pm by pscoe2 » IP Logged
Leo
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Posts: 8
 Re: interesting string problems   « Reply #6 on: Mar 23rd, 2008, 12:09am » Quote Modify

here's an implementation in java ...

String s = "fghqaaaaphgf";
String bestMatch = "";
String ss = Reverse(s);
for (i=0;i<s.length();i++) {
for (int k=ss.length()-1;k>=i+2;k--) {
String subString = s.substring(i, k);
int index = ss.indexOf(subString);
if (index != -1) {
//test for overlap here
if ((s.length() - index) - i - (2 * (k - i)) > 0) {
if (bestMatch.length() < subString.length())
bestMatch = subString;
break;
}
}
}
}

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Jigsaw
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 Re: interesting string problems   « Reply #7 on: Jun 18th, 2008, 4:22am » Quote Modify Remove

on Mar 22nd, 2008, 12:18pm, m_aakash wrote:
 1) Given s string, rearrange characters to form a longest palindrome. If multiple palindromes are possible, return first one in lexicographic order. If no palindrome can be formed then return NULL.   2) Describe an efficient algorithm to find the length of the longest substring that appears both forward and backward in an input string T[1 . n]. The forward and backward  must not overlap.   Ex: redivide   output: 3 (edi)

int n=str.size()-1; //1 based string
for(int i=1;i<=n;i++)
for(int j=n;j>i;j++)
ls[i][j]=((str[i]==str[j])?ls[i-1][j+1]+1:0);

The code is self explanatory I guess. The longest substring ending at i-1 from one direction and at j+1 from other direction can be extended by 1 if a[i] and b[j] are equal. Once you calculate the lcs matrix, if ls[i][j] contains the largest value, i gives the position in string and ls[i][j] gives the length of the substring which has the stated properties.

[edit: replaced all lcs with ls]
 « Last Edit: Jun 23rd, 2008, 9:05am by jagatsastry » IP Logged
curt_cobain
Newbie

Posts: 33
 Re: interesting string problems   « Reply #8 on: Jun 21st, 2008, 12:14am » Quote Modify

1) Order all characters in ascending order.  You have a sequence of characters, some repeated.
Build the palindrome from the ends while scanning the sorted string from left to right.  I.e. start with strings S and E, both empty.
For every repeated character, add half of them at the end of S and another half to the front of S.  Round the halves down.  If any character is left (for an odd number) store the first one you meet as F.
When done with the sorted string, your palindrome is S+F+E. [hide][/hide]

CAN U TELL ME WHAT IS IN E ALSO CAN U ELABORATE UR LOGIC WITH THE EAXAMPLE
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tuxilogy
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Posts: 45
 Re: interesting string problems   « Reply #9 on: Jun 23rd, 2008, 1:33am » Quote Modify

@ Jigsaw,

Can you please xplain your LCS matrix logic, i could not get it
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Jigsaw
Guest

 Re: interesting string problems   « Reply #10 on: Jun 23rd, 2008, 9:02am » Quote Modify Remove

on Jun 23rd, 2008, 1:33am, tuxilogy wrote:
 @ Jigsaw,     Can you please xplain your LCS matrix logic, i could not get it

Yeah, sure. Say str[i-k. . .i-1] and rev(str[j+1. . .k+j]) are equal(i.e. has the desired property) and str[i-k...i-1] is the longest substring(as asked) ending at i-1 and is of length k, then the length of the longest substring ending at i is of length k+1 if str[i] == str[j]. Otherwise it(ls[i][j])  would be of length 0.

E.g.:
str=xyzzy

ls[2][5]=1 (str[2](y)==str[5](y))
ls[3][4]=ls[2][5]+1=2 since str[3](z)==str[4](z)
and
ls[3][5]=0 since str[3](z)!=str[5](y)

After constructing the whole matrix, find the indices i and j such that ls[i][j] is maximum. i is the position where the required substring ends and ls[i][j] is its length.

Here comes the code(I've just coded and tested)
Code:
 string getLcs(const string& str) {  int n=str.size();  vector > ls(n+2, vector(n+2,0));    pair max(0, -1); //Max value, index  for(int i=1;i<=n;i++)   for(int j=n;j>i;j--)     {         ls[i][j]=(str[i-1]==str[j-1])?ls[i-1][j+1]+1:0; //Indices adjusted for 0 based string indices         if(ls[i][j]>max.first)         max.first=ls[i][j], max.second=i;     }  if(max.second==-1)  return "";  else return string(str, max.second-max.first, max.first);   }

[edit: replaced all lcs with "ls"]
 « Last Edit: Jun 23rd, 2008, 9:07am by jagatsastry » IP Logged
manita23
Newbie

Posts: 5
 Re: interesting string problems   « Reply #11 on: Jul 22nd, 2014, 9:54pm » Quote Modify

Here is java method to find longest   Palindrome string[]

public static String longestPalindromeString(String s) {
if (s == null) return null;
String longest = s.substring(0, 1);
for (int i = 0; i < s.length() - 1; i++) {
//odd cases like 121
String palindrome = intermediatePalindrome(s, i, i);
if (palindrome.length() > longest.length()) {
longest = palindrome;
}
//even cases like 1221
palindrome = intermediatePalindrome(s, i, i + 1);
if (palindrome.length() > longest.length()) {
longest = palindrome;
}
}
return longest;
}

 « Last Edit: Aug 13th, 2014, 6:59am by Grimbal » IP Logged
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