题意:n个人围成一圈,另外一个人最开始站在第一个人前面,每次从集合s里面随机选一个数x,这个人顺时针经过x个人后停下来,当前位置的前一个人出队,然后继续进行,求最后剩下的那个人的可能编号。
思路:由于只求最后一个人的编号,可以将一次操作后的人进行重编号,来进行状态转移,转化为子问题用dp来解决。dp方程比较容易写出,注意下细节就好了。
1 #pragma comment(linker, "/STACK:102400000,102400000") 2 3 #include <iostream> 4 #include <cstdio> 5 #include <algorithm> 6 #include <cstdlib> 7 #include <cstring> 8 #include <map> 9 #include <queue> 10 #include <deque> 11 #include <cmath> 12 #include <vector> 13 #include <ctime> 14 #include <cctype> 15 #include <set> 16 #include <bitset> 17 #include <functional> 18 #include <numeric> 19 #include <stdexcept> 20 #include <utility> 21 22 using namespace std; 23 24 #define mem0(a) memset(a, 0, sizeof(a)) 25 #define mem_1(a) memset(a, -1, sizeof(a)) 26 #define lson l, m, rt << 1 27 #define rson m + 1, r, rt << 1 | 1 28 #define define_m int m = (l + r) >> 1 29 #define rep_up0(a, b) for (int a = 0; a < (b); a++) 30 #define rep_up1(a, b) for (int a = 1; a <= (b); a++) 31 #define rep_down0(a, b) for (int a = b - 1; a >= 0; a--) 32 #define rep_down1(a, b) for (int a = b; a > 0; a--) 33 #define all(a) (a).begin(), (a).end() 34 #define lowbit(x) ((x) & (-(x))) 35 #define constructInt4(name, a, b, c, d) name(int a = 0, int b = 0, int c = 0, int d = 0): a(a), b(b), c(c), d(d) {} 36 #define constructInt3(name, a, b, c) name(int a = 0, int b = 0, int c = 0): a(a), b(b), c(c) {} 37 #define constructInt2(name, a, b) name(int a = 0, int b = 0): a(a), b(b) {} 38 #define pchr(a) putchar(a) 39 #define pstr(a) printf("%s", a) 40 #define sstr(a) scanf("%s", a) 41 #define sint(a) scanf("%d", &a) 42 #define sint2(a, b) scanf("%d%d", &a, &b) 43 #define sint3(a, b, c) scanf("%d%d%d", &a, &b, &c) 44 #define pint(a) printf("%d\n", a) 45 #define test_print1(a) cout << "var1 = " << a << endl 46 #define test_print2(a, b) cout << "var1 = " << a << ", var2 = " << b << endl 47 #define test_print3(a, b, c) cout << "var1 = " << a << ", var2 = " << b << ", var3 = " << c << endl 48 49 typedef long long LL; 50 typedef pair<int, int> pii; 51 typedef vector<int> vi; 52 53 const int dx[8] = {0, 0, -1, 1, 1, 1, -1, -1}; 54 const int dy[8] = {-1, 1, 0, 0, 1, -1, 1, -1 }; 55 const int maxn = 2e2 + 7; 56 const int md = 10007; 57 const int inf = 1e9 + 7; 58 const LL inf_L = 1e18 + 7; 59 const double pi = acos(-1.0); 60 const double eps = 1e-6; 61 62 template<class T>T gcd(T a, T b){return b==0?a:gcd(b,a%b);} 63 template<class T>bool max_update(T &a,const T &b){if(b>a){a = b; return true;}return false;} 64 template<class T>bool min_update(T &a,const T &b){if(b<a){a = b; return true;}return false;} 65 template<class T>T condition(bool f, T a, T b){return f?a:b;} 66 template<class T>void copy_arr(T a[], T b[], int n){rep_up0(i,n)a[i]=b[i];} 67 int make_id(int x, int y, int n) { return x * n + y; } 68 69 int p[maxn], f[maxn][maxn], ans[maxn]; 70 int main() { 71 //freopen("in.txt", "r", stdin); 72 int T, n, m; 73 cin >> T; 74 while (T--) { 75 cin >> n >> m; 76 rep_up0(i, m) { 77 sint(p[i]); 78 } 79 mem0(f); 80 f[n][0] = true; 81 for (int i = n - 1; i; i --) { 82 for (int j = 0; j < n - i + 1; j ++) { 83 rep_up0(k, m) { 84 if ((p[k] + n - i) % (n - i + 1) == j) continue; 85 int sta, tmp = p[k] % (n - i + 1); 86 if (j >= tmp) sta = j - tmp; 87 else sta = n - i + 1 - tmp + j; 88 f[i][j] = f[i][j] || f[i + 1][sta]; 89 } 90 } 91 } 92 int cnt = 0; 93 rep_up0(i, n) { 94 if (f[1][i]) ans[cnt ++] = i + 1; 95 } 96 cout << cnt << endl; 97 rep_up0(i, cnt) { 98 printf("%d%c", ans[i], i == cnt - 1? '\n' : ' '); 99 } 100 } 101 return 0; 102 }