【UVA 1636】 （条件概率）

题链：https://cn.vjudge.net/problem/UVA-1636

题意

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给出一把枪的子弹序列，已知开了一枪且无子弹，问下一步的决策是旋转，还是开下一枪

题解

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已知开一枪没子弹，下一枪也没子弹概率设为p1

那么：设P(A)为下一枪无子弹，P(B)为上一枪无子弹。根据条件概率公式

\(P(A|B)=P(AB)\div P(B)\)

即连续两枪无子弹概率除以上一枪无子弹概率，即

\((numof("00")\div n)\div (numof("0")\div n)\)

即

\((numof("00")\div (numof("0")\)

ROTATE无子弹的概率是一个古典概型，即

\(p2=(numof("0")\div n\)

参考代码

import java.io.*;
import java.util.*;

public class Main {
	static final int N=(int)5005;
	static char a[]=new char[105];
    public static void main(String[] args) {
        InputStream sys=System.in;
        InputReader in=new InputReader(sys);
        Scanner sc=new Scanner(new InputStreamReader(sys));
        PrintWriter out=new PrintWriter(System.out);
        while(sc.hasNext()) {
        	String str=sc.next();
        	int c1=0,c2=0;
        	a=str.toCharArray();
        	int n=a.length;
        	for(int i=0;i<n;i++) {
        		if(a[i]=='0'&&a[(i+1)%n]=='0') {
        			c1++;
        		}
        		if(a[i]=='0') c2++;
        	}
        	if(c1*n==c2*c2) out.println("EQUAL");
        	else if(c1*1.0/c2>c2*1.0/n) out.println("SHOOT");
        	else out.println("ROTATE");
        	out.flush();
        }
    }
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}