#include <bits/stdc++.h> #define FOR(i, a, b) for (int i=(a); (i)<(b); (i)++) #define PPC(x) __builtin_popcountll((x)) #define ALL(x) (x).begin(), (x).end() #define pb push_back using namespace std; const int maxN = 1042, maxK = 12; int mod; long long dp[4][maxN][maxK], sp[4][maxN][maxK], cf[maxN][maxN]; int tps[4][2] = {{2, 1}, {3, 1}, {2, 3}, {3, 3}}; int dk[4][2][2] = {{{0, 0}, {0, 0}}, {{1, 0}, {1, 0}}, {{0, 1}, {0, 1}}, {{1, 1}, {0, 0}}}; inline void add(long long& a, long long b) { a = (a + b) % mod; } inline void mult(long long& a, long long b) { a = a * b % mod; } void cntcf() { FOR(n, 0, maxN) { cf[n][0] = cf[n][n] = 1; FOR(k, 1, n) cf[n][k] = (cf[n-1][k-1] + cf[n-1][k]) % mod; } } int main() { int N, K; scanf ("%d%d%d", &N, &K, &mod); if (K >= maxK) K = 0; cntcf(); FOR(t, 1, 4) { dp[t][0][0] = 1; FOR(k, 1, K+1) sp[t][0][k] = 1; } FOR(n, 1, N+1) FOR(k, 1, K+1) { FOR(i, 1, n+1) { long long temp, fr = cf[n-1][i-1]; int n1 = i-1, n2 = n-i; temp = (dp[2][n1][k] * dp[1][n2][k] + dp[2][n1][k] * sp[1][n2][k] + sp[2][n1][k] * dp[1][n2][k]) % mod; add(dp[0][n][k], temp * fr); temp = (dp[3][n1][k-1] * dp[1][n2][k] + dp[3][n1][k-1] * sp[1][n2][k] + sp[3][n1][k-1] * dp[1][n2][k]) % mod; add(dp[1][n][k], temp * fr); temp = (dp[2][n1][k] * dp[3][n2][k-1] + dp[2][n1][k] * sp[3][n2][k-1] + sp[2][n1][k] * dp[3][n2][k-1]) % mod; add(dp[2][n][k], temp * fr); temp = (dp[3][n1][k-1] * dp[3][n2][k-1] + dp[3][n1][k] * sp[3][n2][k] + sp[3][n1][k] * dp[3][n2][k]) % mod; add(dp[3][n][k], temp * fr); } FOR(t, 0, 4) { sp[t][n][k] = sp[t][n][k-1]; add(sp[t][n][k], dp[t][n][k-1]); } } printf("%lld\n", dp[0][N][K]); 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 70 | #include <bits/stdc++.h> #define FOR(i, a, b) for (int i=(a); (i)<(b); (i)++) #define PPC(x) __builtin_popcountll((x)) #define ALL(x) (x).begin(), (x).end() #define pb push_back using namespace std; const int maxN = 1042, maxK = 12; int mod; long long dp[4][maxN][maxK], sp[4][maxN][maxK], cf[maxN][maxN]; int tps[4][2] = {{2, 1}, {3, 1}, {2, 3}, {3, 3}}; int dk[4][2][2] = {{{0, 0}, {0, 0}}, {{1, 0}, {1, 0}}, {{0, 1}, {0, 1}}, {{1, 1}, {0, 0}}}; inline void add(long long& a, long long b) { a = (a + b) % mod; } inline void mult(long long& a, long long b) { a = a * b % mod; } void cntcf() { FOR(n, 0, maxN) { cf[n][0] = cf[n][n] = 1; FOR(k, 1, n) cf[n][k] = (cf[n-1][k-1] + cf[n-1][k]) % mod; } } int main() { int N, K; scanf ("%d%d%d", &N, &K, &mod); if (K >= maxK) K = 0; cntcf(); FOR(t, 1, 4) { dp[t][0][0] = 1; FOR(k, 1, K+1) sp[t][0][k] = 1; } FOR(n, 1, N+1) FOR(k, 1, K+1) { FOR(i, 1, n+1) { long long temp, fr = cf[n-1][i-1]; int n1 = i-1, n2 = n-i; temp = (dp[2][n1][k] * dp[1][n2][k] + dp[2][n1][k] * sp[1][n2][k] + sp[2][n1][k] * dp[1][n2][k]) % mod; add(dp[0][n][k], temp * fr); temp = (dp[3][n1][k-1] * dp[1][n2][k] + dp[3][n1][k-1] * sp[1][n2][k] + sp[3][n1][k-1] * dp[1][n2][k]) % mod; add(dp[1][n][k], temp * fr); temp = (dp[2][n1][k] * dp[3][n2][k-1] + dp[2][n1][k] * sp[3][n2][k-1] + sp[2][n1][k] * dp[3][n2][k-1]) % mod; add(dp[2][n][k], temp * fr); temp = (dp[3][n1][k-1] * dp[3][n2][k-1] + dp[3][n1][k] * sp[3][n2][k] + sp[3][n1][k] * dp[3][n2][k]) % mod; add(dp[3][n][k], temp * fr); } FOR(t, 0, 4) { sp[t][n][k] = sp[t][n][k-1]; add(sp[t][n][k], dp[t][n][k-1]); } } printf("%lld\n", dp[0][N][K]); return 0; } |