POJ1007 DNA Sorting

传送门：POJ 1007
关键词： 水题、排序

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).

一个序列“未排序”的一个衡量标准是该字符串中次序相反的字符对的数目。例如，字母序列“DAABEC”的逆序数是5，因为D比它右边的4个字母大，而E比它右边的1个字母大。这种度量方式被称为序列中的逆序数。序列“AACEDGG”只有1个逆序（E和D）——它已经接近有序——相反，序列“ZWQM”有6个逆序（它是未排序的——完全是反向的排序）。

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.

你要对DNA字符串序列进行分类（序列仅包含4个字母A，C，G和T）。然而，分类不是按字母顺序，而是按“排序”的次序，从“最多已排序”到“最少已排序”进行排列。所有的字符串长度相同。

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.

第一行包含两个整数：一个正整数n（0 < n <= 50）给出字符串的长度，和一个正整数m（0 < m <= 100）给出字符串的数目。接下来的m行，每行为包含长度为n的字符串。

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.

对输入字符串按“最多已排序”到“最少已排序”输出一个列表。两个字符串排序情况相同，则按原来的次序输出。

Sample Input

10 6
AACATGAAGG
TTTTGGCCAA
TTTGGCCAAA
GATCAGATTT
CCCGGGGGGA
ATCGATGCAT

Sample Output

CCCGGGGGGA
AACATGAAGG
GATCAGATTT
ATCGATGCAT
TTTTGGCCAA
TTTGGCCAAA

Source

East Central North America 1998

解析

“最多已排序”的串指的是逆序数最小的串；相反，逆序数最多的串就是“最少已排序”。
题目的数据量不大，对逆序数的统计用冒泡排序就行了。（也可以使用分治法、树状数组来统计）
以逆序数为关键字排序，最终输出即可。

参考代码

#include <iostream>
#include <string>
#include <algorithm>using namespace std;
// 使用C++STL中的string，不需要规定n
const int kMaxM = 101;int n, m;typedef struct DNAInfo_ {string s; // DNA串int x; // 逆序数
} DNAInfo;DNAInfo a[kMaxM];void Swap(char& a, char& b) {char temp = a;a = b;b = temp;
}// 返回逆序数
int Stat(string s) {int count = 0;int len = s.length();// 冒泡排序for (int i = 0; i < len - 1; i++) {for (int j = 0; j < len - 1 - i; j++) {if (s[j] > s[j + 1]) {Swap(s[j], s[j + 1]);++count;}}}return count;
}bool cmp(const DNAInfo& a, const DNAInfo& b) {return a.x < b.x;
}int main() {cin >> n >> m;for (int i = 0; i < m; i++) {cin >> a[i].s;a[i].x = Stat(a[i].s);}sort(a, a + m, cmp);for (int i = 0; i < m; i++) {cout << a[i].s << endl;}return 0;
}