据说是网易游戏面试题
2015-10-25 19:20
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据说是网易游戏面试题
题意:
一条直线上有n个小球,初始坐标及速度已知,且球的初始位置两两不相同。若任意两个球相遇后则两球均消失,找出最后还留在直线上的球。分析:
题意很清楚明了,任意两个小球之间无非两种情况(一起消失、永不相遇)。那么最先相遇的必然是两个相邻的小球,排除掉这俩球后就又回到了最初的状态。所以把所有球按坐标从小到大排序,用带有排序功能的容器保存相邻小球相遇的时间,每次去掉最先相遇的小球直到剩下的球永不相遇或全部消失。时间复杂度为:O(n log n)当然了,这玩意面试的时候空口说起来容易,实打实在纸上敲一边貌似还是有很多细节需要考虑的。举个例子,若当前剩下球a、b、c、d,b和c最先相遇,去掉(b,c)后如何快速定位并删除(a,b)和(c,d)并构建(a,d)。同时还要注意代码的简洁
代码:
#include <bits/stdc++.h> using namespace std; typedef long long ll; #define urp(i,a,b) for(int i=(a),__tzg_##i=(b); i>=__tzg_##i; --i) #define rp(i,b) for(int i=(0), __tzg_##i=(b);i<__tzg_##i;++i) #define rep(i,a,b) for(int i=(a), __tzg_##i=(b);i<__tzg_##i;++i) #define repd(i,a,b) for(int i=(a), __tzg_##i=(b);i<=__tzg_##i;++i) #define mst(a,b) memset(a,b,sizeof(a)) #define px first #define py second #define __0(x) (!(x)) #define __1(x) (x) typedef pair<int,int> pii; const ll mod = 1000000007; const int MAXM = 15; const double eps = 1e-8; const int inf = 0x3f3f3f3f; #define mp(a,b) make_pair(a,b) typedef vector<int> VI; typedef vector<ll> VL; typedef vector<pii> VPII; typedef vector<string> VS; typedef vector<VI> VVI; typedef vector<VL> VVL; const int N = 20; const double INF = 1e100; inline int cmp(double a, double b) { return (a-b>eps) - (a-b<-eps); } inline int cmp(double a) { return cmp(a, 0.0); } class Node; class QueueNode; class Calc; typedef list<Node>::iterator LT; typedef set<QueueNode>::iterator ST; class Node { public: double pos_; double speed_; int removed_; int idx_; Node(double pos, double speed, int idx) { this->pos_ = pos; this->speed_ = speed; this->idx_ = idx; removed_ = 0; } int neverMeet(const Node & nd) const { int b = cmp(pos_, nd.pos_), c = cmp(speed_, nd.speed_); if (b == 0) return 0; if (c == 0) return 1; if (b > 0 && c>=0) return 1; if (b < 0 && c<=0) return 1; return 0; } double getTime(const Node & nd) const { if (neverMeet(nd)) return INF; return fabs(pos_ - nd.pos_)/fabs(speed_ - nd.speed_); } bool operator < (const Node & a) const { return cmp(pos_, a.pos_) < 0; } }; class QueueNode { public: LT t1_, t2_; double time_; int id_; QueueNode(LT t1, LT t2, int id) { this->t1_ = t1; this->t2_ = t2; this->id_ = id; time_ = t1_->getTime(*t2_); } bool operator < (const QueueNode & nd) const { int k = cmp(time_, nd.time_); return k==0?id_<nd.id_:k<0; } }; class Calc { public: VI solve(vector<double> speed, vector<double> pos) { map<pair<Node*,Node*>, ST> mmp; set<QueueNode> sq; vector<Node> nl; int n = speed.size(); rp(i, n) { nl.push_back(Node(pos[i], speed[i], i)); } sort(nl.begin(), nl.end()); list<Node> vn; rp(i, n) { vn.push_back(nl[i]); } LT it = vn.begin(); int id = 1; for (++it; it != vn.end(); ++it) { LT yt = it; --yt; QueueNode nd(yt, it, id++); sq.insert(nd); ST t = sq.find(nd); mmp[make_pair(&*yt, &*it)] = t; } while (!sq.empty()) { ST t = sq.begin(); QueueNode qd = *t; if (qd.time_ >= INF) break; LT t1 = qd.t1_, t2 = qd.t2_, p = vn.end(), q = vn.end(); if (t1 != vn.begin()) { p = t1; --p; sq.erase(mmp[mp(&*p, &*t1)]); } sq.erase(mmp[mp(&*t1, &*t2)]); t1->removed_ = 1; t2->removed_ = 1; q = t2; ++q; if (q != vn.end() ) { sq.erase(mmp[mp(&*t2, &*q)]); } if (p != vn.end() && q != vn.end()) { QueueNode tp(p, q, qd.id_); sq.insert(tp); mmp[mp(&*p, &*q)] = sq.find(tp); } } VI res; for(LT i = vn.begin(); i != vn.end(); ++i) { if (!i->removed_) res.push_back(i->idx_); } return res; } }; int main() { Calc c; VI res = c.solve({-1,0,1,2}, {1,2,-3,-1}); cout<<res.size()<<endl; rp(i, res.size()) { cout<<res[i]<<endl; } return 0; }
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