2019ICPC亚洲区域赛 （银川站） I Base62 【大数进制转换】

Description

As we already know, base64 is a common binary-to-text encoding scheme. Here we define a special series of positional systems that represent numbers using a base (a.k.a. radix) of 2 to 62. The symbols '0' -- '9' represent zero to nine, and 'A' -- 'Z' represent ten to thirty-five, and 'a' -- 'z' represent thirty-six to sixty-one. Now you need to convert some integer z in base x into base y.

Input 

The input contains three integers x,y (2≤x,y≤62) and z (), where the integer z is given in base x.

Output 

Output the integer z in base y.

样例输入 

16 2 FB

样例输出 

11111011

 题目大意：

2-62进制间的进制转换。

分析：

大数用C++写很麻烦，这里贴一个Java的大数进制转换。

具体解释见代码。

import java.math.BigInteger;
import java.util.Stack;
import java.util.Scanner;

public class Main {
    // 理论上支持62进制的转换, 当然可以自己添加一些其他符号来增加进制数
    private static final String TARGET_STR = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
    private static final char[] chs = TARGET_STR.toCharArray();
    private static final BigInteger INTEGER0 = new BigInteger("0");


    /**
     * 10进制转任意进制
     */
    public static String numToRadix(String number, int radix) {
        if(radix < 0 || radix > TARGET_STR.length()){
            radix = TARGET_STR.length();
        }

        BigInteger bigNumber = new BigInteger(number);
        BigInteger bigRadix = new BigInteger(radix + "");

        Stack<Character> stack = new Stack<>();
        StringBuilder result = new StringBuilder(0);
        while (!bigNumber.equals(INTEGER0)) {
            stack.add(chs[bigNumber.remainder(bigRadix).intValue()]);
            bigNumber = bigNumber.divide(bigRadix);
        }
        for (; !stack.isEmpty(); ) {
            result.append(stack.pop());
        }
        return result.length() == 0 ? "0" : result.toString();
    }

    /**
     * 任意进制转10进制
     */
    public static String radixToNum(String number, int radix){
        if(radix < 0 || radix > TARGET_STR.length()){
            radix = TARGET_STR.length();
        }
        if (radix == 10) {
            return number;
        }

        char ch[] = number.toCharArray();
        int len = ch.length;

        BigInteger bigRadix = new BigInteger(radix + "");
        BigInteger result = new BigInteger("0");
        BigInteger base = new BigInteger("1");


        for (int i = len - 1; i >= 0; i--) {
            BigInteger index = new BigInteger(TARGET_STR.indexOf(ch[i]) + "");
            result = result.add(index.multiply(base)) ;
            base = base.multiply(bigRadix);
        }

        return result.toString();
    }


    /**
     * 任意进制之间的互相转换, 先将任意进制转为10进制, 然后在转换为任意进制
     */
    public static String transRadix(String num, int fromRadix, int toRadix) {
        return numToRadix(radixToNum(num, fromRadix), toRadix);
    }

    public static void main(String[] args) {
	Scanner cin = new Scanner(System.in);
	int x = cin.nextInt();
        int y = cin.nextInt();
        String s = cin.next();
        
        System.out.println(Main.transRadix(s, x, y));
    }

}