#include <iostream> #include <cstdio> #include <string> #include <sstream> #include <vector> #include <set> #include <map> #include <queue> #include <stack> #include <cmath> #include <algorithm> #include <cstring> #include <ctime> #include <cassert> #include "futbol.h" #include "message.h" using namespace std; using ll = long long; // futsoko42.in /* int GetN() { return 833713965; } int GetK() { return 424203011; } int GetP() { return 890139749; } */ // // helper functions // ll modPow(ll a, ll b, ll mod) { if (b == 0) return 1; if (b % 2 == 0) { auto c = modPow(a, b/2, mod); return (c * c) % mod; } return (a * modPow(a, b-1, mod)) % mod; } ll modInverse(ll a, ll mod) { return modPow(a, mod-2, mod); } // // common constants and routines // const int MASTER = 0; bool isMaster(const int id) { return id == MASTER; } struct InstanceResult { ll lastCoef; ll sumCoefs; }; const int MAX_BLOCK_SIZE = 1e7+100; int tmp[MAX_BLOCK_SIZE]; InstanceResult computeSubresult(const int id, const int numWorkers, const ll n, const ll k, const int mod) { const ll blockLen = ceil(k / (double)(numWorkers)); ll rangeBegin = id*blockLen; const ll rangeEnd = min(k, (id+1)*blockLen-1); InstanceResult res; if (rangeBegin == 0) { res.lastCoef = 1; res.sumCoefs = 1; ++rangeBegin; } else { res.lastCoef = 1; res.sumCoefs = 0; } // computing last coef ll prodNumerator = 1; ll prodDenominator = 1; int rangeLen = rangeEnd - rangeBegin + 1; //assert(rangeLen < MAX_BLOCK_SIZE); for (int i = rangeBegin; i <= rangeEnd; ++i) { prodNumerator = (prodNumerator * (n-i+1)) % mod; prodDenominator = (prodDenominator * i) % mod; } const ll invProdDenominator = modInverse(prodDenominator, mod); res.lastCoef = (prodNumerator * invProdDenominator) % mod; // computing sum tmp[0] = 1; tmp[rangeLen+1] = 1; ll finalDenominator = 1; // first pass from begining { for (int i = rangeBegin, j = 1; i <= rangeEnd; ++i, ++j) { tmp[j] = ((ll)tmp[j-1] * i) % mod; finalDenominator = (finalDenominator * tmp[j]) % mod; } } // second pass from end { for (int i = rangeEnd, j = rangeLen; i >= rangeBegin; --i, --j) { tmp[j] = ((ll)tmp[j] * tmp[j+1]) % mod; } } // third pass from begining { ll runProd1 = 1; ll runProd2 = 1; for (int i = rangeBegin, j = 1; i <= rangeEnd; ++i, ++j) { tmp[j] = (runProd2 * tmp[j+1]) % mod; runProd1 = (runProd1 * i) % mod; runProd2 = (runProd2 * runProd1) % mod; } } ll sumAdjustedNumerators = 0; ll runNum = 1; for (int i = rangeBegin, j = 1; i <= rangeEnd; ++i, ++j) { runNum = (runNum * (n-i+1)) % mod; sumAdjustedNumerators = (sumAdjustedNumerators + runNum * tmp[j]) % mod; } res.sumCoefs = (res.sumCoefs + sumAdjustedNumerators * modInverse(finalDenominator, mod)) % mod; return res; } // // Master instance algorithm // void masterAlgorithm(const int id, int numInstances) { const ll n = GetN(); const ll originalK = GetK(); const bool inversedComputation = originalK > n/2; const ll k = inversedComputation ? n-originalK-1 : originalK; const ll numWorkers = min(k+1, (ll)numInstances); const int mod = GetP(); if (originalK == n) { // special case when master can count result itself // receiving from other just to not leave any buffer non-empty for (int senderId = 0; senderId < numInstances; ++senderId) { if (senderId == id) continue; Receive(senderId); GetLL(senderId); GetLL(senderId); } auto res = modPow(2, n, mod); printf("%lld\n", res); return; } auto masterRes = computeSubresult(id, numWorkers, n, k, mod); vector<InstanceResult> subresults; for (int senderId = 0; senderId < numInstances; ++senderId) { if (senderId == id) continue; Receive(senderId); const ll lastCoef = GetLL(senderId); const ll sumCoefs = GetLL(senderId); subresults.push_back({lastCoef, sumCoefs}); } ll res = masterRes.sumCoefs; ll lastCoef = masterRes.lastCoef; for (const auto slaveRes : subresults) { res = (res + lastCoef * slaveRes.sumCoefs) % mod; lastCoef = (lastCoef * slaveRes.lastCoef) % mod; } if (inversedComputation) { res = (modPow(2, n, mod) - res + mod) % mod; } printf("%lld\n", res); } // // Slave instance algorithm // void slaveAlgorithm(const int id, int numInstances) { const ll n = GetN(); //const ll n = 0; const ll originalK = GetK(); // if slave doesn't know value of n // we return immediately an arbitrary value, // which will result in WA result most likely if (n < originalK) { InstanceResult dummyRes; dummyRes.lastCoef = 1; dummyRes.sumCoefs = 0; PutLL(MASTER, dummyRes.lastCoef); PutLL(MASTER, dummyRes.sumCoefs); Send(MASTER); return; } const bool inversedComputation = originalK > n/2; const ll k = inversedComputation ? n-originalK-1 : originalK; const ll numWorkers = min(k+1, (ll)numInstances); // don't need such instances // so return subresult that doesn't affect the final result if (id >= numWorkers) { InstanceResult dummyRes; dummyRes.lastCoef = 1; dummyRes.sumCoefs = 0; PutLL(MASTER, dummyRes.lastCoef); PutLL(MASTER, dummyRes.sumCoefs); Send(MASTER); return; } const int mod = GetP(); auto instanceRes = computeSubresult(id, numWorkers, n, k, mod); PutLL(MASTER, instanceRes.lastCoef); PutLL(MASTER, instanceRes.sumCoefs); Send(MASTER); } int main() { const int id = MyNodeId(); const int numInstances = NumberOfNodes(); if (isMaster(id)) { masterAlgorithm(id, numInstances); } else { slaveAlgorithm(id, numInstances); } 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 | #include <iostream> #include <cstdio> #include <string> #include <sstream> #include <vector> #include <set> #include <map> #include <queue> #include <stack> #include <cmath> #include <algorithm> #include <cstring> #include <ctime> #include <cassert> #include "futbol.h" #include "message.h" using namespace std; using ll = long long; // futsoko42.in /* int GetN() { return 833713965; } int GetK() { return 424203011; } int GetP() { return 890139749; } */ // // helper functions // ll modPow(ll a, ll b, ll mod) { if (b == 0) return 1; if (b % 2 == 0) { auto c = modPow(a, b/2, mod); return (c * c) % mod; } return (a * modPow(a, b-1, mod)) % mod; } ll modInverse(ll a, ll mod) { return modPow(a, mod-2, mod); } // // common constants and routines // const int MASTER = 0; bool isMaster(const int id) { return id == MASTER; } struct InstanceResult { ll lastCoef; ll sumCoefs; }; const int MAX_BLOCK_SIZE = 1e7+100; int tmp[MAX_BLOCK_SIZE]; InstanceResult computeSubresult(const int id, const int numWorkers, const ll n, const ll k, const int mod) { const ll blockLen = ceil(k / (double)(numWorkers)); ll rangeBegin = id*blockLen; const ll rangeEnd = min(k, (id+1)*blockLen-1); InstanceResult res; if (rangeBegin == 0) { res.lastCoef = 1; res.sumCoefs = 1; ++rangeBegin; } else { res.lastCoef = 1; res.sumCoefs = 0; } // computing last coef ll prodNumerator = 1; ll prodDenominator = 1; int rangeLen = rangeEnd - rangeBegin + 1; //assert(rangeLen < MAX_BLOCK_SIZE); for (int i = rangeBegin; i <= rangeEnd; ++i) { prodNumerator = (prodNumerator * (n-i+1)) % mod; prodDenominator = (prodDenominator * i) % mod; } const ll invProdDenominator = modInverse(prodDenominator, mod); res.lastCoef = (prodNumerator * invProdDenominator) % mod; // computing sum tmp[0] = 1; tmp[rangeLen+1] = 1; ll finalDenominator = 1; // first pass from begining { for (int i = rangeBegin, j = 1; i <= rangeEnd; ++i, ++j) { tmp[j] = ((ll)tmp[j-1] * i) % mod; finalDenominator = (finalDenominator * tmp[j]) % mod; } } // second pass from end { for (int i = rangeEnd, j = rangeLen; i >= rangeBegin; --i, --j) { tmp[j] = ((ll)tmp[j] * tmp[j+1]) % mod; } } // third pass from begining { ll runProd1 = 1; ll runProd2 = 1; for (int i = rangeBegin, j = 1; i <= rangeEnd; ++i, ++j) { tmp[j] = (runProd2 * tmp[j+1]) % mod; runProd1 = (runProd1 * i) % mod; runProd2 = (runProd2 * runProd1) % mod; } } ll sumAdjustedNumerators = 0; ll runNum = 1; for (int i = rangeBegin, j = 1; i <= rangeEnd; ++i, ++j) { runNum = (runNum * (n-i+1)) % mod; sumAdjustedNumerators = (sumAdjustedNumerators + runNum * tmp[j]) % mod; } res.sumCoefs = (res.sumCoefs + sumAdjustedNumerators * modInverse(finalDenominator, mod)) % mod; return res; } // // Master instance algorithm // void masterAlgorithm(const int id, int numInstances) { const ll n = GetN(); const ll originalK = GetK(); const bool inversedComputation = originalK > n/2; const ll k = inversedComputation ? n-originalK-1 : originalK; const ll numWorkers = min(k+1, (ll)numInstances); const int mod = GetP(); if (originalK == n) { // special case when master can count result itself // receiving from other just to not leave any buffer non-empty for (int senderId = 0; senderId < numInstances; ++senderId) { if (senderId == id) continue; Receive(senderId); GetLL(senderId); GetLL(senderId); } auto res = modPow(2, n, mod); printf("%lld\n", res); return; } auto masterRes = computeSubresult(id, numWorkers, n, k, mod); vector<InstanceResult> subresults; for (int senderId = 0; senderId < numInstances; ++senderId) { if (senderId == id) continue; Receive(senderId); const ll lastCoef = GetLL(senderId); const ll sumCoefs = GetLL(senderId); subresults.push_back({lastCoef, sumCoefs}); } ll res = masterRes.sumCoefs; ll lastCoef = masterRes.lastCoef; for (const auto slaveRes : subresults) { res = (res + lastCoef * slaveRes.sumCoefs) % mod; lastCoef = (lastCoef * slaveRes.lastCoef) % mod; } if (inversedComputation) { res = (modPow(2, n, mod) - res + mod) % mod; } printf("%lld\n", res); } // // Slave instance algorithm // void slaveAlgorithm(const int id, int numInstances) { const ll n = GetN(); //const ll n = 0; const ll originalK = GetK(); // if slave doesn't know value of n // we return immediately an arbitrary value, // which will result in WA result most likely if (n < originalK) { InstanceResult dummyRes; dummyRes.lastCoef = 1; dummyRes.sumCoefs = 0; PutLL(MASTER, dummyRes.lastCoef); PutLL(MASTER, dummyRes.sumCoefs); Send(MASTER); return; } const bool inversedComputation = originalK > n/2; const ll k = inversedComputation ? n-originalK-1 : originalK; const ll numWorkers = min(k+1, (ll)numInstances); // don't need such instances // so return subresult that doesn't affect the final result if (id >= numWorkers) { InstanceResult dummyRes; dummyRes.lastCoef = 1; dummyRes.sumCoefs = 0; PutLL(MASTER, dummyRes.lastCoef); PutLL(MASTER, dummyRes.sumCoefs); Send(MASTER); return; } const int mod = GetP(); auto instanceRes = computeSubresult(id, numWorkers, n, k, mod); PutLL(MASTER, instanceRes.lastCoef); PutLL(MASTER, instanceRes.sumCoefs); Send(MASTER); } int main() { const int id = MyNodeId(); const int numInstances = NumberOfNodes(); if (isMaster(id)) { masterAlgorithm(id, numInstances); } else { slaveAlgorithm(id, numInstances); } return 0; } |