DNA Sorting

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 67603		Accepted: 26858

Description

One measure of ``unsortedness'' in a sequence is the number of pairs of entries that are out of order with respect to each other. For instance, in the letter sequence ``DAABEC'', this measure is 5, since D is greater than four letters to its right and E is greater than one letter to its right. This measure is called the number of inversions in the sequence. The sequence ``AACEDGG'' has only one inversion (E and D)---it is nearly sorted---while the sequence ``ZWQM'' has 6 inversions (it is as unsorted as can be---exactly the reverse of sorted).

You are responsible for cataloguing a sequence of DNA strings (sequences containing only the four letters A, C, G, and T). However, you want to catalog them, not in alphabetical order, but rather in order of ``sortedness'', from ``most sorted'' to ``least sorted''. All the strings are of the same length.

Input

The first line contains two integers: a positive integer n (0 < n <= 50) giving the length of the strings; and a positive integer m (0 < m <= 100) giving the number of strings. These are followed by m lines, each containing a string of length n.

Output

Output the list of input strings, arranged from ``most sorted'' to ``least sorted''. Since two strings can be equally sorted, then output them according to the orginal order.

Sample Input

10 6AACATGAAGGTTTTGGCCAATTTGGCCAAAGATCAGATTTCCCGGGGGGAATCGATGCAT

Sample Output

CCCGGGGGGAAACATGAAGGGATCAGATTTATCGATGCATTTTTGGCCAATTTGGCCAAA

Source

 

#include 
     
      #include 
      
       using namespace std;typedef struct{    string dna;    int count;}DNA;DNA dna[101];int cmp(const void *a,const void *b){    DNA *aa = (DNA *)a;    DNA *bb = (DNA *)b;    return aa->count-bb->count;}int main(){    int n,m;    char c;    cin>>n>>m;    for(int i = 0; i < m; i++)    {        cin>>dna[i].dna;        dna[i].count = 0;        for(int j = 0; j < n; j++)        for(int k = j+1; k < n; k++)        {            if(dna[i].dna[j]>dna[i].dna[k])            dna[i].count++;        }    }    qsort(dna,m,sizeof(dna[0]),cmp);    for(int i = 0; i < m; i++)    cout<
       
        <