题目链接:https://atcoder.jp/contests/abc130/tasks/abc130_f
题目大意
给定地图上 N 个点的坐标和移动方向,它们会以每秒 1 个单位的速度移动,设 Ans(t) 为在 t 时刻,$(x_{max} - x_{min}) * (y_{max} - y_{min})$的值,求 Ans(t) 的最小值。(最小值可能不是一个整数)
分析
稍加思考可以发现,不是所有点的所有坐标都对答案有影响,很多点完全可以忽略不计,下面以 Y 坐标为例,讨论影响$(y_{max} - y_{min})$的值。
首先我们把 N 个点分为 3 类,向下移动的,向上移动的和水平方向移动的,具体如下图所示:
其中,UU 代表往下移动的点中 Y 坐标最大值,UD 代表往下移动的点中 Y 坐标最小值,其余同理。
我们发现,影响$(y_{max} - y_{min})$就是这 6 个值,当它们某两个值重合时就有可能改变答案。
X 坐标方向上也是同理,只要旋转一下即可。
当我们把 X 和 Y 坐标上对应的 6 个值都算出来的时候,把它们两两组合,暴力枚举所有可能时刻,就能求出最终答案。
代码如下
1 #include <bits/stdc++.h> 2 using namespace std; 3 4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); 5 #define Rep(i,n) for (int i = 0; i < (n); ++i) 6 #define For(i,s,t) for (int i = (s); i <= (t); ++i) 7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i) 8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i) 9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i) 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i) 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i) 12 13 #define pr(x) cout << #x << " = " << x << " " 14 #define prln(x) cout << #x << " = " << x << endl 15 16 #define LOWBIT(x) ((x)&(-x)) 17 18 #define ALL(x) x.begin(),x.end() 19 #define INS(x) inserter(x,x.begin()) 20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end()) 21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower); 23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper); 24 25 #define ms0(a) memset(a,0,sizeof(a)) 26 #define msI(a) memset(a,inf,sizeof(a)) 27 #define msM(a) memset(a,-1,sizeof(a)) 28 29 #define MP make_pair 30 #define PB push_back 31 #define ft first 32 #define sd second 33 34 template<typename T1, typename T2> 35 istream &operator>>(istream &in, pair<T1, T2> &p) { 36 in >> p.first >> p.second; 37 return in; 38 } 39 40 template<typename T> 41 istream &operator>>(istream &in, vector<T> &v) { 42 for (auto &x: v) 43 in >> x; 44 return in; 45 } 46 47 template<typename T1, typename T2> 48 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) { 49 out << "[" << p.first << ", " << p.second << "]" << "\n"; 50 return out; 51 } 52 53 inline int gc(){ 54 static const int BUF = 1e7; 55 static char buf[BUF], *bg = buf + BUF, *ed = bg; 56 57 if(bg == ed) fread(bg = buf, 1, BUF, stdin); 58 return *bg++; 59 } 60 61 inline int ri(){ 62 int x = 0, f = 1, c = gc(); 63 for(; c<48||c>57; f = c==‘-‘?-1:f, c=gc()); 64 for(; c>47&&c<58; x = x*10 + c - 48, c=gc()); 65 return x*f; 66 } 67 68 template<class T> 69 inline string toString(T x) { 70 ostringstream sout; 71 sout << x; 72 return sout.str(); 73 } 74 75 inline int toInt(string s) { 76 int v; 77 istringstream sin(s); 78 sin >> v; 79 return v; 80 } 81 82 //min <= aim <= max 83 template<typename T> 84 inline bool BETWEEN(const T aim, const T min, const T max) { 85 return min <= aim && aim <= max; 86 } 87 88 typedef long long LL; 89 typedef unsigned long long uLL; 90 typedef pair< double, double > PDD; 91 typedef pair< int, int > PII; 92 typedef pair< int, PII > PIPII; 93 typedef pair< string, int > PSI; 94 typedef pair< int, PSI > PIPSI; 95 typedef set< int > SI; 96 typedef set< PII > SPII; 97 typedef vector< int > VI; 98 typedef vector< double > VD; 99 typedef vector< VI > VVI; 100 typedef vector< SI > VSI; 101 typedef vector< PII > VPII; 102 typedef map< int, int > MII; 103 typedef map< int, string > MIS; 104 typedef map< int, PII > MIPII; 105 typedef map< PII, int > MPIII; 106 typedef map< string, int > MSI; 107 typedef map< string, string > MSS; 108 typedef map< PII, string > MPIIS; 109 typedef map< PII, PII > MPIIPII; 110 typedef multimap< int, int > MMII; 111 typedef multimap< string, int > MMSI; 112 //typedef unordered_map< int, int > uMII; 113 typedef pair< LL, LL > PLL; 114 typedef vector< LL > VL; 115 typedef vector< VL > VVL; 116 typedef priority_queue< int > PQIMax; 117 typedef priority_queue< int, VI, greater< int > > PQIMin; 118 const double EPS = 1e-8; 119 const LL inf = 0x7fffffff; 120 const LL infLL = 0x7fffffffffffffffLL; 121 const LL mod = 1e9 + 7; 122 const int maxN = 1e5 + 7; 123 const LL ONE = 1; 124 const LL evenBits = 0xaaaaaaaaaaaaaaaa; 125 const LL oddBits = 0x5555555555555555; 126 127 #define UU A[0] 128 #define UD A[1] 129 #define MU A[2] 130 #define MD A[3] 131 #define DU A[4] 132 #define DD A[5] 133 134 struct State{ 135 double A[6] = {-inf, inf, -inf, inf, -inf, inf}; 136 double _max = -inf, _min = inf; 137 138 State operator+ (const double &x) const { 139 State ret = *this; 140 if(fabs(ret.UU) < 1e9) ret.UU -= x; 141 if(fabs(ret.UD) < 1e9) ret.UD -= x; 142 if(fabs(ret.DU) < 1e9) ret.DU += x; 143 if(fabs(ret.DD) < 1e9) ret.DD += x; 144 145 Rep(i, 6) { 146 if(fabs(ret.A[i]) < 1e9) { 147 ret._max = max(ret._max, ret.A[i]); 148 ret._min = min(ret._min, ret.A[i]); 149 } 150 } 151 return ret; 152 } 153 }; 154 155 int N; 156 State X, Y; 157 double ans = infLL; 158 set< double > T; // 记录关键时间节点 159 160 int main(){ 161 //freopen("MyOutput.txt","w",stdout); 162 //freopen("input.txt","r",stdin); 163 //INIT(); 164 cin >> N; 165 Rep(i, N) { 166 double x, y; 167 string d; 168 cin >> x >> y >> d; 169 170 if(d[0] == ‘U‘) { 171 Y.DU = max(Y.DU, y); 172 Y.DD = min(Y.DD, y); 173 174 X.MU = max(X.MU, x); 175 X.MD = min(X.MD, x); 176 } 177 if(d[0] == ‘D‘) { 178 Y.UU = max(Y.UU, y); 179 Y.UD = min(Y.UD, y); 180 181 X.MU = max(X.MU, x); 182 X.MD = min(X.MD, x); 183 } 184 if(d[0] == ‘R‘) { 185 X.DU = max(X.DU, x); 186 X.DD = min(X.DD, x); 187 188 Y.MU = max(Y.MU, y); 189 Y.MD = min(Y.MD, y); 190 } 191 if(d[0] == ‘L‘) { 192 X.UU = max(X.UU, x); 193 X.UD = min(X.UD, x); 194 195 Y.MU = max(Y.MU, y); 196 Y.MD = min(Y.MD, y); 197 } 198 } 199 200 Rep(i, 6) { 201 Rep(j, 6) { 202 T.insert(fabs(X.A[i] - X.A[j])); 203 T.insert(fabs(X.A[i] - X.A[j]) / 2); 204 T.insert(fabs(Y.A[i] - Y.A[j])); 205 T.insert(fabs(Y.A[i] - Y.A[j]) / 2); 206 T.insert(fabs(X.A[i] - Y.A[j])); 207 T.insert(fabs(X.A[i] - Y.A[j]) / 2); 208 } 209 } 210 211 foreach(i, T) { 212 if(*i > 1e9) break; 213 State tmpX = X + *i; 214 State tmpY = Y + *i; 215 216 ans = min(ans, (tmpX._max - tmpX._min) * (tmpY._max - tmpY._min)); 217 } 218 219 printf("%.10f\n", ans); 220 return 0; 221 }
原文地址:https://www.cnblogs.com/zaq19970105/p/11106168.html
时间: 2024-10-08 11:07:12