基础练习 Sine之舞

资源限制
时间限制：1.0s 内存限制：512.0MB
问题描述
　　最近FJ为他的奶牛们开设了数学分析课，FJ知道若要学好这门课，必须有一个好的三角函数基本功。所以他准备和奶牛们做一个“Sine之舞”的游戏，寓教于乐，提高奶牛们的计算能力。
　　不妨设
　　An=sin(1–sin(2+sin(3–sin(4+…sin(n))…)
　　Sn=(…(A1+n)A2+n-1)A3+…+2)An+1
　　FJ想让奶牛们计算Sn的值，请你帮助FJ打印出Sn的完整表达式，以方便奶牛们做题。
输入格式
　　仅有一个数：N<201。
输出格式
　　请输出相应的表达式Sn，以一个换行符结束。输出中不得含有多余的空格或换行、回车符。
样例输入
3
样例输出
((sin(1)+3)sin(1–sin(2))+2)sin(1–sin(2+sin(3)))+1

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Iterator;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.regex.Pattern;

import javax.management.monitor.Monitor;


//** Class for buffered reading int and double values *//*
class Reader {
	static BufferedReader reader;
	static StringTokenizer tokenizer;

	// ** call this method to initialize reader for InputStream *//*
	static void init(InputStream input) {
		reader = new BufferedReader(new InputStreamReader(input));
		tokenizer = new StringTokenizer("");
	}

	// ** get next word *//*
	static String next() throws IOException {
		while (!tokenizer.hasMoreTokens()) {
			// TODO add ceck for eof if necessary
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}
	static boolean hasNext()throws IOException {
		return tokenizer.hasMoreTokens();
	}
	static String nextLine() throws IOException{
		return reader.readLine();
	}
	static char nextChar() throws IOException{
		return next().charAt(0);
	}
	static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	static long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	static float nextFloat() throws IOException {
		return Float.parseFloat(next());
	}
	static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	static void close() throws IOException {
		reader.close();
	}
}
class Writer{
	static BufferedWriter writer;
	static void init(OutputStream outputStream) {
		writer = new BufferedWriter(new OutputStreamWriter(outputStream));
	}
	static void print(Object object) throws IOException {
		writer.write(object.toString());
	}
	static void println(Object object) throws IOException {
		writer.write(object.toString());
		writer.write("\n");
	}
	static void close() throws IOException {
		// TODO Auto-generated method stub
		writer.close();
	}
}
public class Main {

	public static void main(String[] args) throws IOException {
		Reader.init(System.in);
		Writer.init(System.out);
		solve();
		Reader.close();
		Writer.close();
	}
	private static void solve() throws IOException {
		int n = Reader.nextInt();
		Writer.println(s(n,n));
	}
	static String s(int n,int i)
	{
		if(i==1)
		{
			return a(i,1)+"+"+n;
		}
		else {
			return "("+s(n,i-1)+")"+a(i,1)+"+"+(n-i+1);
		}
	}

	static String a(int n,int i)
	{
		if (i+1>n) {
			return "sin("+i+")";
		}else {
			if (i%2==0) {
				return "sin("+i+"+"+a(n,i+1)+")";
			}else {
				return "sin("+i+"-"+a(n,i+1)+")";
			}
		}
	}
}