标签：des style blog http color os io java ar
Alice and Bob
Time Limit: 6000/3000MS (Java/Others)Memory Limit: 256000/128000KB (Java/Others)SubmitStatisticNext ProblemProblem Description
Here is Alice and Bob again !
Alice and Bob are playing a game. There are several numbers.First, Alice choose a number n.Then he can replace n (n > 1)with one of its positive factor but not itself or he can replace n with a and b.Here a*b = n and a > 1 and b > 1.For example, Alice can replace 6 with 2 or 3 or (2, 3).But he can’t replace 6 with 6 or (1, 6). But you can replace 6 with 1. After Alice’s turn, it’s Bob’s turn.Alice and Bob take turns to do so.Who can’t do any replace lose the game.
Alice and Bob are both clever enough. Who is the winner?
Input
This problem contains multiple test cases. The first line contains one number n(1 <= n <= 100000).
The second line contains n numbers.
All the numbers are positive and less than of equal to 5000000.
Output
For each test case, if Alice can win, output “Alice”, otherwise output “Bob”.
Sample Input
2 2 2 3 2 2 4Sample Output
Bob AliceSource
yehuijieManager
/*************************************************************************
> File Name: 1112.cpp
> Author: Stomach_ache
> Mail: sudaweitong@gmail.com
> Created Time: 2014年09月05日 星期五 11时35分09秒
> Propose:
************************************************************************/
#include <set>
#include <cmath>
#include <string>
#include <cstdio>
#include <fstream>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
/*Let‘s fight!!!*/
const int MAX_N = 5000005;
int n, pnum, p[MAX_N], mindiv[MAX_N], cnt[MAX_N];
bool vis[MAX_N];
//线性筛，可以很方便的保存每个数最小的质因子,
//和每个数不同质因子的个数
void get_prime(int n) {
pnum = 0; vis[1] = true; cnt[1] = 0;
for (int i = 2; i <= n; i++) {
if (!vis[i]) {
p[pnum++] = i; mindiv[i] = i; cnt[i] = 1;
}
for (int j = 0; j < pnum; j++) {
if (p[j] * i > n) break;
vis[p[j] * i] = true;
mindiv[p[j] * i] = p[j];
cnt[p[j] * i] = cnt[i] + 1;
if (i % p[j] == 0) break;
}
}
}
//记忆化搜索所用数组，初始化为-1
int sg[35];
int dfs(int n) {
if (sg[n] != -1) return sg[n];
set<int> S;
//第一种转移变为因子a
for (int i = 0; i < n; i++) S.insert(dfs(i));
//第二种转移变为两个因子a * b
for (int i = 1; i < n; i++) S.insert(dfs(i)^dfs(n - i));
int g = 0;
while (S.find(g) != S.end()) g++;
return sg[n] = g;
}
void get_SG() {
get_prime(5000000);
memset(sg, -1, sizeof(sg));
sg[0] = 0;
for (int i = 1; i <= 33; i++) {
sg[i] = dfs(i);
}
}
int main(void) {
get_SG(); //预处理sg值
int n;
while (~scanf("%d", &n)) {
int ans = 0;
for (int i = 0; i < n; i++) {
int x;
scanf("%d", &x);
ans ^= sg[cnt[x]];
}
if (ans) puts("Alice");
else puts("Bob");
}
return 0;
}
标签：des style blog http color os io java ar
原文地址：http://www.cnblogs.com/Stomach-ache/p/3958143.html
