#include <bits/stdc++.h> using namespace std; typedef long long val_t; long double solve(int maxVelocity, vector <int> &velocity, vector <vector<val_t>> &cars) { vector <int> allVelocities = velocity; allVelocities.insert(allVelocities.begin(), maxVelocity); long long denom = 1; for (int i = 0; i < 4; i++) for (int j = i + 1; j < 4; j++) { denom *= allVelocities[i] - allVelocities[j]; } vector <int> nCars(3); vector <vector<pair<val_t,int>>> carsUnblocked(3); vector <vector<int>> carBlockStart(3); vector <vector<val_t>> dp(3); for (int lane = 0; lane < 3; lane++) { nCars[lane] = cars[lane].size(); dp[lane].resize(nCars[lane], -1); carBlockStart[lane].resize(nCars[lane]); int blockStart = 0; for (int carId = 0; carId < nCars[lane]; carId++) { carBlockStart[lane][carId] = blockStart; if (carId == nCars[lane] - 1 || cars[lane][carId + 1] > cars[lane][carId] + 1) { carsUnblocked[lane].push_back({denom * cars[lane][carId], carId}); blockStart = carId + 1; } } } for (int lane = 0; lane < 3; lane++) for (val_t &x : cars[lane]) { x *= denom; } dp[2][0] = 0; set <pair<val_t, pair<int,int>>> q; q.insert({0, {2, 0}}); while (!q.empty()) { auto [_, s] = *q.begin(); q.erase(q.begin()); auto [refLane, carId] = s; if (carId == nCars[refLane] - 1) { continue; } val_t currTime = dp[refLane][carId]; val_t pos = cars[refLane][carId] + currTime * velocity[refLane]; vector <val_t> nextCarId(3); vector <val_t> switchDelay(3, 0); for (int lane = 0; lane < 3; lane++) { val_t threshold = 2 * denom + pos - currTime * velocity[lane]; nextCarId[lane] = lower_bound( cars[lane].begin(), cars[lane].end(), threshold ) - cars[lane].begin(); int blockingCarId = nextCarId[lane] - 1; if (blockingCarId >= 0) { val_t blockingPos = cars[lane][blockingCarId] + currTime * velocity[lane]; val_t posDiff = blockingPos - pos; if (posDiff > 0) { if (lane < refLane) { int blockStart = carBlockStart[lane][blockingCarId]; val_t blockingPart = denom * (blockingCarId - blockStart + 2) - posDiff; switchDelay[lane] = blockingPart / (velocity[lane] - velocity[refLane]); nextCarId[lane] = blockStart; } else { switchDelay[lane] = -1; } } } } if (refLane != 1) { int flipLane = 2 - refLane; if (switchDelay[1] == -1) { switchDelay[flipLane] = -1; } else if (switchDelay[flipLane] != -1) { switchDelay[flipLane] = max(switchDelay[flipLane], switchDelay[1]); } } for (int lane = 0; lane < 3; lane++) if (switchDelay[lane] != -1) { val_t currTimeWithDelay = currTime + switchDelay[lane]; val_t posWithDelay = cars[refLane][carId] + currTimeWithDelay * velocity[refLane]; for (int otherLane = 0; otherLane < 3; otherLane++) if (abs(lane - otherLane) == 1) { val_t threshold = posWithDelay - currTimeWithDelay * velocity[otherLane]; int firstIdx = lower_bound( carsUnblocked[otherLane].begin(), carsUnblocked[otherLane].end(), make_pair(threshold, -1) ) - carsUnblocked[otherLane].begin(); for (int idx : {firstIdx, firstIdx + 1}) { if (idx == (int) carsUnblocked[otherLane].size()) { break; } int otherCarId = carsUnblocked[otherLane][idx].second; val_t posDiff = cars[otherLane][otherCarId] - threshold, extraTime; if (posDiff <= 0) { extraTime = 0; } else { val_t catchUpTime = posDiff / (maxVelocity - velocity[otherLane]); if (nextCarId[lane] < nCars[lane]) { val_t nextCarPos = cars[lane][nextCarId[lane]] + currTimeWithDelay * velocity[lane]; val_t gapSize = nextCarPos - posWithDelay - 2 * denom; val_t maxVelocityTime = gapSize / (maxVelocity - velocity[lane]); if (catchUpTime <= maxVelocityTime) { extraTime = catchUpTime; } else if (lane < otherLane) { posDiff -= maxVelocityTime * (maxVelocity - velocity[otherLane]); extraTime = maxVelocityTime + posDiff / (velocity[lane] - velocity[otherLane]); } else { break; } } else { extraTime = catchUpTime; } } val_t newSol = currTimeWithDelay + extraTime; val_t oldSol = dp[otherLane][otherCarId]; if (oldSol == -1 || newSol < oldSol) { if (oldSol != -1) { q.erase({oldSol, {otherLane, otherCarId}}); } dp[otherLane][otherCarId] = newSol; q.insert({newSol, {otherLane, otherCarId}}); } } } } } val_t ans = -1; for (int lane = 0; lane < 3; lane++) if (nCars[lane] > 0) { val_t currTime = dp[lane].back(); if (currTime == -1) { continue; } val_t pos = cars[lane].back() + currTime * velocity[lane], extraTime = 0; for (int otherLane = 0; otherLane < 3; otherLane++) if (nCars[otherLane] > 0) { val_t otherPos = cars[otherLane].back() + currTime * velocity[otherLane]; val_t posDiff = otherPos - pos; if (posDiff > 0) { extraTime = max(extraTime, posDiff / (maxVelocity - velocity[otherLane])); } } val_t ansHere = currTime + extraTime; if (ans == -1 || ansHere < ans) { ans = ansHere; } } return ((long double) ans) / denom; } int main() { ios_base::sync_with_stdio(false); cout << setprecision(15) << fixed; int len, maxVelocity; cin >> len >> maxVelocity; vector <int> velocity(3); for (int lane = 0; lane < 3; lane++) { cin >> velocity[lane]; } vector <vector<val_t>> cars(3); for (int lane = 0; lane < 3; lane++) { string s; cin >> s; if (lane < 2) { s = "." + s; } else { s[0] = '.'; s = "#" + s; } for (int x = 0; x <= len; x++) if (s[x] == '#') { cars[lane].push_back(x); } } cout << solve(maxVelocity, velocity, cars); 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 | #include <bits/stdc++.h> using namespace std; typedef long long val_t; long double solve(int maxVelocity, vector <int> &velocity, vector <vector<val_t>> &cars) { vector <int> allVelocities = velocity; allVelocities.insert(allVelocities.begin(), maxVelocity); long long denom = 1; for (int i = 0; i < 4; i++) for (int j = i + 1; j < 4; j++) { denom *= allVelocities[i] - allVelocities[j]; } vector <int> nCars(3); vector <vector<pair<val_t,int>>> carsUnblocked(3); vector <vector<int>> carBlockStart(3); vector <vector<val_t>> dp(3); for (int lane = 0; lane < 3; lane++) { nCars[lane] = cars[lane].size(); dp[lane].resize(nCars[lane], -1); carBlockStart[lane].resize(nCars[lane]); int blockStart = 0; for (int carId = 0; carId < nCars[lane]; carId++) { carBlockStart[lane][carId] = blockStart; if (carId == nCars[lane] - 1 || cars[lane][carId + 1] > cars[lane][carId] + 1) { carsUnblocked[lane].push_back({denom * cars[lane][carId], carId}); blockStart = carId + 1; } } } for (int lane = 0; lane < 3; lane++) for (val_t &x : cars[lane]) { x *= denom; } dp[2][0] = 0; set <pair<val_t, pair<int,int>>> q; q.insert({0, {2, 0}}); while (!q.empty()) { auto [_, s] = *q.begin(); q.erase(q.begin()); auto [refLane, carId] = s; if (carId == nCars[refLane] - 1) { continue; } val_t currTime = dp[refLane][carId]; val_t pos = cars[refLane][carId] + currTime * velocity[refLane]; vector <val_t> nextCarId(3); vector <val_t> switchDelay(3, 0); for (int lane = 0; lane < 3; lane++) { val_t threshold = 2 * denom + pos - currTime * velocity[lane]; nextCarId[lane] = lower_bound( cars[lane].begin(), cars[lane].end(), threshold ) - cars[lane].begin(); int blockingCarId = nextCarId[lane] - 1; if (blockingCarId >= 0) { val_t blockingPos = cars[lane][blockingCarId] + currTime * velocity[lane]; val_t posDiff = blockingPos - pos; if (posDiff > 0) { if (lane < refLane) { int blockStart = carBlockStart[lane][blockingCarId]; val_t blockingPart = denom * (blockingCarId - blockStart + 2) - posDiff; switchDelay[lane] = blockingPart / (velocity[lane] - velocity[refLane]); nextCarId[lane] = blockStart; } else { switchDelay[lane] = -1; } } } } if (refLane != 1) { int flipLane = 2 - refLane; if (switchDelay[1] == -1) { switchDelay[flipLane] = -1; } else if (switchDelay[flipLane] != -1) { switchDelay[flipLane] = max(switchDelay[flipLane], switchDelay[1]); } } for (int lane = 0; lane < 3; lane++) if (switchDelay[lane] != -1) { val_t currTimeWithDelay = currTime + switchDelay[lane]; val_t posWithDelay = cars[refLane][carId] + currTimeWithDelay * velocity[refLane]; for (int otherLane = 0; otherLane < 3; otherLane++) if (abs(lane - otherLane) == 1) { val_t threshold = posWithDelay - currTimeWithDelay * velocity[otherLane]; int firstIdx = lower_bound( carsUnblocked[otherLane].begin(), carsUnblocked[otherLane].end(), make_pair(threshold, -1) ) - carsUnblocked[otherLane].begin(); for (int idx : {firstIdx, firstIdx + 1}) { if (idx == (int) carsUnblocked[otherLane].size()) { break; } int otherCarId = carsUnblocked[otherLane][idx].second; val_t posDiff = cars[otherLane][otherCarId] - threshold, extraTime; if (posDiff <= 0) { extraTime = 0; } else { val_t catchUpTime = posDiff / (maxVelocity - velocity[otherLane]); if (nextCarId[lane] < nCars[lane]) { val_t nextCarPos = cars[lane][nextCarId[lane]] + currTimeWithDelay * velocity[lane]; val_t gapSize = nextCarPos - posWithDelay - 2 * denom; val_t maxVelocityTime = gapSize / (maxVelocity - velocity[lane]); if (catchUpTime <= maxVelocityTime) { extraTime = catchUpTime; } else if (lane < otherLane) { posDiff -= maxVelocityTime * (maxVelocity - velocity[otherLane]); extraTime = maxVelocityTime + posDiff / (velocity[lane] - velocity[otherLane]); } else { break; } } else { extraTime = catchUpTime; } } val_t newSol = currTimeWithDelay + extraTime; val_t oldSol = dp[otherLane][otherCarId]; if (oldSol == -1 || newSol < oldSol) { if (oldSol != -1) { q.erase({oldSol, {otherLane, otherCarId}}); } dp[otherLane][otherCarId] = newSol; q.insert({newSol, {otherLane, otherCarId}}); } } } } } val_t ans = -1; for (int lane = 0; lane < 3; lane++) if (nCars[lane] > 0) { val_t currTime = dp[lane].back(); if (currTime == -1) { continue; } val_t pos = cars[lane].back() + currTime * velocity[lane], extraTime = 0; for (int otherLane = 0; otherLane < 3; otherLane++) if (nCars[otherLane] > 0) { val_t otherPos = cars[otherLane].back() + currTime * velocity[otherLane]; val_t posDiff = otherPos - pos; if (posDiff > 0) { extraTime = max(extraTime, posDiff / (maxVelocity - velocity[otherLane])); } } val_t ansHere = currTime + extraTime; if (ans == -1 || ansHere < ans) { ans = ansHere; } } return ((long double) ans) / denom; } int main() { ios_base::sync_with_stdio(false); cout << setprecision(15) << fixed; int len, maxVelocity; cin >> len >> maxVelocity; vector <int> velocity(3); for (int lane = 0; lane < 3; lane++) { cin >> velocity[lane]; } vector <vector<val_t>> cars(3); for (int lane = 0; lane < 3; lane++) { string s; cin >> s; if (lane < 2) { s = "." + s; } else { s[0] = '.'; s = "#" + s; } for (int x = 0; x <= len; x++) if (s[x] == '#') { cars[lane].push_back(x); } } cout << solve(maxVelocity, velocity, cars); return 0; } |