Uva 12124 Assemble

题目链接：http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=3276

题目大意：有b块的预算，要组装一台电脑，给出n个配件，每个配件标明种类，名称，品质和价格，要求每种配件各买一个，从价格不超过b，且品质最低的配件的品质尽可能大。输出最小品质配件的品质。

解题关键：“最小值最大”问题常用方法是二分法，对所有配件的品质进行二分。假设二分得到的值为x，在每种配件中选择品质大于等于x的最便宜配件，若最后花费<b则ans>=x,否则ans<x.

import java.util.*;class Component{String name;int price;int quality;public Component(String name,int price,int quality){this.name=name;this.price=price;this.quality=quality;}}public class Main {static int n,b;static int count;static Map<String,Integer> kind_num=new HashMap<String,Integer>();static ArrayList<ArrayList<Component>> comp=null;static int ID(String type){int res=0;if(kind_num.containsKey(type)){res=kind_num.get(type);}else{kind_num.put(type, count);res=count;count++;}return res;}static int min(int a,int b){return a<b?a:b;}static boolean OK(int M){int sum=0;for(int i=0;i<count;i++){ArrayList<Component> temp=comp.get(i);int cheapest=b+1;for(int j=0;j<temp.size();j++){if(temp.get(j).quality>=M) cheapest=min(cheapest,temp.get(j).price);}if(cheapest==b+1) return false;sum=sum+cheapest;if(sum>b) return false;}return true;}/** * @param args */public static void main(String[] args) {// TODO Auto-generated method stubint t;Scanner in=new Scanner(System.in);t=in.nextInt();for(;t>0;t--){kind_num.clear();n=in.nextInt();b=in.nextInt();comp=new ArrayList<ArrayList<Component>>();for(int i=0;i<n;i++){ArrayList<Component> tem=new ArrayList<Component>();comp.add(tem);}int type_num=0;count=0;int max=Integer.MIN_VALUE,min=Integer.MAX_VALUE;for(int i=0;i<n;i++){String type=in.next();String name=in.next();int price=in.nextInt();int quality=in.nextInt();if(quality>=max)max=quality;if(quality<min)min=quality;int num=ID(type);Component temp=new Component(name,price,quality);comp.get(num).add(temp);}int L=min,R=max;while(L<R){int M=L+(R-L+1)/2;if(OK(M)){L=M;}else{R=M-1;}}System.out.println(L);}}}