odds(a)java_SGU 112 a^b-b^a (Java Edition)

迷南。 2022-11-09 12:55 110阅读 0赞

You are given natural numbers a and b. Find ab-ba.

Input

Input contains numbers a and b (1≤a,b≤100).

Output

Write answer to output.

Sample Input

2 3

Sample Output

\-1

一看到这种题目，就想到高精度算法，Java的大数。

此举确实流氓了一点，不过确实过了，鄙人的第一题SGU啊，不许打击。

过段时间看看能不能写出 (C++ Edition) ,啥也别说了，上代码。

![cbef093dcc044b2793832001e2365e43.png][]importjava.math.\*;

![cbef093dcc044b2793832001e2365e43.png][]importjava.util.\*;

![cbef093dcc044b2793832001e2365e43.png][]

![cbef093dcc044b2793832001e2365e43.png][]publicclassSolution

![2f88ce130b654eb5dc6788e02dbcfc90.png][]

![dbf989d57862681739b642d8621fe1f0.png][]![918e8df969f9f8c8d002f25cda86cade.png][]\{

![df37983f39daa189b8c814e01a6a9011.png][]publicstaticvoidmain(String\[\] args)

![f70a0fde2b51b7dd92a70e712e540cf6.png][]

![edb48e6f68462ea23d9a824f01de40c5.png][]![918e8df969f9f8c8d002f25cda86cade.png][]\{

![df37983f39daa189b8c814e01a6a9011.png][]      Scanner in=newScanner(System.in);

![df37983f39daa189b8c814e01a6a9011.png][]inta=in.nextInt();

![df37983f39daa189b8c814e01a6a9011.png][]intb=in.nextInt();

![df37983f39daa189b8c814e01a6a9011.png][]

![df37983f39daa189b8c814e01a6a9011.png][]      BigInteger A=BigInteger.valueOf(a);

![df37983f39daa189b8c814e01a6a9011.png][]      BigInteger B=BigInteger.valueOf(b);//A^B![df37983f39daa189b8c814e01a6a9011.png][]BigInteger rA=BigInteger.valueOf(a);

![df37983f39daa189b8c814e01a6a9011.png][]      BigInteger rB=BigInteger.valueOf(b);//store the result after computing![df37983f39daa189b8c814e01a6a9011.png][]![df37983f39daa189b8c814e01a6a9011.png][]for(inti=1; irA=rA.multiply(A);

![df37983f39daa189b8c814e01a6a9011.png][]for(inti=1; i

![df37983f39daa189b8c814e01a6a9011.png][]          rB=rB.multiply(B);

![df37983f39daa189b8c814e01a6a9011.png][]      System.out.println(rA.subtract(rB));//sub![4a5daaec04350a363f186a4d2c5ed6ce.png][]\}![0ac3a2d53663ec01c7f7225264eeefae.png][]\}

附《Core Java I》里关于 大数的简单介绍，讲的算比较清晰的了：

Big Numbers

If the precision of the basic integer and floating-point types is not sufficient, you can

turn to a couple of handy classes in the java.math package: BigInteger and BigDecimal. These

are classes for manipulating numbers with an arbitrarily long sequence of digits. The

BigInteger class implements arbitrary precision integer arithmetic, and BigDecimal does the

same for floating-point numbers.

Use the static valueOf method to turn an ordinary number into a big number:

BigInteger a = BigInteger.valueOf(100);

Unfortunately, you cannot use the familiar mathematical operators such as + and \* to

combine big numbers. Instead, you must use methods such as add and multiply in the big

number classes.

BigInteger c = a.add(b); // c = a + b

BigInteger d = c.multiply(b.add(BigInteger.valueOf(2))); // d = c \* (b + 2)

C++ NOTE: Unlike C++, Java has no programmable operator overloading. There was no way

for the programmer of the BigInteger class to redefine the + and \* operators to give the add and

multiply operations of the BigInteger classes. The language designers did overload the + operator

to denote concatenation of strings. They chose not to overload other operators, and they

did not give Java programmers the opportunity to overload operators in their own classes.

Listing 3–6 shows a modification of the lottery odds program of Listing 3–5, updated to

work with big numbers. For example, if you are invited to participate in a lottery in

which you need to pick 60 numbers out of a possible 490 numbers, then this program

will tell you that your odds are 1 in 7163958434619955574151162225400929334117176

12789263493493351 013459481104668848. Good luck!

The program in Listing 3–5 computed the statement

lotteryOdds = lotteryOdds \* (n - i + 1) / i;

When big numbers are used, the equivalent statement becomes

lotteryOdds = lotteryOdds.multiply(BigInteger.valueOf(n - i + 1)).divide(BigInteger.valueOf(i));

Listing 3–6 BigIntegerTest.java

1. import java.math.\*;

2. import java.util.\*;

4. /\*\*

5. \* This program uses big numbers to compute the odds of winning the grand prize in a lottery.

6. \* @version 1.20 2004-02-10

7. \* @author Cay Horstmann

8. \*/

9. public class BigIntegerTest

10. \{

11. public static void main(String\[\] args)

12. \{

13. Scanner in = new Scanner(System.in);

14.

15. System.out.print("How many numbers do you need to draw? ");

16. int k = in.nextInt();

17.

18. System.out.print("What is the highest number you can draw? ");

19. int n = in.nextInt();

20.

21. /\*

22. \* compute binomial coefficient n\*(n-1)\*(n-2)\*...\*(n-k+1)/(1\*2\*3\*...\*k)

23. \*/

24.

25. BigInteger lotteryOdds = BigInteger.valueOf(1);

26.

27. for (int i = 1; i <= k; i++)

28. lotteryOdds = lotteryOdds.multiply(BigInteger.valueOf(n - i + 1)).divide(

29. BigInteger.valueOf(i));

30.

31. System.out.println("Your odds are 1 in " + lotteryOdds + ". Good luck!");

32. \}

33. \}

java.math.BigInteger

? BigInteger add(BigInteger other)

? BigInteger subtract(BigInteger other)

? BigInteger multiply(BigInteger other)

? BigInteger divide(BigInteger other)

? BigInteger mod(BigInteger other)

returns the sum, difference, product, quotient, and remainder of this big integer and

other.

? int compareTo(BigInteger other)

returns 0 if this big integer equals other, a negative result if this big integer is less

than other, and a positive result otherwise.

? static BigInteger valueOf(long x)

returns a big integer whose value equals x.

? BigDecimal add(BigDecimal other)

? BigDecimal subtract(BigDecimal other)

? BigDecimal multiply(BigDecimal other)

? BigDecimal divide(BigDecimal other, RoundingMode mode) 5.0

returns the sum, difference, product, or quotient of this big decimal and other.

To compute the quotient, you must supply a rounding mode. The mode

RoundingMode.HALF\_UP is the rounding mode that you learned in school (i.e., round

down digits 0 . . . 4, round up digits 5 . . . 9). It is appropriate for routine

calculations. See the API documentation for other rounding modes.

? int compareTo(BigDecimal other)

returns 0 if this big decimal equals other, a negative result if this big decimal is less

than other, and a positive result otherwise.

? static BigDecimal valueOf(long x)

? static BigDecimal valueOf(long x, int scale)

returns a big decimal whose value equals x or x /10scale.

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