BNU 4260 ——Trick or Treat——————【三分求抛物线顶点】
2015-04-28 21:09
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Johnny and his friends have decided to spend Halloween night doing the usual candy collection from the households of their village. As the village is too big for a single group to collect the candy from all houses sequentially, Johnny and his friends have decided to split up so that each of them goes to a different house, collects the candy (or wreaks havoc if the residents don't give out candy), and returns to a meeting point arranged in advance.
There are n houses in the village, the positions of which can be identified with their Cartesian coordinates on the Euclidean plane. Johnny's gang is also made up of n people (including Johnny himself). They have decided to distribute the candy after everybody comes back with their booty. The houses might be far away, but Johnny's interest is in eating the candy as soon as possible.
Keeping in mind that, because of their response to the hospitality of some villagers, some children might be wanted by the local authorities, they have agreed to fix the meeting point by the river running through the village, which is the line y = 0. Note that there may be houses on both sides of the river, and some of the houses may be houseboats (y = 0). The walking speed of every child is 1 meter per second, and they can move along any direction on the plane.
At exactly midnight, each child will knock on the door of the house he has chosen, collect the candy instantaneously, and walk back along the shortest route to the meeting point. Tell Johnny at what time he will be able to start eating the candy.
A blank line follows each case. A line with n = 0 indicates the end of the input; do not write any output for this case.
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Submit Status Statistics Discuss
Next
Type:
None
None
Graph Theory
2-SAT
Articulation/Bridge/Biconnected Component
Cycles/Topological Sorting/Strongly Connected Component
Shortest Path
Bellman Ford
Dijkstra/Floyd Warshall
Euler Trail/Circuit
Heavy-Light Decomposition
Minimum Spanning Tree
Stable Marriage Problem
Trees
Directed Minimum Spanning Tree
Flow/Matching
Graph Matching
Bipartite Matching
Hopcroft–Karp Bipartite Matching
Weighted Bipartite Matching/Hungarian Algorithm
Flow
Max Flow/Min Cut
Min Cost Max Flow
DFS-like
Backtracking with Pruning/Branch and Bound
Basic Recursion
IDA* Search
Parsing/Grammar
Breadth First Search/Depth First Search
Advanced Search Techniques
Binary Search/Bisection
Ternary Search
Geometry
Basic Geometry
Computational Geometry
Convex Hull
Pick's Theorem
Game Theory
Green Hackenbush/Colon Principle/Fusion Principle
Nim
Sprague-Grundy Number
Matrix
Gaussian Elimination
Matrix Exponentiation
Data Structures
Basic Data Structures
Binary Indexed Tree
Binary Search Tree
Hashing
Orthogonal Range Search
Range Minimum Query/Lowest Common Ancestor
Segment Tree/Interval Tree
Trie Tree
Sorting
Disjoint Set
String
Aho Corasick
Knuth-Morris-Pratt
Suffix Array/Suffix Tree
Math
Basic Math
Big Integer Arithmetic
Number Theory
Chinese Remainder Theorem
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Inclusion/Exclusion
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Group Theory/Burnside's lemma
Counting
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Brute Force
Implementation
Constructive Algorithms
Two Pointer
Bitmask
Beginner
Discrete Logarithm/Shank's Baby-step Giant-step Algorithm
Greedy
Divide and Conquer
Dynamic Programming
Tag it!
Johnny and his friends have decided to spend Halloween night doing the usual candy collection from the households of their village. As the village is too big for a single group to collect the candy from all houses sequentially, Johnny and his friends have decided to split up so that each of them goes to a different house, collects the candy (or wreaks havoc if the residents don't give out candy), and returns to a meeting point arranged in advance.
There are n houses in the village, the positions of which can be identified with their Cartesian coordinates on the Euclidean plane. Johnny's gang is also made up of n people (including Johnny himself). They have decided to distribute the candy after everybody comes back with their booty. The houses might be far away, but Johnny's interest is in eating the candy as soon as possible.
Keeping in mind that, because of their response to the hospitality of some villagers, some children might be wanted by the local authorities, they have agreed to fix the meeting point by the river running through the village, which is the line y = 0. Note that there may be houses on both sides of the river, and some of the houses may be houseboats (y = 0). The walking speed of every child is 1 meter per second, and they can move along any direction on the plane.
At exactly midnight, each child will knock on the door of the house he has chosen, collect the candy instantaneously, and walk back along the shortest route to the meeting point. Tell Johnny at what time he will be able to start eating the candy.
Input
Each test case starts with a line indicating the number n of houses ( 1<=n<=50 000). The next n lines describe the positions of the houses; each of these lines contains two floating point numbers x and y ( -200 000 <= x, y <= 200 000), the coordinates of a house in meters. All houses are at different positions.A blank line follows each case. A line with n = 0 indicates the end of the input; do not write any output for this case.
Output
For each test case, print two numbers in a line separated by a space: the coordinate x of the meeting point on the line y = 0 that minimizes the time the last child arrives, and this time itself (measured in seconds after midnight). Your answer should be accurate to within an absolute or relative error of 10-5.Sample Input
2 1.5 1.5 3 0 1 0 0 4 1 4 4 4 -3 3 2 4 5 4 7 -4 0 7 -6 -2 4 8 -5 0
Sample Output
1.500000000 1.500000000 0.000000000 0.000000000 1.000000000 5.000000000 3.136363636 7.136363636 题目大意:有n个人要回到x上的某个聚集点,问所有人都回到该点的最短时间。 解题思路:利用三分,求出x点坐标,最后求出最远的点到该点的距离。
#include<bits/stdc++.h> using namespace std; struct Cor{ double x,y; }cor[55000]; #define mid (L+R)/2.0 #define mid_L (mid+L)/2.0 const double eps=1e-10; const double INF=1e9; int n; double dis(Cor a,Cor b){ return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y); } double calcu(double tx){ double ret=-INF; Cor tmp_; tmp_.x=tx,tmp_.y=0; for(int i=0;i<n;i++){ if(ret<dis(cor[i],tmp_)){ ret=dis(cor[i],tmp_); } } return sqrt(ret); } double three_div(double L,double R){ while(R-L>eps){ if(calcu(mid)>calcu(mid_L)){ R=mid; }else{ L=mid_L; } } return mid; } int main(){ while(scanf("%d",&n)!=EOF&&n){ for(int i=0;i<n;i++){ scanf("%lf%lf",&cor[i].x,&cor[i].y); } double ans_x,ans_d; ans_x= three_div(-200000.0,200000.0); ans_d=calcu(ans_x); printf("%.9lf %.9lf\n",ans_x,ans_d); } return 0; }
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