hdu1009 FatMouse' Trade(贪心)

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此问题探讨了FatMouse利用猫粮与守卫仓库的猫咪交易其最爱的食物——Java豆的过程。通过数学模型，解决如何最大化获取Java豆的问题。

FatMouse' Trade

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 39355 Accepted Submission(s): 12989

Problem Description

FatMouse prepared M pounds of cat food, ready to trade with the cats guarding the warehouse containing his favorite food, JavaBean.
The warehouse has N rooms. The i-th room contains J[i] pounds of JavaBeans and requires F[i] pounds of cat food. FatMouse does not have to trade for all the JavaBeans in the room, instead, he may get J[i]* a% pounds of JavaBeans if he pays F[i]* a% pounds of cat food. Here a is a real number. Now he is assigning this homework to you: tell him the maximum amount of JavaBeans he can obtain.

Input

The input consists of multiple test cases. Each test case begins with a line containing two non-negative integers M and N. Then N lines follow, each contains two non-negative integers J[i] and F[i] respectively. The last test case is followed by two -1's. All integers are not greater than 1000.

Output

For each test case, print in a single line a real number accurate up to 3 decimal places, which is the maximum amount of JavaBeans that FatMouse can obtain.

Sample Input

Sample Output

13.333
31.500

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.FileReader;
import java.io.PrintWriter;
import java.io.OutputStreamWriter;
import java.io.StreamTokenizer;
import java.io.IOException;
import java.util.Arrays;

class Main
{
	public static final boolean DEBUG = false;
	public StreamTokenizer tokenizer;
	public PrintWriter cout;
	
	public void init() throws IOException
	{
		
		BufferedReader cin;
		if (DEBUG) {
			cin = new BufferedReader(new FileReader("d:\\OJ\\uva_in.txt"));
		} else {
			cin = new BufferedReader(new InputStreamReader(System.in));
		}
		tokenizer = new StreamTokenizer(cin);
		
		cout = new PrintWriter(new OutputStreamWriter(System.out));
	}
	
	public int next() throws IOException
	{
		
		tokenizer.nextToken();
		if (tokenizer.ttype == StreamTokenizer.TT_NUMBER) {
			return (int)tokenizer.nval;
		}
		return -1;
	}
	
	static class Node implements Comparable<Node>
	{
		int J, F;
		
		public int compareTo(Node other)
		{
			return other.J * F - other.F * J;
		}
	}
	
	public void solve(Node[] node, int n, int m)
	{
		double ans = 0;
		
		
		Arrays.sort(node);
		
		for (int i = 0; i < n; i++) {
			if (m > node[i].F) {
				ans += node[i].J;
				m -= node[i].F;
			} else {
				ans += (double)node[i].J / node[i].F * m;
				break;
			}
		}
		
		cout.printf("%.3f", ans);
		cout.println();
		cout.flush();
	}
	public static void main(String[] args) throws IOException
	{
		Main solver = new Main();
		solver.init();
		
		
		while (true) {
			int m = solver.next();
			int n = solver.next();
			
			if (m == -1 && n == -1) break;
			
			Node[] node = new Node[n];
			for (int i = 0; i < n; i++) {
				node[i] = new Node();
				node[i].J = solver.next();
				node[i].F = solver.next();
			}
			
			solver.solve(node, n, m);
		}
		
	}
}