A - Relations
Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u
Description
Background
Consider a specific set of comparable objects. Between two objects a and b, there exits one of the following three classified relations:
a = b
a < b
b < a
a < b
b < a
Because relation '=' is symmetric, it is not repeated above.
So, with 3 objects ( a, b, c), there can exist 13 classified relations:
a = b = c a = b < c c < a = b a < b = c
b = c < a a = c < b b < a = c a < b < c
a < c < b b < a < c b < c < a c < a < b
c < b < a
b = c < a a = c < b b < a = c a < b < c
a < c < b b < a < c b < c < a c < a < b
c < b < a
Problem
Given N, determine the number of different classified relations between N objects.
Input
Includes many integers N (in the range from 2 to 10), each number on one line. Ends with −1.
Output
For each N of input, print the number of classified relations found, each number on one line.
Sample Input
| input | output |
|---|---|
2 |
3 |
题目大意：给你n个人，让你给n个人排名，可以有并列，问你有多少种排名情况。
解题思路：定义dp[i][j]表示j个人有i个名次，那么dp[1][i] = 1，而dp[i][i] = (i!) i的阶乘。dp[i][j] = i*dp[i][j-1] + i*dp[i-1][j-1]。表示当第j个人加入的话，要么第j个人跟某些人等名次，要么有一个单独的名次。当第j个人跟其他人等名次的时候，他可以选择i种名次中的任意一种，当第j个人有单独的名次的时候，他可以在i-1种名次形成的i个空中选一个。 思路转自：http://www.zhihu.com/question/30200444?sort=created
#include<stdio.h>
#include<algorithm>
#include<string.h>
using namespace std;
typedef long long LL;
LL fact[20],dp[20][20];
void fac(){
fact[0] = 1;
for(LL i =1; i <= 15; i++){
fact[i] = fact[i-1]*i;
}
}
void prin(){
for(int i = 1; i <= 12; i++){
dp[1][i] = 1;
dp[i][i] = fact[i];
}
for(int i = 2; i <= 12; i++){
for(int j = i+1; j <= 12; j++){
dp[i][j] = i*(dp[i][j-1] + dp[i-1][j-1]);
}
}
}
int main(){
LL n;
fac();
prin();
while(scanf("%lld",&n)!=EOF&&n!=-1){
LL ans = 0;
for(int i = 1; i <= n; i++){
ans += dp[i][n];
}
printf("%lld\n",ans);
}
return 0;
}
uralID： 196348LD