#include <iostream> #include <vector> using namespace std; typedef long long ll; int main() { ios_base::sync_with_stdio(0); int n, k, p; cin >> n >> k >> p; vector<vector<int>> bi(n+1, vector<int>(n+1, 0)); bi[0][0] = 1; for (int i = 1; i <= n; i++) { bi[i][0] = bi[i][i] = 1; for (int j = 1; j < i; j++) { bi[i][j] = ((ll)bi[i-1][j] + bi[i-1][j-1]) % p; } } vector<vector<vector<int>>> a(n, vector<vector<int>>(min(n, k+1), vector<int>(2, 0))); vector<vector<int>> b(n, vector<int>(k+1, 0)); a[1][1][0] = a[1][1][1] = 1; b[1][1] = 1; for (int i = 2; i < n; i++) { for (int j = 1; j <= min(i, k); j++) { ll x = a[i-1][j][0]; for (int l = 1; l < i-1; l++) { x = (x + (ll)a[l][j-1][1] * b[i-1-l][j-1] * bi[i-1][l]) % p; } x += a[i-1][j-1][1]; a[i][j][0] = x % p; b[i][j] = ((ll)b[i][j-1] + x) % p; x = (2 * a[i-1][j][1]) % p; for (int l = 1; l < i-1; l++) { x = (x + (ll)a[l][j-1][1] * a[i-1-l][j-1][1] * bi[i-1][l]) % p; } a[i][j][1] = x; } } ll res = (2 * a[n-1][k][0]) % p; for (int l = 1; l < n-1; l++) { ll tmpr = 0; tmpr += (ll)a[l][k][0] * a[n-1-l][k][0]; tmpr %= p; tmpr += (ll)a[l][k][0] * b[n-1-l][k-1]; tmpr %= p; tmpr += (ll)b[l][k-1] * a[n-1-l][k][0]; tmpr %= p; res = (res + (ll)bi[n-1][l] * tmpr) % p; } cout << res << endl; return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | #include <iostream> #include <vector> using namespace std; typedef long long ll; int main() { ios_base::sync_with_stdio(0); int n, k, p; cin >> n >> k >> p; vector<vector<int>> bi(n+1, vector<int>(n+1, 0)); bi[0][0] = 1; for (int i = 1; i <= n; i++) { bi[i][0] = bi[i][i] = 1; for (int j = 1; j < i; j++) { bi[i][j] = ((ll)bi[i-1][j] + bi[i-1][j-1]) % p; } } vector<vector<vector<int>>> a(n, vector<vector<int>>(min(n, k+1), vector<int>(2, 0))); vector<vector<int>> b(n, vector<int>(k+1, 0)); a[1][1][0] = a[1][1][1] = 1; b[1][1] = 1; for (int i = 2; i < n; i++) { for (int j = 1; j <= min(i, k); j++) { ll x = a[i-1][j][0]; for (int l = 1; l < i-1; l++) { x = (x + (ll)a[l][j-1][1] * b[i-1-l][j-1] * bi[i-1][l]) % p; } x += a[i-1][j-1][1]; a[i][j][0] = x % p; b[i][j] = ((ll)b[i][j-1] + x) % p; x = (2 * a[i-1][j][1]) % p; for (int l = 1; l < i-1; l++) { x = (x + (ll)a[l][j-1][1] * a[i-1-l][j-1][1] * bi[i-1][l]) % p; } a[i][j][1] = x; } } ll res = (2 * a[n-1][k][0]) % p; for (int l = 1; l < n-1; l++) { ll tmpr = 0; tmpr += (ll)a[l][k][0] * a[n-1-l][k][0]; tmpr %= p; tmpr += (ll)a[l][k][0] * b[n-1-l][k-1]; tmpr %= p; tmpr += (ll)b[l][k-1] * a[n-1-l][k][0]; tmpr %= p; res = (res + (ll)bi[n-1][l] * tmpr) % p; } cout << res << endl; return 0; } |