D. Deleting Divisors

合集 - 记录随手刷过的编程题(69)

1.E. Arranging The Sheep2024-02-282.C. Team2024-02-293.C. RationalLee2024-03-014.B. Preparing Olympiad2024-03-055.B. Find The Array2024-03-056.E. Accidental Victory2024-03-067.A. Learning Languages2024-03-078.A. k-th divisor2024-03-089.B. Quasi Binary2024-03-0910.蓝桥杯-地宫取宝2024-03-0911.D. Divide by three, multiply by two2024-03-1212.D. Game With Array2024-03-1313.B. Composite Coloring2024-03-1414.洛谷 P1204 [USACO1.2] 挤牛奶Milking Cows2024-04-2015.洛谷 P3353 在你窗外闪耀的星星2024-04-2216.洛谷 P8818 [CSP-S 2022] 策略游戏2024-04-2317.Educational Codeforces Round 164 (Rated for Div. 2)2024-04-2518.E. Chain Reaction2024-04-2619.Manthan, Codefest 18 (rated, Div. 1 + Div. 2) D. Valid BFS?2024-04-2920.D. Distance in Tree2024-04-2921.D. Multiplication Table2024-04-3022.C. Mixing Water2024-05-0123.B. Greg and Graph2024-05-0624.D. Another Problem About Dividing Numbers2024-05-0725.Acwing 143. 最大异或对2024-05-0726.Acwing 3485. 最大异或和2024-05-0727.C. Checkposts2024-05-0828.E. Lomsat gelral2024-05-1129.D. Powerful array2024-05-15

30.D. Deleting Divisors2024-05-16

31.Codeforces Round 950 (Div. 3)2024-06-0432.Codeforces Round 951 (Div. 2)2024-06-0733.SuntoryProgrammingContest2024（AtCoder Beginner Contest 357）2024-06-0934.Codeforces Round 952 (Div. 4)2024-06-1235.AtCoder Beginner Contest 3582024-06-1736.B. Modulo Sum2024-06-2137.D. Soldier and Number Game2024-06-2238.AtCoder Beginner Contest 3592024-06-2439.Codeforces Round 954 (Div. 3)2024-06-2440.Codeforces Round 955 (Div. 2, with prizes from NEAR!)2024-06-2641.AtCoder Regular Contest 1802024-06-3042.D - Ghost Ants2024-07-0343.AtCoder Beginner Contest 361）2024-07-0744.Codeforces Round 957 (Div. 3)2024-07-1245.E. Decode2024-07-2946.Educational Codeforces Round 168 (Rated for Div. 2)2024-08-0647.B. Parity and Sum2024-08-0848.P1972 [SDOI2009] HH的项链2024-08-1249.Codeforces Round 966 (Div. 3) VP2024-08-1550.https://codeforces.com/contest/2004/problem/B2024-08-1951.C. Splitting Items2024-08-1952.D. Colored Portals2024-08-2053.Codeforces Round 967 (Div. 2)2024-08-2154.D. Determine Winning Islands in Race2024-08-2355.C. Turtle and Good Pairs2024-08-2856.Codeforces Round 970 (Div. 3)（VP）2024-09-0357.G. Sakurako's Task2024-09-0458.Codeforces Round 971 (Div. 4)2024-09-0459.C. Lazy Narek2024-09-1960.B. Regular Bracket Sequence02-2161.C. News Distribution02-2162.B. Karen and Coffee02-2163.G. 2^Sort02-2564.C. Johnny and Another Rating Drop03-0465.A. Greg and Array03-0566.D2. Magic Powder - 203-0667.C. Schedule Management03-0668.C. Constanze's Machine03-0769.C. Soldier and Cards03-08

收起

https://codeforces.com/contest/1537/problem/D

题意：给定数n，alice和bob博弈，alice先手。每次操作可以减去当前n的一个因子，并且该因子不能为n和1。问谁必胜。

思路：策略分析。基础分析：如果n是奇数，那么没有偶数因子。如果n是偶数，可能有偶数因子和奇数因子，如果只有偶数因子，n是2的整数次方。如果n是奇数，n要么是质数，要么一次操作后变成偶数。所以如果先手alice是奇数，必败。考虑偶数的情况，如果有奇数因子，那么一次操作后变成奇数，此时相当于奇数先手，所以bob必败。如果只有偶数因子，那么每次操作必须减去(n / 2)这个因子，假如减去了n / 4这个因子，可能会出现包含了奇数的偶数，那么此时就处于一个必败态了，比如8 - 2 = 6。所以此时看谁先拿到质因子2，谁拿到质因子2，谁就必败，统计二进制下末尾0的数量。如果是奇数个bob必胜。

总结：很巧妙的分析题，需要分析每种情况才行，一开始完全没有任何想法，纯纯的暴力找了个没逻辑的规律，不出意外tc2就挂了。

/*
  偶数，有奇因子，那么alice必胜。
  偶数，没有奇因子，说明是2的整数次方。此时的策略必须是减去最大的因子，(1 << (k -1))，否则相减后出现奇数因子必败。
        所以该情况下看谁拿到2，谁输。
  奇数，必败。
*/

void solve(){
    int n;
    cin >> n;

    if (n & 1){
        cout << "Bob\n";
    }
    else{
        if (__builtin_popcount(n) == 1 && (__builtin_ctz(n) & 1)){
            cout << "Bob\n";
        }
        else{
            cout << "Alice\n";
        }
    }
}