C - Log Calculator FZU - 2036

题意：

已知a和b，满足a=log₂x，b=log₂y
求log₂(x+y)

题解：

因为a=log₂x，b=log₂y
所以x=2^a, y=a^b
log₂(x+y)=log₂(2^a+2^b)=log₂(2^b(1+2^a-b))=b+log₂(2^a-b+1)
x>=32时，b+log₂(2^x+1)=x+b

代码：

import java.util.Scanner;
import java.math.BigInteger;
import java.math.BigDecimal;
import java.math.*;public class Main
{public static void main(String[] args){Scanner scanner = new Scanner(System.in);BigDecimal a, b, ans, c;c = BigDecimal.valueOf(32);int t = scanner.nextInt();for(int i = 1; i <= t; i++) {a = scanner.nextBigDecimal();b = scanner.nextBigDecimal();if(a.compareTo(b) <= 0) {ans = a;a = b;b = ans;}a = a.subtract(b);if(a.compareTo(c) >= 0) ans = a.add(b);else {double tmp = Math.pow(2, a.doubleValue()) + 1;tmp = Math.log(tmp)/Math.log((double)2);ans = b.add(BigDecimal.valueOf(tmp));}ans = ans.setScale(9, BigDecimal.ROUND_HALF_UP);System.out.println("Case " + i + ": " + ans.toPlainString());}}
}