DNA Sorting

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 96532		Accepted: 38867

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

 

 

1 #include 
      
        2 #include 
       
         3 #include 
        
          4 using namespace std; 5 struct DNA 6 { 7     string str; 8     int r; 9 }d[105];10 bool cmp(const DNA &a,const DNA &b)11 {12     return a.r
         
          >n>>m)18     {19         for(int i=0;i
          
           >d[i].str;22             num=0;23             for(int j=0;j
           
            d[i].str[k])27 num++;28 }29 d[i].r=num;30 }31 sort(d,d+m,cmp);32 for(int i=0;i