DNA Sorting
Problem 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.
This problem contains multiple test cases!
The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.
The output format consists of N output blocks. There is a blank line between output blocks.
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.
This problem contains multiple test cases!
The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.
The output format consists of N output blocks. There is a blank line between output blocks.
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 (1 < 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''. If two or more strings are equally sorted, list them in the same order they are in the input file.
Sample Input
1 10 6
AACATGAAGG
TTTTGGCCAA
TTTGGCCAAA
GATCAGATTT
CCCGGGGGGA
ATCGATGCAT
Sample Output
CCCGGGGGGA
AACATGAAGG
GATCAGATTT
ATCGATGCAT
TTTTGGCCAA
TTTGGCCAAA
虽然此题傻暴力求逆序数即可，但是归并排序更快。
代码：
1 #include<cstdio> 2 #include<cstring> 3 #include<malloc.h> 4 #include<algorithm> 5 using namespace std; 6 7 int ans; 8 9 struct str 10 { 11 char s[105]; 12 char sort_s[105]; 13 int Num; 14 }; 15 16 bool cmp(struct str a,struct str b) 17 { 18 return a.Num<b.Num; 19 } 20 21 void MergeArray(char a[],int L,int Mid,int R,char temp[]) 22 { 23 int k=0; 24 int i=L,j=Mid+1; 25 int m=Mid,n=R; 26 while(i<=m&&j<=n) 27 { 28 if(a[i]<=a[j]) 29 temp[k++]=a[i++]; 30 else 31 { 32 temp[k++]=a[j++]; 33 ans+=m-i+1; 34 } 35 } 36 while(i<=m) 37 temp[k++]=a[i++]; 38 while(j<=n) 39 temp[k++]=a[j++]; 40 for(i=0;i<k;i++) 41 a[L+i]=temp[i]; 42 } 43 44 void MergeSort(char a[],int L,int R,char temp[]) 45 { 46 if(L<R) 47 { 48 int Mid=(L+R)/2; 49 MergeSort(a,L,Mid,temp); 50 MergeSort(a,Mid+1,R,temp); 51 MergeArray(a,L,Mid,R,temp); 52 } 53 } 54 55 int main() 56 { 57 struct str S[55]; 58 int i,m,n,t; 59 scanf("%d",&t); 60 while(t--) 61 { 62 scanf("%d%d",&m,&n); 63 for(i=0;i<n;i++) 64 scanf("%s",S[i].s); 65 for(i=0;i<n;i++) 66 { 67 ans=0; 68 int len=strlen(S[i].s); 69 strcpy(S[i].sort_s,S[i].s); 70 char *p=(char*)malloc(sizeof(char)*(len+1)); 71 MergeSort(S[i].sort_s,0,len-1,p); 72 S[i].Num=ans; 73 free(p); 74 } 75 sort(S,S+n,cmp); 76 for(i=0;i<n;i++) 77 printf("%s ",S[i].s); 78 } 79 return 0; 80 }