[博弈论] cf317 D Game with Powers_gamewith net-优快云博客

本文链接：https://blog.youkuaiyun.com/gdymind/article/details/61425381

本文深入探讨了一种基于博弈论的游戏算法实现，通过分析不同状态下的游戏策略选择，利用Sprague-Grundy定理计算了特定游戏状态的SG函数值，并结合素数筛法优化求解过程。

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[博弈论] cf317 D Game with Powers

@(ACM题目)[博弈论]

#include<iostream>
#include<cstdio>
#include <cstring>
#include<cmath>
#include<cstdlib>
#include<climits>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<list>
#include<stack>
using namespace std;
typedef long long LL;
/*
const int maxn = 1e9+1e8;
char sg[maxn];
int getsg(int S)
{
    if(sg[S] != -1) return sg[S];
    bool vis[31] = {0};
    for(int i = 1; i <= 30; i++)
        if(S&(1<<(i-1)))
        {
            int tmp = S;
            for(int j = i; j <= 30; j += i)
            {
                if(S&(1<<(j-1))) tmp -= 1<<(j-1);
            }
            vis[getsg(tmp)] = 1;
        }
    for(int i = 0; i <= 30; i++)
        if(!vis[i]) return sg[S] = i;
}
int main()
{
    memset(sg, -1, sizeof sg);
    sg[0] = 0;
    getsg((1<<29)-1);
    for(int i = 0; i < 30; i++) cout<<(int)sg[(1<<i)-1]<<",";
    return 0;
}
*/

const int maxn = 1e5;
int sg[] = {0,1,2,1,4,3,2,1,5,6,2,1,8,7,5,9,8,7,3,4,7,4,2,1,10,9,3,6,11,12};
bool vis[maxn] = {0};

int main()
{
    int n, m; cin>>n;
    if(n==1) return puts("Vasya"), 0;
    m = sqrt(n+0.5);
    int res = sg[1];
    int dif = 0;
    for(int i = 2; i <= m; i++)
        if(!vis[i])
        {
            int k = 0;
            for(LL j = i; j <= n; j *= i)
            {
                if(j <= m) vis[j] = true;
                else dif++;
                k++;
            }
            res ^= sg[k];
        }
    if((n-m-dif)&1) res ^= sg[1];
    puts(res?"Vasya":"Petya");
    return 0;
}