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### 11584 - Partitioning by Palindromes

Posted: **Sun Feb 22, 2009 11:01 am**

by **srinivas**

Hi,

Any Hints on this problem .

I was only able to think of a O ( n ^ 3 ) dp solution which timed out when i submitted it .

Please help me.

Thanks a billion for your reply in advance

### Re: 11584 - Partitioning by Palindromes

Posted: **Sun Feb 22, 2009 11:42 am**

by **SerailHydra**

It's O(N^2) DP

### Re: 11584 - Partitioning by Palindromes

Posted: **Sun Feb 22, 2009 12:03 pm**

by **mice123456789**

Is it possible to solve this problem with no DP? Sample input/output please. Thanks in advance

### Re: 11584 - Partitioning by Palindromes

Posted: **Sun Feb 22, 2009 1:33 pm**

by **Igor9669**

I solved this problem with the help of BFS!

### Re: 11584 - Partitioning by Palindromes

Posted: **Sun Feb 22, 2009 7:08 pm**

by **srinivas**

Thanks alot SerailHydra for that hint .

I got ACC in that problem .

Igor9669 , can you please give some details of your BFS approach .

I wasn't able to think anything related to BFS for that problem

Thanks alot for your reply in advance .

### Re: 11584 - Partitioning by Palindromes

Posted: **Sun Feb 22, 2009 9:15 pm**

by **Igor9669**

I construct a graph, where vertices were symbols of the string, and edges connected a pair of such symbols(X,Y),where in X the palindrom begined and before Y it ended. So, now the problem is to find the shortest path from the first symbol to the (last+1).

To find all palindroms in the string I use O(N^2) algo in worse case.

Sorry for my English

!!!

### Re: 11584 - Partitioning by Palindromes

Posted: **Tue Feb 24, 2009 5:49 am**

by **sapnil**

**I use Dijkstra & get lot of WR, please help me:**

### Re: 11584 - Partitioning by Palindromes

Posted: **Tue Feb 24, 2009 7:19 pm**

by **Igor9669**

Try this tests:

2

asaaaa

azzaa

correct answer are:

2 (asa aaa)

2 (azza a)

Your programm output:

1

1

And you should modify your algo to find palindroms, because you will get TLE with it.Try to make O(n^2)algo

### Re: 11584 - Partitioning by Palindromes

Posted: **Tue Feb 24, 2009 10:00 pm**

by **mice123456789**

Hi Igor,

I dont know complex algo for this problem, just used the simple one. But still get WA. Is there any special case that i do not handle? Thanks.

Code: Select all

```
#include <stdio.h>
#include <string.h>
int ispalindrom(char *s, int index, int size)
{
int i;
for (i = 0; i < (size / 2); i++)
{
if (s[index + i] != s[index + size - i - 1])
return 0;
}
return 1;
}
int main()
{
char s[10000];
int i, j, len, size, group, N;
scanf("%d\n", &N);
for (j = 0; j < N; j++)
{
gets(s);
len = strlen(s);
i = 0;
group = 0;
size = len;
while (i < len)
{
for (size = len - i; size >= 1; size--)
if (ispalindrom(s, i, size))
{
i += size;
group++;
break;
}
}
printf("%d\n", group);
}
return 0;
}
```

### Re: 11584 - Partitioning by Palindromes

Posted: **Thu Feb 26, 2009 12:42 pm**

by **Igor9669**

Try this:

Code: Select all

```
7
amadam
madama
zzxzcc
qwerty
zzxxxz
zxxxzz
zxzczxxzc
```

Answer:

### Re: 11584 - Partitioning by Palindromes

Posted: **Thu Feb 26, 2009 5:23 pm**

by **mice123456789**

Thanks, Igor. This problem is not easy as I thought. Can you clarify the group no below?

amadam = 2: {a}, {madam}

madama = 2: {madam}, {a}

zzxzcc = 3: {z}, {zxz}, {cc}

qwerty = 6: {q}, {w}, {e}, {r}, {t}, {y}

zzxxxz = 2: {z}, {zxxxz}

zxxxzz = 2: {zxxxz}, {z}

zxzczxxzc = 2: {zxz}, {czxxzc}

Seemed likely we have to find the largest palidrome first. Correct me...

### Re: 11584 - Partitioning by Palindromes

Posted: **Sat Feb 28, 2009 9:17 am**

by **Igor9669**

I had discripted my algo above!

I don't need to find the largest palindrom at first!!!

### Re: 11584 - Partitioning by Palindromes

Posted: **Sun Mar 01, 2009 4:07 am**

by **f74956227**

Could someone give me a hint how to use a O(N^2) DP to solve this problem?

I use a N^3 with TLE.

### Re: 11584 - Partitioning by Palindromes

Posted: **Sun Mar 29, 2009 8:44 am**

by **Igor9669**

For example we have a string s;

O(n^2) how to find palindromes:

Code: Select all

```
int l,r;
s[0]='*';
s[s.length()]='*';
for(int i=1;i<s.length();++i)
{
l=i-1;
r=i+1;
while(s[l]==s[r])
{
//some code
.......
l--;r++;
}
l=i;
r=i+1;
while(s[l]==s[r])
{
//some code
.......
l--;r++;
}
//also the string form i to i is a palindrom!
}
```

### Re: 11584 - Partitioning by Palindromes

Posted: **Thu Jul 23, 2009 7:07 pm**

by **whateva**

the o(n^2) DP is like this :

let's say that v* stores the minimum number of group up to the i-th character. Then for every position j ( 0 <= j < i ), we check which one is the minimum one. That is, we only take every j in which the substring from j+1 to i is a palindrome, and we check if current v** < v[j]+1 (it's 1, since the substring from j+1 to i is already a palindrome). Of course, we'll need to precompute a boolean table which store each substring's status (palindrome or not), which is also can be done in o(n^2) (look for the previous post in this thread, for a hint). Therefore, the time complexity is o(n^2).*

I hope this will help... ^^