csuoj1828Dictionary (康托展开)
来源:互联网 发布:乔艾莉·波妮身世知乎 编辑:程序博客网 时间:2024/05/21 03:25
Description
The isolated people of MacGuffin Island have a unique culture, and one of the most interesting things about them is their language. Their alphabet consists of the first 9 letters of the Roman alphabet (a, b, c, d, e, f, g, h, i). All of their words are exactly 9 letters long and use each of these 9 letters exactly once. They have a word for every possible permutation of these letters. In the library of their most sacred temple is a dictionary, and each word in their language has its own page. By coincidence they order their words exactly as they would be in ordered in English, so the word ‘abcdefghi’ is on the first page, and the word ‘ihgfedcba’ is on the last. The question is, given a list of random words from the MacGuffin language, can you say on which page of the MacGuffin dictionary each appears?
Input
The first line of the input file is a positive integer. This integer tells you how many words will follow. The upper limit for this number is 6000. Every subsequent line contains a single word from the MacGuffin language, so if the first number is 1000 there will be 1000 lines after it, each containing a single word.
Output
Each line of output will contain an integer. This integer should be the page number for the corresponding word.
Sample Input
4abcdefgihabcdefghiabcdefgihihgfedcba
Sample Output
212362880
这个就是裸的求康托展开
九位数先把阶乘打表(这么小的数打不打其实无所谓)
康托展开的大意就是一个排列在它的全排列中按字典序排序时所处位置
比如213,它的全排列有123、132、213、231、312、321(已按字典序排好),所以它的康托展开为2,没错是2,因为康托展开是从0开始计数
的,所以学长教我们一个新的记法——康托展开的大小即为在此排列前存在的排列的个数。
求法自然有公式的呀——
表示第i个元素在未出现的元素中排列第几,n的大小为字符串的长度
比如213这个例子,n=3,然后2排第1,所以a3=1,1排第0,所以a2=0,3排第2,所以a3=2,所以
ans=1*2+0*1+2*0=2
代码
#include<iostream>#include<cstdio>using namespace std;#define ll long longint f[10];void init(){ f[1]=1; for(int i=2;i<10;i++) f[i]=f[i-1]*i;}int main(){ int N,M; char s[10]; init(); scanf("%d",&N); while(N--) { int ans=0; scanf("%s",s); for(int i=0;i<9;i++) { int temp=0; for(int j=i+1;j<9;j++) if(s[j]<s[i])temp++; ans+=temp*f[9-i-1]; } printf("%d\n",ans+1); } return 0;}
阅读全文
0 0
- csuoj1828Dictionary (康托展开)
- 排列(康托展开)
- 康托展开/逆康托展开
- 康托展开 & 康托逆展开
- 康托展开&逆康托展开
- 康托展开 康托逆展开
- loj 1165(bfs+康托展开)
- Cantor expansion(康托展开)
- 康托展开(哈希方法)
- 八数码(康托展开)
- 全排列计算(康托展开)
- 排列序数(康托展开)
- 排列序列 (康托展开)
- 康托展开(逆序数)
- HDU 1043 Eight(康托展开)
- 康托展开(八数码问题)
- 康托展开
- 康托展开
- numpy、matplotlib
- 功能强大的Android开发库:Anko
- 运算优先级的坑a[i++] = a[j]
- 编写QT多窗口程序
- CodeForces
- csuoj1828Dictionary (康托展开)
- ros::init源码分析(未完待续。)
- char、unsigned char区别
- java学习初探6之UML
- 2017多校联合第十场/HDU 6180 Schedule (贪心)
- 斯坦福大学吴恩达教授《machine learning》课程学习笔记—— week 1
- 并查集基础
- 好玩的xcode模拟器快捷键
- 如何在子线程中直接new Handler