#include <cstdio> #include <cmath> #include <iostream> #include <algorithm> #include <queue> #include <list> #include <vector> #include <map> #include <set> #include <string> #include <cstring> #include <cassert> #include <limits.h> using namespace std; typedef long long LL; typedef long double LD; typedef vector<int> VI; typedef pair<int,int> PII; #define REP(i,n) for(int i=0;i<(n);i++) #define FOR(i,a,b) for(VAR(i,a);i<=(b);++i) #define FORD(i,a,b) for(VAR(i,a);i>=(b);--i) #define FORE(a,b) for(VAR(a,(b).begin());a!=(b).end();++a) #define VAR(a,b) __typeof(b) a=(b) #define SIZE(a) ((int)((a).size())) #define ALL(x) (x).begin(),(x).end() #define CLR(x,a) memset(x,a,sizeof(x)) #define ZERO(x) memset(x,0,sizeof(x)) #define S(t,i) scanf("%" ## t, &i) #define SI(i) scanf("%d", &i) const int INF=INT_MAX-400000; const int MAXL=200000+5; const long double EPS=0.0000000001; int L, v[4]; long double result; struct Slot { int x; int l; long double vt=INF; long double vx=INF; bool visited=false; }; Slot lane[3][MAXL/2]; int laneLength[3]; struct SlotCoordinate { int lane; int slot; long double t; long double x; }; inline bool comparePossitionsWithinSlot(long double t1, long double x1, long double t2, long double x2) { long double diff = t1 + (x2-x1)/v[3] - t2; return abs(diff) < EPS ? t1 < t2 : diff < 0; // long double diff = t1 - t2; // return abs(diff) < EPS ? x1<x2 : t1 < t2; } auto compareSlots = [](const SlotCoordinate &b, const SlotCoordinate &a) { // return abs(a.t-b.t) <EPS ? a.x>b.x : a.t<b.t; return comparePossitionsWithinSlot(a.t, a.x, b.t, b.x); }; priority_queue<SlotCoordinate, std::vector<SlotCoordinate>, decltype(compareSlots)> q(compareSlots); long double getIntersectionTime(long double ta, long double xa, long double va, long double xs, long double vs) { return max(ta, ((xs-xa)+ta*va)/(va-vs)); } int getFirstSlotInLane(int targetLaneId, long double x0) { Slot *targetLane = &lane[targetLaneId][0]; int l=-1; int r=laneLength[targetLaneId]; while (l+1<r) { int k=(l+r)/2; Slot &s = targetLane[k]; if (s.visited || (x0 - (s.x+(long double)s.l-1) > EPS)) { l=k; } else { r=k; } } return l+1; // int firstSlotInLane = (int) (lower_bound(&targetLane[0], &targetLane[laneLength[targetLaneId]], x0, [](Slot &s, long double value){ // return s.visited || s.x+(long double)s.l-1 - value < EPS; // }) - targetLane); // return firstSlotInLane; } inline void addToQueue(long double intersetionTime, long double intersetionX, int targetLaneId, int targetSlotId) { Slot &targetSlot = lane[targetLaneId][targetSlotId]; if (comparePossitionsWithinSlot(intersetionTime, intersetionX, targetSlot.vt, targetSlot.vx)) { targetSlot.vt =intersetionTime; targetSlot.vx =intersetionX; SlotCoordinate new_sc; new_sc.lane = targetLaneId; new_sc.slot = targetSlotId; new_sc.t = intersetionTime; new_sc.x = intersetionX; q.push(new_sc); // printf("a %d %d %.10Lf %.10Lf\n", new_sc.lane, new_sc.slot, new_sc.t, new_sc.x); // assert(targetSlot.x+intersetionTime*v[targetLaneId] <= intersetionX+EPS); // assert(targetSlot.x+(long double)targetSlot.l-1+intersetionTime*v[targetLaneId] >= intersetionX-EPS); // return true; } // return false; } long double findmaxval (long double num1, long double num2){ return num1 > num2 ? num1 : num2; } int main() { ios_base::sync_with_stdio(0); SI(L); SI(v[3]); REP(i, 3) { SI(v[i]); } FOR(i, 0, 2) { char c, prevc; scanf(" "); fread(&c, 1, sizeof(char), stdin); c='.'; laneLength[i]=1; lane[i][0].l=1; lane[i][0].x=0; lane[i][0].vt=INF; lane[i][0].vx=INF; FOR(x, 1, L-1) { prevc=c; fread(&c, 1, sizeof(char), stdin); if (c=='.') { if (prevc == '.') { Slot &s = lane[i][laneLength[i]-1]; s.l++; } else { laneLength[i]++; Slot &s = lane[i][laneLength[i]-1]; s.x = x; s.l = 1; s.vt=INF; s.vx=INF; } } } if (c=='#') { laneLength[i]++; Slot &s = lane[i][laneLength[i]-1]; s.x = L; s.l = INF; } else { Slot &s = lane[i][laneLength[i]-1]; s.l = INF; } } SlotCoordinate new_sc; new_sc.lane = 2; new_sc.slot = 0; new_sc.t = 0; new_sc.x = 0; lane[2][0].vt = 0; lane[2][0].vx = 0; q.push(new_sc); while (!q.empty()) { SlotCoordinate sc = q.top(); q.pop(); Slot &s = lane[sc.lane][sc.slot]; if (!s.visited) { // printf("v %d %d %.10Lf %.10Lf\n", sc.lane, sc.slot, s.vt, s.vx); s.visited = true; int currentLaneId = sc.lane; if (sc.lane < 2) { int targetLaneId = sc.lane+1; Slot *targetLane = &lane[targetLaneId][0]; long double x0 = s.vx - v[sc.lane]*s.vt; int firstSlotInLane = getFirstSlotInLane(targetLaneId, s.vx - v[targetLaneId]*s.vt); FORD(targetSlotId, laneLength[targetLaneId]-1, firstSlotInLane) { long double intersetionTime = getIntersectionTime(s.vt, s.vx, v[3], targetLane[targetSlotId].x, v[targetLaneId]); long double maxFullSpeedTime = (s.x + (long double)s.l-1 - x0)/(v[3]-v[currentLaneId]); long double intersetionX; if (maxFullSpeedTime + EPS >= intersetionTime - s.vt) { intersetionX = s.vx+(intersetionTime - s.vt)*v[3]; } else { long double timeAtTheEndOdSlot = maxFullSpeedTime + s.vt; long double positionAtTheEndOdSlot = s.vx + maxFullSpeedTime*v[3]; intersetionTime = getIntersectionTime(timeAtTheEndOdSlot, positionAtTheEndOdSlot, v[currentLaneId], targetLane[targetSlotId].x, v[targetLaneId]); intersetionX = positionAtTheEndOdSlot+(intersetionTime - timeAtTheEndOdSlot)*v[currentLaneId]; } addToQueue(intersetionTime, intersetionX, targetLaneId, targetSlotId); // if (!qaddresult) { // break; // } } } if (sc.lane > 0) { int targetLaneId = sc.lane-1; Slot *targetLane = &lane[targetLaneId][0]; long double x0 = s.vx - v[sc.lane]*s.vt; // int firstSlotInLane = getFirstSlotInLane(targetLaneId, x0); int firstSlotInLane = getFirstSlotInLane(targetLaneId, s.vx - v[targetLaneId]*s.vt); long double maxFullSpeedTime = (s.x + (long double)s.l-1 - x0)/(v[3]-v[currentLaneId]); int lastSlotInLane = max(firstSlotInLane, getFirstSlotInLane(targetLaneId, s.vx+v[3]*maxFullSpeedTime - v[targetLaneId]*(s.vt+maxFullSpeedTime))-1); FOR(targetSlotId, lastSlotInLane, laneLength[targetLaneId]-1) { long double intersetionTime = getIntersectionTime(s.vt, s.vx, v[3], targetLane[targetSlotId].x, v[targetLaneId]); // long double maxFullSpeedTime = ((long double)s.l-1 + v[currentLaneId]*s.vt - s.vx)/(v[3]-v[currentLaneId]); long double maxFullSpeedTime = (s.x + (long double)s.l-1 - x0)/(v[3]-v[currentLaneId]); long double intersetionX; if (maxFullSpeedTime + EPS >= intersetionTime - s.vt) { intersetionX = s.vx+(intersetionTime - s.vt)*v[3]; } else { break; } addToQueue(intersetionTime, intersetionX, targetLaneId, targetSlotId); } if (firstSlotInLane > 0) { int targetSlotId = firstSlotInLane-1; if (targetLane[targetSlotId].visited == false) { // long double intersetionTime = getIntersectionTime(s.vt, s.vx, v[currentLaneId], targetLane[targetSlotId].x, v[targetLaneId]); long double intersetionTime = getIntersectionTime(s.vt, targetLane[targetSlotId].x+targetLane[targetSlotId].l-1 + s.vt*v[targetLaneId], v[targetLaneId], s.vx - s.vt*v[currentLaneId], v[currentLaneId]); long double intersetionX = s.vx+(intersetionTime - s.vt)*v[currentLaneId]; addToQueue(intersetionTime, intersetionX, targetLaneId, targetSlotId); } } } } } result = findmaxval(findmaxval(lane[0][laneLength[0]-1].vt, lane[1][laneLength[1]-1].vt), lane[2][laneLength[2]-1].vt); printf("%.12Lf\n", result); 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 | #include <cstdio> #include <cmath> #include <iostream> #include <algorithm> #include <queue> #include <list> #include <vector> #include <map> #include <set> #include <string> #include <cstring> #include <cassert> #include <limits.h> using namespace std; typedef long long LL; typedef long double LD; typedef vector<int> VI; typedef pair<int,int> PII; #define REP(i,n) for(int i=0;i<(n);i++) #define FOR(i,a,b) for(VAR(i,a);i<=(b);++i) #define FORD(i,a,b) for(VAR(i,a);i>=(b);--i) #define FORE(a,b) for(VAR(a,(b).begin());a!=(b).end();++a) #define VAR(a,b) __typeof(b) a=(b) #define SIZE(a) ((int)((a).size())) #define ALL(x) (x).begin(),(x).end() #define CLR(x,a) memset(x,a,sizeof(x)) #define ZERO(x) memset(x,0,sizeof(x)) #define S(t,i) scanf("%" ## t, &i) #define SI(i) scanf("%d", &i) const int INF=INT_MAX-400000; const int MAXL=200000+5; const long double EPS=0.0000000001; int L, v[4]; long double result; struct Slot { int x; int l; long double vt=INF; long double vx=INF; bool visited=false; }; Slot lane[3][MAXL/2]; int laneLength[3]; struct SlotCoordinate { int lane; int slot; long double t; long double x; }; inline bool comparePossitionsWithinSlot(long double t1, long double x1, long double t2, long double x2) { long double diff = t1 + (x2-x1)/v[3] - t2; return abs(diff) < EPS ? t1 < t2 : diff < 0; // long double diff = t1 - t2; // return abs(diff) < EPS ? x1<x2 : t1 < t2; } auto compareSlots = [](const SlotCoordinate &b, const SlotCoordinate &a) { // return abs(a.t-b.t) <EPS ? a.x>b.x : a.t<b.t; return comparePossitionsWithinSlot(a.t, a.x, b.t, b.x); }; priority_queue<SlotCoordinate, std::vector<SlotCoordinate>, decltype(compareSlots)> q(compareSlots); long double getIntersectionTime(long double ta, long double xa, long double va, long double xs, long double vs) { return max(ta, ((xs-xa)+ta*va)/(va-vs)); } int getFirstSlotInLane(int targetLaneId, long double x0) { Slot *targetLane = &lane[targetLaneId][0]; int l=-1; int r=laneLength[targetLaneId]; while (l+1<r) { int k=(l+r)/2; Slot &s = targetLane[k]; if (s.visited || (x0 - (s.x+(long double)s.l-1) > EPS)) { l=k; } else { r=k; } } return l+1; // int firstSlotInLane = (int) (lower_bound(&targetLane[0], &targetLane[laneLength[targetLaneId]], x0, [](Slot &s, long double value){ // return s.visited || s.x+(long double)s.l-1 - value < EPS; // }) - targetLane); // return firstSlotInLane; } inline void addToQueue(long double intersetionTime, long double intersetionX, int targetLaneId, int targetSlotId) { Slot &targetSlot = lane[targetLaneId][targetSlotId]; if (comparePossitionsWithinSlot(intersetionTime, intersetionX, targetSlot.vt, targetSlot.vx)) { targetSlot.vt =intersetionTime; targetSlot.vx =intersetionX; SlotCoordinate new_sc; new_sc.lane = targetLaneId; new_sc.slot = targetSlotId; new_sc.t = intersetionTime; new_sc.x = intersetionX; q.push(new_sc); // printf("a %d %d %.10Lf %.10Lf\n", new_sc.lane, new_sc.slot, new_sc.t, new_sc.x); // assert(targetSlot.x+intersetionTime*v[targetLaneId] <= intersetionX+EPS); // assert(targetSlot.x+(long double)targetSlot.l-1+intersetionTime*v[targetLaneId] >= intersetionX-EPS); // return true; } // return false; } long double findmaxval (long double num1, long double num2){ return num1 > num2 ? num1 : num2; } int main() { ios_base::sync_with_stdio(0); SI(L); SI(v[3]); REP(i, 3) { SI(v[i]); } FOR(i, 0, 2) { char c, prevc; scanf(" "); fread(&c, 1, sizeof(char), stdin); c='.'; laneLength[i]=1; lane[i][0].l=1; lane[i][0].x=0; lane[i][0].vt=INF; lane[i][0].vx=INF; FOR(x, 1, L-1) { prevc=c; fread(&c, 1, sizeof(char), stdin); if (c=='.') { if (prevc == '.') { Slot &s = lane[i][laneLength[i]-1]; s.l++; } else { laneLength[i]++; Slot &s = lane[i][laneLength[i]-1]; s.x = x; s.l = 1; s.vt=INF; s.vx=INF; } } } if (c=='#') { laneLength[i]++; Slot &s = lane[i][laneLength[i]-1]; s.x = L; s.l = INF; } else { Slot &s = lane[i][laneLength[i]-1]; s.l = INF; } } SlotCoordinate new_sc; new_sc.lane = 2; new_sc.slot = 0; new_sc.t = 0; new_sc.x = 0; lane[2][0].vt = 0; lane[2][0].vx = 0; q.push(new_sc); while (!q.empty()) { SlotCoordinate sc = q.top(); q.pop(); Slot &s = lane[sc.lane][sc.slot]; if (!s.visited) { // printf("v %d %d %.10Lf %.10Lf\n", sc.lane, sc.slot, s.vt, s.vx); s.visited = true; int currentLaneId = sc.lane; if (sc.lane < 2) { int targetLaneId = sc.lane+1; Slot *targetLane = &lane[targetLaneId][0]; long double x0 = s.vx - v[sc.lane]*s.vt; int firstSlotInLane = getFirstSlotInLane(targetLaneId, s.vx - v[targetLaneId]*s.vt); FORD(targetSlotId, laneLength[targetLaneId]-1, firstSlotInLane) { long double intersetionTime = getIntersectionTime(s.vt, s.vx, v[3], targetLane[targetSlotId].x, v[targetLaneId]); long double maxFullSpeedTime = (s.x + (long double)s.l-1 - x0)/(v[3]-v[currentLaneId]); long double intersetionX; if (maxFullSpeedTime + EPS >= intersetionTime - s.vt) { intersetionX = s.vx+(intersetionTime - s.vt)*v[3]; } else { long double timeAtTheEndOdSlot = maxFullSpeedTime + s.vt; long double positionAtTheEndOdSlot = s.vx + maxFullSpeedTime*v[3]; intersetionTime = getIntersectionTime(timeAtTheEndOdSlot, positionAtTheEndOdSlot, v[currentLaneId], targetLane[targetSlotId].x, v[targetLaneId]); intersetionX = positionAtTheEndOdSlot+(intersetionTime - timeAtTheEndOdSlot)*v[currentLaneId]; } addToQueue(intersetionTime, intersetionX, targetLaneId, targetSlotId); // if (!qaddresult) { // break; // } } } if (sc.lane > 0) { int targetLaneId = sc.lane-1; Slot *targetLane = &lane[targetLaneId][0]; long double x0 = s.vx - v[sc.lane]*s.vt; // int firstSlotInLane = getFirstSlotInLane(targetLaneId, x0); int firstSlotInLane = getFirstSlotInLane(targetLaneId, s.vx - v[targetLaneId]*s.vt); long double maxFullSpeedTime = (s.x + (long double)s.l-1 - x0)/(v[3]-v[currentLaneId]); int lastSlotInLane = max(firstSlotInLane, getFirstSlotInLane(targetLaneId, s.vx+v[3]*maxFullSpeedTime - v[targetLaneId]*(s.vt+maxFullSpeedTime))-1); FOR(targetSlotId, lastSlotInLane, laneLength[targetLaneId]-1) { long double intersetionTime = getIntersectionTime(s.vt, s.vx, v[3], targetLane[targetSlotId].x, v[targetLaneId]); // long double maxFullSpeedTime = ((long double)s.l-1 + v[currentLaneId]*s.vt - s.vx)/(v[3]-v[currentLaneId]); long double maxFullSpeedTime = (s.x + (long double)s.l-1 - x0)/(v[3]-v[currentLaneId]); long double intersetionX; if (maxFullSpeedTime + EPS >= intersetionTime - s.vt) { intersetionX = s.vx+(intersetionTime - s.vt)*v[3]; } else { break; } addToQueue(intersetionTime, intersetionX, targetLaneId, targetSlotId); } if (firstSlotInLane > 0) { int targetSlotId = firstSlotInLane-1; if (targetLane[targetSlotId].visited == false) { // long double intersetionTime = getIntersectionTime(s.vt, s.vx, v[currentLaneId], targetLane[targetSlotId].x, v[targetLaneId]); long double intersetionTime = getIntersectionTime(s.vt, targetLane[targetSlotId].x+targetLane[targetSlotId].l-1 + s.vt*v[targetLaneId], v[targetLaneId], s.vx - s.vt*v[currentLaneId], v[currentLaneId]); long double intersetionX = s.vx+(intersetionTime - s.vt)*v[currentLaneId]; addToQueue(intersetionTime, intersetionX, targetLaneId, targetSlotId); } } } } } result = findmaxval(findmaxval(lane[0][laneLength[0]-1].vt, lane[1][laneLength[1]-1].vt), lane[2][laneLength[2]-1].vt); printf("%.12Lf\n", result); return 0; } |