POJ1167

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#include<cmath> #include<iostream> #include<cstdio> #include<algorithm> #include <vector> using namespace std; class Route { public: Route(int firstTime_, int interval_, int frequence_) : firstTime(firstTime_) , interval(interval_) , frequence(frequence_) { } bool operator <(const Route &lhs) const { return frequence > lhs.frequence; } int firstTime; int interval; int frequence; }; int visited[60] = { 0 }; std::vector <Route> routes; //firstTime < interval, otherwise firstTime - interval earlier than firstTime (1) //firstTime + interval <= 59 => interval <= 59 - firstTime (2) //(1)(2)==> firstTime < interval <= 59 - firstTime => 2*firstTime < interval => firstTime <= 29 (3) //firstTime >= 0 // => 0 <= firstTime <= 29, 1 <= interval <= 59 (4) // first + frequency * interval > 59 => frequency > (59 - first) / interval // first + (frequency - 1) * interval <= 59 => frequency <= (59 - first) / interval + 1 // => frequency = (59 - first) / interval + 1 (4) void prepareRoutes() { routes.reserve(900); for (int firstTime = 0; firstTime <= 29; ++firstTime) { if (!visited[firstTime]) continue; for (int interval = firstTime + 1; interval <= 59 - firstTime; ++interval) { bool suffice = true; for (int k = firstTime + interval; k <= 59; k += interval) { if (!visited[k]) { suffice = false; break; } } if (suffice) { int fre = 1 + (59 - firstTime) / interval; routes.push_back(Route(firstTime, interval, fre)); } } } sort(routes.begin(), routes.end()); }//prepareRoutes int nMinRoutes = 17; bool isValidRoute(int firstTime, int interval) { int t = firstTime; for (; t <= 59; t += interval) { if (!visited[t]) return false; } return true; } //std::vector <Route> bestX; //std::vector <Route> currentX; //在搜索時，如果還有n個未被覆蓋，用頻率爲f的線路來覆蓋，至少需要n/f條，顯然f>n的線路是不可能符合條件的 void solve(int currentRouteNumber, int nCurrentRoutes, int nRemain) { if (nRemain == 0) { if (nCurrentRoutes < nMinRoutes) { nMinRoutes = nCurrentRoutes; //bestX = currentX; } //else //{ // currentX.clear(); //} return; } while (currentRouteNumber < (int)routes.size() && routes[currentRouteNumber].frequence > nRemain) ++currentRouteNumber; for (;currentRouteNumber < (int)routes.size(); ++currentRouteNumber) { if (nCurrentRoutes + 1 + (nRemain - 1) / routes[currentRouteNumber].frequence >= nMinRoutes) return; if (isValidRoute(routes[currentRouteNumber].firstTime, routes[currentRouteNumber].interval)) { //currentX.push_back(routes[currentRouteNumber]); for (int i = routes[currentRouteNumber].firstTime; i <= 59; i += routes[currentRouteNumber].interval) { --visited[i]; --nRemain; } solve(currentRouteNumber, nCurrentRoutes + 1, nRemain);//線路不同的公交路線可能有相同的起始時間和間隔 for (int i = routes[currentRouteNumber].firstTime; i <= 59; i += routes[currentRouteNumber].interval) { ++visited[i]; ++nRemain; } //currentX.pop_back(); } } } int main() { int n; scanf ("%d", &n); int tmp; for (int i = 0; i < n; ++i) { scanf("%d", &tmp); visited[tmp]++; } prepareRoutes(); solve(0, 0, n); printf("%d/n", nMinRoutes); return 0; }