#include <bits/stdc++.h> #define forn(i, n) for(int i = 0; i < n; ++i) using namespace std; typedef long long ll; typedef pair<int, int> pint; ll n,p; int k; ll dwumian[1042][1042]; void policz_dwumian() { for (int i=0; i<1042; i++) { dwumian[i][i] = 1; dwumian[i][0] = 1; } for (int i=2; i<1042; i++) { for (int j=1; j<i; j++) { dwumian[i][j] = (dwumian[i-1][j-1] + dwumian[i-1][j]) % p; } } } ll dp[1042][1042][3]; // dl przedzialu, czas trwania rozpadu, 0=z lewej staly, 1 = w srodku, 2 = z prawej staly int max_t[1042]; void cnt_dp() { for (int i=0; i<1042; i++) { for (int j=0; j<1042; j++) { for (int k=0; k<3; k++) { dp[i][j][k] = 0; } } } dp[1][1][0] = 1; dp[1][1][1] = 1; dp[1][1][2] = 1; max_t[1] = 1; for (int len = 2; len < n; len++) { // max po lewej for (int t1 = 1; t1 <= max_t[len-1]; t1++) { dp[len][t1+1][0] = (dp[len][t1+1][0] + dp[len-1][t1][1]) % p; max_t[len] = max(max_t[len], t1+1); dp[len][t1][1] = (dp[len][t1][1] + dp[len-1][t1][1]) % p; max_t[len] = max(max_t[len], t1); } for (int t2 = 1; t2 <= max_t[len-1]; t2++) { dp[len][t2][2] = (dp[len][t2][2] + dp[len-1][t2][2]) % p; max_t[len] = max(max_t[len], t2); } // max w srodku for (int left = 1; left < len - 1; left++) { int right = len - left - 1; ll ways = dwumian[len-1][left]; for (int tl = 1; tl <= max_t[left]; tl++) { for (int tr = 1; tr <= max_t[right]; tr++) { int t = max(tl,tr); if (t == min(tl,tr)) t++; dp[len][t][0] = ( dp[len][t][0] + ( ( (ways * dp[left][tl][0] ) % p) * dp[right][tr][1] ) % p ) % p; dp[len][t][1] = ( dp[len][t][1] + ( ( (ways * dp[left][tl][1] ) % p) * dp[right][tr][1] ) % p ) % p; dp[len][t][2] = ( dp[len][t][2] + ( ( (ways * dp[left][tl][1] ) % p) * dp[right][tr][2] ) % p ) % p; max_t[len] = max(max_t[len], t); } } } // max po prawej for (int t0 = 1; t0 <= max_t[len-1]; t0++) { dp[len][t0][0] = (dp[len][t0][0] + dp[len-1][t0][0]) % p; max_t[len] = max(max_t[len], t0); } for (int t1 = 1; t1 <= max_t[len-1]; t1++) { dp[len][t1][1] = (dp[len][t1][1] + dp[len-1][t1][1]) % p; max_t[len] = max(max_t[len], t1); dp[len][t1+1][2] = (dp[len][t1+1][2] + dp[len-1][t1][1]) % p; max_t[len] = max(max_t[len], t1+1); } max_t[len] = min(max_t[len], k); } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cin >> n >> k >> p; if (k > 15) { cout << 0; return 0; } policz_dwumian(); cnt_dp(); // for (int l=1; l<=n; l++) // { // for (int i=1; i<=max_t[l]; i++) // { // for (int j=0; j<3; j++) // { // cout << "dp[" << l << "][" << i << "][" << j << "] = " << dp[l][i][j] << "\n"; // } // } // } ll ans = dp[n-1][k][2]; //cout << "1 " << dp[n-1][k][2] << "\n"; ans = ( ans + dp[n-1][k][0] ) % p; //cout << "2 " << dp[n-1][k][0] << "\n"; for (int left = 1; left < n-1; left++) { int right = n - left - 1; for (int sm = 1; sm < k; sm++) { ll ways = dwumian[n-1][left]; ans = ( ans + ( (( ways * dp[left][k][0] ) % p) * dp[right][sm][2] ) % p ) % p; ans = ( ans + ( (( ways * dp[left][sm][0] ) % p) * dp[right][k][2] ) % p ) % p; } ll ways = dwumian[n-1][left]; ans = ( ans + ( (( ways * dp[left][k][0] ) % p) * dp[right][k][2] ) % p ) % p; } cout << ans << "\n"; 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 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 | #include <bits/stdc++.h> #define forn(i, n) for(int i = 0; i < n; ++i) using namespace std; typedef long long ll; typedef pair<int, int> pint; ll n,p; int k; ll dwumian[1042][1042]; void policz_dwumian() { for (int i=0; i<1042; i++) { dwumian[i][i] = 1; dwumian[i][0] = 1; } for (int i=2; i<1042; i++) { for (int j=1; j<i; j++) { dwumian[i][j] = (dwumian[i-1][j-1] + dwumian[i-1][j]) % p; } } } ll dp[1042][1042][3]; // dl przedzialu, czas trwania rozpadu, 0=z lewej staly, 1 = w srodku, 2 = z prawej staly int max_t[1042]; void cnt_dp() { for (int i=0; i<1042; i++) { for (int j=0; j<1042; j++) { for (int k=0; k<3; k++) { dp[i][j][k] = 0; } } } dp[1][1][0] = 1; dp[1][1][1] = 1; dp[1][1][2] = 1; max_t[1] = 1; for (int len = 2; len < n; len++) { // max po lewej for (int t1 = 1; t1 <= max_t[len-1]; t1++) { dp[len][t1+1][0] = (dp[len][t1+1][0] + dp[len-1][t1][1]) % p; max_t[len] = max(max_t[len], t1+1); dp[len][t1][1] = (dp[len][t1][1] + dp[len-1][t1][1]) % p; max_t[len] = max(max_t[len], t1); } for (int t2 = 1; t2 <= max_t[len-1]; t2++) { dp[len][t2][2] = (dp[len][t2][2] + dp[len-1][t2][2]) % p; max_t[len] = max(max_t[len], t2); } // max w srodku for (int left = 1; left < len - 1; left++) { int right = len - left - 1; ll ways = dwumian[len-1][left]; for (int tl = 1; tl <= max_t[left]; tl++) { for (int tr = 1; tr <= max_t[right]; tr++) { int t = max(tl,tr); if (t == min(tl,tr)) t++; dp[len][t][0] = ( dp[len][t][0] + ( ( (ways * dp[left][tl][0] ) % p) * dp[right][tr][1] ) % p ) % p; dp[len][t][1] = ( dp[len][t][1] + ( ( (ways * dp[left][tl][1] ) % p) * dp[right][tr][1] ) % p ) % p; dp[len][t][2] = ( dp[len][t][2] + ( ( (ways * dp[left][tl][1] ) % p) * dp[right][tr][2] ) % p ) % p; max_t[len] = max(max_t[len], t); } } } // max po prawej for (int t0 = 1; t0 <= max_t[len-1]; t0++) { dp[len][t0][0] = (dp[len][t0][0] + dp[len-1][t0][0]) % p; max_t[len] = max(max_t[len], t0); } for (int t1 = 1; t1 <= max_t[len-1]; t1++) { dp[len][t1][1] = (dp[len][t1][1] + dp[len-1][t1][1]) % p; max_t[len] = max(max_t[len], t1); dp[len][t1+1][2] = (dp[len][t1+1][2] + dp[len-1][t1][1]) % p; max_t[len] = max(max_t[len], t1+1); } max_t[len] = min(max_t[len], k); } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cin >> n >> k >> p; if (k > 15) { cout << 0; return 0; } policz_dwumian(); cnt_dp(); // for (int l=1; l<=n; l++) // { // for (int i=1; i<=max_t[l]; i++) // { // for (int j=0; j<3; j++) // { // cout << "dp[" << l << "][" << i << "][" << j << "] = " << dp[l][i][j] << "\n"; // } // } // } ll ans = dp[n-1][k][2]; //cout << "1 " << dp[n-1][k][2] << "\n"; ans = ( ans + dp[n-1][k][0] ) % p; //cout << "2 " << dp[n-1][k][0] << "\n"; for (int left = 1; left < n-1; left++) { int right = n - left - 1; for (int sm = 1; sm < k; sm++) { ll ways = dwumian[n-1][left]; ans = ( ans + ( (( ways * dp[left][k][0] ) % p) * dp[right][sm][2] ) % p ) % p; ans = ( ans + ( (( ways * dp[left][sm][0] ) % p) * dp[right][k][2] ) % p ) % p; } ll ways = dwumian[n-1][left]; ans = ( ans + ( (( ways * dp[left][k][0] ) % p) * dp[right][k][2] ) % p ) % p; } cout << ans << "\n"; return 0; } |