find all palindromes inside a string - c++

Question

I am stuck and cant seem to figure out where I should go from here.
I would appreciate any hints or tips on how I should approach this problem. Been trying to figure this out for over 9 hrs no luck.
The question is as follows:
A string s is said to be palindromic if it reads the same backwards and forwards. A decomposition of s is a set of non-overlapping sub-strings of s whose concatenation is s.
Write a C++ program that takes as input a string and computes all its palin-
dromic decompositions. For example.if s is the string 0204451881 then the
decomposition 020, 44 5 1881 is a palindromic decomposition. So is
0 2 0 4 4 5 1 8 8 1
0 2 0 4 4 5 1 88 1
0 2 0 4 4 5 1881
0 2 0 44 5 1 8 8 1
0 2 0 44 5 1 88 1
020 4 4 5 1 8 8 1
020 4 4 5 1 88 1
020 4 4 5 1881
020 44 5 1 8 8 1
020 44 5 1 88 1
020 44 5 1881
this is a class project.
so far I have:
#include <iostream>
#include <string>
using namespace std;
void palDecom(string str1);
bool isPal(const string &str);
void subPal(string str1);
int main()
{
string s = "0204451881";
palDecom(s);
subPal(s);
return 0;
}
//shows the decomposition as the single char of the string
//takes a string as input
void palDecom(string str1)
{
int stringLastIndex = (str1.length());
for (int i = 0; i < stringLastIndex; i++)
{
cout<< str1[i] <<" ";
}
cout<<endl;
}
void subPal(string str1)
{
int stringLastIndex = (str1.length());
for (int curIndx = 0; curIndx < stringLastIndex; curIndx++)
{
for(int comparIndx = 1; comparIndx < stringLastIndex; comparIndx++)
{
//cout<< "i was in this loop"<<endl;
if (isPalindrome((str1,curIndx,comparIndx)))
//cout<<str1.substr(0,curIndx-1)<<" "<< str1.substr(curIndx,comparIndx) <<" "<< str1.substr(comparIndx,stringLastIndex)<<endl;
}
}
}
bool isPal(const string &str)
{
int start=0, end=str.length()-1;
while (start < end) {
if (str[start++] != str[end--])
return false;
}
return true;
}

Answer 1

Actually, I just managed to realize this:
Palindromes decompose to combination splits.
What this means is that each palindrome will "split" into additional sub-palindromes based on how many "layers" of palindrome it possesses.
For example: The sequence
12213443
-> 1221 + 3443
-> 1 + 22 + 1 + 3 + 44 + 3
-> 1 + 2 + 2 + 1 + 3 + 44 + 3
As you parse down the string, the possibilities will just increase by the amount of palindromes a larger one can decompose to until you have palindromes of 1 character width.
Granted, I realize that palindromes can overlap:
1221221
-> 1221 + 22 + 1
OR -> 1 + 22 + 1221
This is an additional quandary, but is definitely solvable.
Additionally, you can choose to think about smaller palindromes coming together to create larger ones.
Personally, I think this line of thought will lead to a better algorithm and method of solving from the above, as composing new palindromes while iterating in one direction is probably easier than decomposing them in just one direction.
I think the best course is to start playing with palindromes and map out the possible decompositions. By analysing this, you should be able to find a repetitive pattern that can then be mapped to a recursive solution.
Regardless, this answer definitely can use recursion. There is a clear pattern here; you just need to explore it more and find it.
I wish I had a more definitive answer but I myself am struggling with the problem. I hope someone else can edit this and pick up the threads?

Answer 2

Use recursion to solve this problem by scanning the string from left to right.
Keep a stack of the previous palindrome partitions that have already been found "to the left" of the "current position" in the overall string. This stack could be an array or std::vector of pointers to the ends (i.e. - one past the last character) of each previously found palindrome. In this case, the "current position" is indicated by the top element of the stack, or the beginning of the string if the stack is empty.
The base/exit case of the recursion is when the current position refers to the end of the entire string. In that case you've already exhausted the string. Print out the palindromes as indicated by the palindrome stack (starting from the bottom) and then return. (Hint: Don't alter the original string to insert nul terminators to print each palindrome as a string. Instead, just print each palindrome character-by-character according to the partitions on the stack, print spaces between the palindromes and a newline at the end of the stack.)
Otherwise, have a loop that goes from 1 up through the number of characters remaining in the string starting from the current position. At each iteration, test if the current position is a palindrome of length equal to your loop index. If it is such a palindrome, then push a partition for that palindrome onto the stack and recurse down to one level deeper.
That should do it.
I wouldn't use a std::stack to implement the stack. Instead use a std::vector or an array. If you use std::vector, then don't do structural operations (e.g. - push_back, pop_back, etc.) on it in the recursion. Instead, just resize() it to hold up to strlen(str) partition elements before you begin recursing because the deepest stack will be when each character of the string is a palindrome. Then in your recursion, you simply pass the logical, current size of the stack. This tells you the index where the next palindrome partition should be placed (i.e. - at index size) and allows you to access any previously existing top element of the stack (i.e. - at index size - 1). This approach will work for an array or a std::vector.
If you do want to use std::vector::push_back() (or std::stack), then you just need to remember to std::vector::pop_back() after you return from each recursion. This approach would allow you to not need to pass the "logical" size of the stack explicitly around as the vector itself would know its correct size.

Answer 3

#include <iostream>
#include <cstdlib>
#include <cctype>
#include <cstring>
#include <iomanip>
using std:: cin;
using std:: cout;
using std:: endl;
using std:: setw;
const int MAX_LEN = 100;
int palDecom(const char str[]);
bool isPal(const char str[], int start, int end);
int main()
{
char str[MAX_LEN];
cin >> setw(MAX_LEN) >> str;
cout << palDecom(str) ;
return EXIT_SUCCESS;
}
int palDecom(const char str[])
{
int counter=0;
for (int i = 1; i < strlen(str) ; i++)
for(int lastindex = strlen(str)-1; lastindex < strlen(str) ; lastindex--)
{
if(isPal(str, i , lastindex-1))
counter ++;
}
return counter;
}
bool isPal(const char str[], int start, int end)
{
if(start == strlen(str))
return 1;
if (str[start] == str[end]){
isPal(str, str[start], str[end-1]);
return true;
}
return false;
}