Java大数类 BigInteger

Posted 2020-11-22 --- 锅老官扎起哦!

package bigint;

/**
 * This class encapsulates a BigInteger, i.e. a positive or negative integer
 * with any number of digits, which overcomes the computer storage length
 * limitation of an integer.
 * 
 */
public class BigInteger {

    /**
     * True if this is a negative integer
     */
    boolean negative;

    /**
     * Number of digits in this integer
     */
    int numDigits;

    /**
     * Reference to the first node of this integer‘s linked list representation
     * NOTE: The linked list stores the Least Significant Digit in the FIRST node.
     * For instance, the integer 235 would be stored as: 5 --> 3 --> 2
     * 
     * Insignificant digits are not stored. So the integer 00235 will be stored as:
     * 5 --> 3 --> 2 (No zeros after the last 2)
     */
    DigitNode front;

    /**
     * Initializes this integer to a positive number with zero digits, in other
     * words this is the 0 (zero) valued integer.
     */
    public BigInteger() {
        negative = false;
        numDigits = 0;
        front = null;
    }

    /**
     * Parses an input integer string into a corresponding BigInteger instance. A
     * correctly formatted integer would have an optional sign as the first
     * character (no sign means positive), and at least one digit character
     * (including zero). Examples of correct format, with corresponding values
     * Format Value +0 0 -0 0 [phone] 0012 12 0 0 -123 -123 -001 -1 +000
     * 0
     * 
     * Leading and trailing spaces are ignored. So " +123 " will still parse
     * correctly, as +123, after ignoring leading and trailing spaces in the input
     * string.
     * 
     * Spaces between digits are not ignored. So "12 345" will not parse as an
     * integer - the input is incorrectly formatted.
     * 
     * An integer with value 0 will correspond to a null (empty) list - see the
     * BigInteger constructor
     * 
     * @param integer Integer string that is to be parsed
     * @return BigInteger instance that stores the input integer.
     * @throws IllegalArgumentException If input is incorrectly formatted
     */
    public static BigInteger parse(String integer) throws IllegalArgumentException {

        boolean f = false;
        /* IMPLEMENT THIS METHOD */
        int len = integer.length();
        StringBuffer buffer = new StringBuffer(integer).reverse();
        char[] cs = buffer.toString().toCharArray();
        DigitNode head = null;
        DigitNode node1 = new DigitNode(0, null);
        DigitNode node2 = new DigitNode(0, null);
        head = node1;
        for (int i = 0; i < len; i++) {
            if (cs[i] == ‘-‘) {
                f = true;
                len--;
                continue;
            }
            if(cs[i] == ‘+‘) {
                len--;
                continue;
            }
            if (Character.isDigit(cs[i])) {
                node2 = new DigitNode(cs[i] - ‘0‘, null);
                node1.next = node2;
                node1 = node2;
            } else {
                throw new IllegalArgumentException("Incorrect Format");
            }

        }
        BigInteger integer2 = new BigInteger();
        integer2.front = head.next;
        integer2.numDigits = len;
        integer2.negative = f;
        // following line is a placeholder for compilation
        return integer2;
    }

    private static void printList(DigitNode head) {
        while (head != null) {
            System.out.print(head.digit + " ");
            head = head.next;
        }
    }


    /**
     * Adds the first and second big integers, and returns the result in a NEW
     * BigInteger object. DOES NOT MODIFY the input big integers.
     * 
     * NOTE that either or both of the input big integers could be negative. (Which
     * means this method can effectively subtract as well.)
     * 
     * @param first  First big integer
     * @param second Second big integer
     * @return Result big integer
     */
    public static BigInteger add(BigInteger first, BigInteger second) {

        /* IMPLEMENT THIS METHOD */
        BigInteger bigc = new BigInteger();
        bigc.front = new DigitNode(0, null);
        int carry = 0;
        DigitNode a = (first.front);
        DigitNode b = (second.front);
        DigitNode head = bigc.front;
        DigitNode c = bigc.front;
        BigInteger d = null;
        for (int i = 0; i < first.numDigits || i < second.numDigits; i++) {
            if(b==null) {
                b=new DigitNode(0, null);
            }
            int temp = carry + a.digit + b.digit;
            c.digit = temp % 10;
            bigc.numDigits++;
            d = new BigInteger();
            d.front = new DigitNode(0, null);
            c.next = d.front;
            c = d.front;
            carry = temp / 10;
            a = a.next;
            b = b.next;
        }

        if (carry != 0) {
            c.digit = carry;
            bigc.numDigits++;
        }
        bigc.negative=first.negative==second.negative?false:true;
        bigc.front = head;
        // following line is a placeholder for compilation
        return bigc;
    }

    public static DigitNode reverseList(DigitNode head) {
        if (head == null || head.next == null)
            return head;
        DigitNode pre = head;
        DigitNode cur = head.next;

        while (cur != null) {
            DigitNode temp = cur.next;
            cur.next = pre;
            pre = cur;
            cur = temp;
        }

        head.next = null;
        return head;

    }

    /**
     * Returns the BigInteger obtained by multiplying the first big integer with the
     * second big integer
     * 
     * This method DOES NOT MODIFY either of the input big integers
     * 
     * @param first  First big integer
     * @param second Second big integer
     * @return A new BigInteger which is the product of the first and second big
     *         integers
     */
    public static BigInteger multiply(BigInteger first, BigInteger second) {
        DigitNode front2 = second.front;
        String retval = front2.digit + "";
        for (DigitNode curr = front2.next; curr != null; curr = curr.next) {
            if (curr.digit == 0)
                continue;
            retval = curr.digit + retval;
        }
           int b=Integer.parseInt(retval);
           DigitNode a = (first.front);
           BigInteger bigc=new BigInteger();
           bigc.front = new DigitNode(0, null);
           BigInteger d = null;
           DigitNode c = bigc.front;
        int carry=0;
        for(int i=0;i<first.numDigits;i++){
            int temp=a.digit*b+carry;
            c.digit=temp%10;
            bigc.numDigits++;
            d = new BigInteger();
            d.front = new DigitNode(0, null);
            c.next = d.front;
            c = d.front;
            carry=temp/10;
            a = a.next;
        }
        while(carry!=0){//乘法的进位可能不止一位
            c.digit=carry%10;
            bigc.numDigits++;
            d = new BigInteger();
            d.front = new DigitNode(0, null);
            c.next = d.front;
            c = d.front;
            carry/=10;
        }
        bigc.negative=first.negative==second.negative?false:true;
       // return c;
        // following line is a placeholder for compilation
        return bigc;
    }
    public static void main(String[] args) {
        BigInteger parse = BigInteger.parse("123");
    }
    
    public boolean StrToInteger(String str) {
        StringBuffer buffer = new StringBuffer(str);
        for(int i=0;i<buffer.length();i++) {
            if(buffer.charAt(i)==‘0‘) {
                return false;
            }
        }
        return true;
        
    }
    
    /*
     * (non-Javadoc)
     * 
     * @see java.lang.Object#toString()
     */
    public String toString() {
        if (front == null) {
            return "0";
        }
        String retval = front.digit + "";
        for (DigitNode curr = front.next; curr != null; curr = curr.next) {
            //if (curr.digit == 0&&Integer.parseInt(retval)!=0)
            if (curr.digit == 0&&StrToInteger(retval))
                continue;
            retval = curr.digit + retval;
        }

        if (negative) {
            retval = ‘-‘ + retval;
        }
        return retval;
    }
}

 

package bigint;

import java.io.IOException;
import java.util.Scanner;

public class BigTest {

    static Scanner sc;
    
    public static void parse() 
    throws IOException {
        System.out.print("	Enter integer => ");
        String integer = sc.nextLine();
        try {
            BigInteger bigInteger = BigInteger.parse(integer);
            System.out.println("		Value = " + bigInteger);
        } catch (IllegalArgumentException e) {
            System.out.println("		Incorrect Format");
        }
    }
    
    public static void add() 
    throws IOException {
        System.out.print("	Enter first integer => ");
        String integer = sc.nextLine();
        BigInteger firstBigInteger = BigInteger.parse(integer);
        
        System.out.print("	Enter second integer => ");
        integer = sc.nextLine();
        BigInteger secondBigInteger = BigInteger.parse(integer);
        
        BigInteger result = BigInteger.add(firstBigInteger,secondBigInteger);
        System.out.println("		Sum: " + result);
    }
    
    public static void multiply() 
    throws IOException {
        System.out.print("	Enter first integer => ");
        String integer = sc.nextLine();
        BigInteger firstBigInteger = BigInteger.parse(integer);
        
        System.out.print("	Enter second integer => ");
        integer = sc.nextLine();
        BigInteger secondBigInteger = BigInteger.parse(integer);
        
        BigInteger result = BigInteger.multiply(firstBigInteger,secondBigInteger);
        System.out.println("		Product: " + result);
        
    }
    
    public static void main(String[] args) 
    throws IOException {
        
        // TODO Auto-generated method stub
        sc = new Scanner(System.in);
        
        char choice;
        while ((choice = getChoice()) != ‘q‘) {
            switch (choice) {
                case ‘p‘ : parse(); break;
                case ‘a‘ : add(); break;
                case ‘m‘ : multiply(); break;
                default: System.out.println("Incorrect choice"); 
            }
        }
    }

    private static char getChoice() {
        System.out.print("
(p)arse, (a)dd, (m)ultiply, or (q)uit? => ");
        String in = sc.nextLine();
        char choice;
        if (in == null || in.length() == 0) {
            choice = ‘ ‘;
        } else {
            choice = in.toLowerCase().charAt(0);
        }
        return choice;
    }

}

package bigint;

/**
 * This class encapsulates a linked list for a digit of a big integer.
 * 
 * @author Sesh Venugopal (RU NB CS 112)
 *
 */
public class DigitNode {
    /**
     * The digit
     */
    int digit;
    
    /**
     * Pointer to next digit in the linked list
     */
    DigitNode next;
    
    /**
     * Initializes this digit node with a digit and next pointer
     * 
     * @param digit Digit
     * @param next Next pointer
     */
    DigitNode(int digit, DigitNode next) {
        this.digit = digit;
        this.next = next;
    }
    
    /* (non-Javadoc)
     * @see java.lang.Object#toString()
     */
    public String toString() {
        return digit + "";
    }
}