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a. 更好地算法,以找到若干座标的下一个阵容。
原标题:A better algorithm to find the next palindrome of a number string

首先,问题是:

如果在从左边到右边和从左边到右边的亲子系统中的代表权相同,那么,就把积极的愤怒称为棕榈树。 一位人数不超过100 000位数的正面的K级表示,最小的棕榈地的价值大于K级。 这些数字总是显示为零。

投入:第一行包含的是惯性t,测试案例的数量。 下面是K类。

产出: For each K, output the smallest palindrome larger than K. Example

投入:

2 P-4, 2 P-3, 2 FS, 2 NS

808

2 P-4, 2 P-3, 2 FS, 2 NS133

产出:

818

2 P-4, 2 P-3, 2 FS, 2 NS2 P-4, 2 P-3, 2 FS, 2 NS2 P-4, 2 P-3, 2 FS, 2 NS2 P-4, 2 P-3, 2 FS, 2 NS

第二是我的法典:

// I know it is bad practice to not cater for erroneous input,
// however for the purpose of the execise it is omitted
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.lang.Exception;
import java.math.BigInteger;

public class Main
{    
    public static void main(String [] args){   
        try{
            Main instance = new Main(); // create an instance to access non-static
                                        // variables
        
            // Use java.util.Scanner to scan the get the input and initialise the
            // variable
            Scanner sc=null;

            BufferedReader r = new BufferedReader(new InputStreamReader(System.in));

            String input = "";

            int numberOfTests = 0;

            String k; // declare any other variables here
            
            if((input = r.readLine()) != null){
                sc = new Scanner(input);
                numberOfTests = sc.nextInt();
            }

            for (int i = 0; i < numberOfTests; i++){
                if((input = r.readLine()) != null){
                    sc = new Scanner(input);
                    k=sc.next(); // initialise the remainder of the variables sc.next()
                    instance.palindrome(k);
                } //if
            }// for
        }// try

        catch (Exception e)
        {
            e.printStackTrace();
        }
    }// main

    public void palindrome(String number){

        StringBuffer theNumber = new StringBuffer(number);
        int length = theNumber.length();
        int left, right, leftPos, rightPos;
        // if incresing a value to more than 9 the value to left (offset) need incrementing
        int offset, offsetPos;
        boolean offsetUpdated;
        // To update the string with new values
        String insert;
        boolean hasAltered = false;

        for(int i = 0; i < length/2 P-4, 2 P-3, 2 FS, 2 NS; i++){
            leftPos = i; 
            rightPos = (length-1) - i;
            offsetPos = rightPos -1; offsetUpdated = false;
            
            // set values at opposite indices and offset
            left = Integer.parseInt(String.valueOf(theNumber.charAt(leftPos)));
            right = Integer.parseInt(String.valueOf(theNumber.charAt(rightPos)));
            offset = Integer.parseInt(String.valueOf(theNumber.charAt(offsetPos)));

            if(left != right){
                // if r > l then offest needs updating
                if(right > left){
                    // update and replace
                    right = left;
                    insert = Integer.toString(right);

                    theNumber.replace(rightPos, rightPos + 1, insert);
                
                    offset++; if (offset == 10) offset = 0;
                    insert = Integer.toString(offset);

                    theNumber.replace(offsetPos, offsetPos + 1, insert);
                    offsetUpdated = true;
               
                    // then we need to update the value to left again
                    while (offset == 0 && offsetUpdated){ 
                        offsetPos--;
                        offset =
                            Integer.parseInt(String.valueOf(theNumber.charAt(offsetPos)));
                        offset++; if (offset == 10) offset = 0;
                        // replace
                        insert = Integer.toString(offset);
                        theNumber.replace(offsetPos, offsetPos + 1, insert);
                    }
                    // finally incase right and offset are the two middle values
                    left = Integer.parseInt(String.valueOf(theNumber.charAt(leftPos)));
                    if (right != left){
                        right = left;
                        insert = Integer.toString(right);
                        theNumber.replace(rightPos, rightPos + 1, insert);
                    }
                }// if r > l
                else
                    // update and replace
                    right = left;
                    insert = Integer.toString(right);
                    theNumber.replace(rightPos, rightPos + 1, insert);           
            }// if l != r
        }// for i
        System.out.println(theNumber.toString());
    }// palindrome
}

最后,我的解释和问题。

My code compares either end and then moves in
    if left and right are not equal
        if right is greater than left
            (increasing right past 9 should increase the digit
             to its left i.e 09 ---- > 10) and continue to do
             so if require as for 89999, increasing the right
             most 9 makes the value 90000
        
             before updating my string we check that the right
             and left are equal, because in the middle e.g 78849887
             we set the 9 --> 4 and increase 4 --> 5, so we must cater for this.

问题来自网上法官系统。 我的法典适用于所有测试,但当我提交时,我获得的时间限制超过了错误,我的回答没有被接受。

没有人就如何改进我的算法提出建议。 在撰写这个问题时,我认为,我可以不考虑我的时段(决字=0 & 0amp;&被抵消),而是利用一种保.,确保我下届[i]大赛中被抵消。 我确认我的意见或建议将受到赞赏,我也想知道,是否有必要使我的问题更加明确。

最佳回答

这似乎像许多法典一样。 你们是否尝试了非常冷静的做法? 检查是否是棕榈树实际上非常简单。

private boolean isPalindrome(int possiblePalindrome) {
    String stringRepresentation = String.valueOf(possiblePalindrome);
    if ( stringRepresentation.equals(stringRepresentation.reverse()) ) {
       return true;
    }
}

既然这也许不是执行最强的法典,但它给你一个真正简单的起点:

private int nextLargestPalindrome(int fromNumber) {
    for ( int i = fromNumber + 1; ; i++ ) {
        if ( isPalindrome( i ) ) {
            return i;
        }
    }
}

现在,如果说这太快,你就能够将其用作参考,并努力减少算法的复杂性。

实际应该有固定时间(现在,在投入数上线),以找到下一个最大的棕榈树。 我将给出一个算法,假设数字甚至连数长(但可扩大到奇数位数)。

  1. Find the decimal representation of the input number ("2133").
  2. Split it into the left half and right half ("21", "33");
  3. Compare the last digit in the left half and the first digit in the right half.
    a. If the right is greater than the left, increment the left and stop. ("22")
    b. If the right is less than the left, stop.
    c. If the right is equal to the left, repeat step 3 with the second-last digit in the left and the second digit in the right (and so on).
  4. Take the left half and append the left half reversed. That s your next largest palindrome. ("2222")

适用于更复杂的数字:

1.    1234567887654322
2.    12345678   87654322
3.    12345678   87654322
             ^   ^         equal
3.    12345678   87654322
            ^     ^        equal
3.    12345678   87654322
           ^       ^       equal
3.    12345678   87654322
          ^         ^      equal
3.    12345678   87654322
         ^           ^     equal
3.    12345678   87654322
        ^             ^    equal
3.    12345678   87654322
       ^               ^   equal
3.    12345678   87654322
      ^                 ^  greater than, so increment the left

3.    12345679

4.    1234567997654321  answer

这似乎与你所描述的算法相似,但从内部数字开始,向外移。

问题回答

在唯一的必要行动是简单增加的情况下,没有理由与个别数字相距。 The following Code is based on Raks response

守则强调,故意夸张执行速度。

import static org.junit.Assert.assertEquals;

import java.math.BigInteger;
import org.junit.Test;

public class NextPalindromeTest {

    public static String nextPalindrome(String num) {
        int len = num.length();
        String left = num.substring(0, len / 2);
        String middle = num.substring(len / 2, len - len / 2);
        String right = num.substring(len - len / 2);

        if (right.compareTo(reverse(left)) < 0)
            return left + middle + reverse(left);

        String next = new BigInteger(left + middle).add(BigInteger.ONE).toString();
        return next.substring(0, left.length() + middle.length())
             + reverse(next).substring(middle.length());
    }

    private static String reverse(String s) {
        return new StringBuilder(s).reverse().toString();
    }

    @Test
    public void testNextPalindrome() {
        assertEquals("5", nextPalindrome("4"));
        assertEquals("11", nextPalindrome("9"));
        assertEquals("22", nextPalindrome("15"));
        assertEquals("101", nextPalindrome("99"));
        assertEquals("151", nextPalindrome("149"));
        assertEquals("123454321", nextPalindrome("123450000"));
        assertEquals("123464321", nextPalindrome("123454322"));
    }
}

我总是有秩序解决办法(在座标数中,千方千方千位数)

Lets take some examples suppose n=17208

divide the number into two parts from middle and reversibly write the most significant part onto the less significant one. ie, 17271 if the so generated number is greater than your n it is your palindrome, if not just increase the center number(pivot) ie, you get 17371

其他例子

n=17286 palidrome-attempt=17271(since it is less than n increment the pivot, 2 in this case) so palidrome=17371

n=5684 palidrome1=5665 palidrome=5775

n=458322 palindrome=458854

now suppose n = 1219901 palidrome1=1219121 incrementing the pivot makes my number smaller here so increment the number adjacent pivot too 1220221

可扩展这一逻辑

public class NextPalindrome 
{   
    int rev, temp;
    int printNextPalindrome(int n) 
    {
        int num = n;
        for (int i = num+1; i >= num; i++) 
        {
            temp = i;
            rev = 0;
            while (temp != 0) 
            {
                int remainder = temp % 10;
                rev = rev * 10 + remainder;
                temp = temp / 10;
            }
            if (rev == i) 
            {
                break;
            }
        }
        return rev;
    }
    public static void main(String args[]) 
    {
        NextPalindrome np = new NextPalindrome();
        int nxtpalin = np.printNextPalindrome(11);
        System.out.println(nxtpalin);
    }



}

我的法典就是在这里。 全文见

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        System.out.println("Enter number of tests: ");
        int t = sc.nextInt();

        for (int i = 0; i < t; i++) {
            System.out.println("Enter number: ");
            String numberToProcess = sc.next(); // ne proveravam dal su brojevi
            nextSmallestPalindrom(numberToProcess);
        }
    }

    private static void nextSmallestPalindrom(String numberToProcess) {
        

        int i, j;

        int length = numberToProcess.length();
        int[] numberAsIntArray = new int[length];
        for (int k = 0; k < length; k++)
            numberAsIntArray[k] = Integer.parseInt(String
                    .valueOf(numberToProcess.charAt(k)));

        numberToProcess = null;

        boolean all9 = true;
        for (int k = 0; k < length; k++) {
            if (numberAsIntArray[k] != 9) {
                all9 = false;
                break;
            }
        }
        // case 1, sve 9ke
        if (all9) {
            whenAll9(length);
            return;
        }

        int mid = length / 2;
        if (length % 2 == 0) {
            i = mid - 1;
            j = mid;
        } else {
            i = mid - 1;
            j = mid + 1;
        }
        
        while (i >= 0 && numberAsIntArray[i] == numberAsIntArray[j]) {
            i--;
            j++;
        }
        // case 2 already polindrom
        if (i == -1) {
            if (length % 2 == 0) {
                i = mid - 1;
                j = mid;
            } else {
                i = mid;
                j = i;
            }
            addOneToMiddleWithCarry(numberAsIntArray, i, j, true);

        } else {
            // case 3 not polindrom
            if (numberAsIntArray[i] > numberAsIntArray[j]) { // 3.1)
                
                while (i >= 0) {
                    numberAsIntArray[j] = numberAsIntArray[i];
                    i--;
                    j++;
                }
                for (int k = 0; k < numberAsIntArray.length; k++)
                    System.out.print(numberAsIntArray[k]);
                System.out.println();
            } else { // 3.2 like case 2
                if (length % 2 == 0) {
                    i = mid - 1;
                    j = mid;
                } else {
                    i = mid;
                    j = i;
                }
                addOneToMiddleWithCarry(numberAsIntArray, i, j, false);
            }
        }
    }

    private static void whenAll9(int length) {
        
        for (int i = 0; i <= length; i++) {
            if (i == 0 || i == length)
                System.out.print( 1 );
            else
                System.out.print( 0 );
        }
    }

    private static void addOneToMiddleWithCarry(int[] numberAsIntArray, int i,
            int j, boolean palindrom) {
        numberAsIntArray[i]++;
        numberAsIntArray[j] = numberAsIntArray[i];
        while (numberAsIntArray[i] == 10) {
            numberAsIntArray[i] = 0;
            numberAsIntArray[j] = numberAsIntArray[i];
            i--;
            j++;
            numberAsIntArray[i]++;
            numberAsIntArray[j] = numberAsIntArray[i];
        }
        
        if (!palindrom)
            while (i >= 0) {
                numberAsIntArray[j] = numberAsIntArray[i];
                i--;
                j++;
            }
        
        for (int k = 0; k < numberAsIntArray.length; k++)
            System.out.print(numberAsIntArray[k]);
        System.out.println();
    }

}

引言

public static String genNextPalin(String base){
    //check if it is 1 digit
    if(base.length()==1){
        if(Integer.parseInt(base)==9)
            return "11";
        else
            return (Integer.parseInt(base)+1)+"";
    }
    boolean check = true;
    //check if it is all 9s
    for(char a: base.toCharArray()){
        if(a!= 9 )
            check = false;
    }
    if(check){
        String num = "1";
        for(int i=0; i<base.length()-1; i++)
            num+="0";
        num+="1";
        return num;
    }

    boolean isBasePalin = isPalindrome(base);
    int mid = base.length()/2;
    if(isBasePalin){
        //if base is palin and it is odd increase mid and return
        if(base.length()%2==1){
            BigInteger leftHalf = new BigInteger(base.substring(0,mid+1));
            String newLeftHalf = leftHalf.add(BigInteger.ONE).toString();
            String newPalin = genPalin2(newLeftHalf.substring(0,mid),newLeftHalf.charAt(mid));
            return newPalin;
        }
        else{
            BigInteger leftHalf = new BigInteger(base.substring(0,mid));
            String newLeftHalf = leftHalf.add(BigInteger.ONE).toString();
            String newPalin = genPalin(newLeftHalf.substring(0,mid));
            return newPalin;
        }
    }
    else{
        if(base.length()%2==1){
            BigInteger leftHalf = new BigInteger(base.substring(0,mid));
            BigInteger rightHalf = new BigInteger(reverse(base.substring(mid+1,base.length())));

            //check if leftHalf is greater than right half
            if(leftHalf.compareTo(rightHalf)==1){
                String newPalin = genPalin2(base.substring(0,mid),base.charAt(mid));
                return newPalin;
            }
            else{
                BigInteger leftHalfMid = new BigInteger(base.substring(0,mid+1));
                String newLeftHalfMid = leftHalfMid.add(BigInteger.ONE).toString();
                String newPalin = genPalin2(newLeftHalfMid.substring(0,mid),newLeftHalfMid.charAt(mid));
                return newPalin;
            }
        }
        else{
            BigInteger leftHalf = new BigInteger(base.substring(0,mid));
            BigInteger rightHalf = new BigInteger(reverse(base.substring(mid,base.length())));

            //check if leftHalf is greater than right half
            if(leftHalf.compareTo(rightHalf)==1){
                return genPalin(base.substring(0,mid));
            }
            else{
                BigInteger leftHalfMid = new BigInteger(base.substring(0,mid));
                String newLeftHalfMid = leftHalfMid.add(BigInteger.ONE).toString(); 
                return genPalin(newLeftHalfMid);
            }
        }
    }
}

public static String genPalin(String base){
    return base + new StringBuffer(base).reverse().toString();
}
public static String genPalin2(String base, char middle){
    return base + middle +new StringBuffer(base).reverse().toString();
}

public static String reverse(String in){
    return new StringBuffer(in).reverse().toString();
}

static boolean isPalindrome(String str) {    
    int n = str.length();
    for( int i = 0; i < n/2; i++ )
        if (str.charAt(i) != str.charAt(n-i-1)) 
            return false;
    return true;    
}

iii 这里是另一个简单的算法,使用假日,

  def is_palindrome(n):
      if len(n) <= 1:
          return False
      else:
          m = len(n)/2
          for i in range(m):
              j = i + 1
              if n[i] != n[-j]:
                  return False
          return True

  def next_palindrome(n):
      if not n:
          return False
      else:
          if is_palindrome(n) is True:
              return n
          else:
             return next_palindrome(str(int(n)+1))

  print next_palindrome( 1000010 )

我已提出书面意见,以澄清本金法典中的每一步骤。

需要考虑的一件事是,投入可能很大,我们不能简单地进行仓促行动。 因此,把投入作为扼杀手段,然后加以操纵,将变得非常容易。

tests = int(input())
results = []
for i in range(0, tests):
    pal = input().strip()
    palen = len(pal)
    mid = int(palen/2)
    if palen % 2 != 0:
        if mid == 0: # if the number is of single digit e.g. next palindrome for 5 is 6 
            ipal = int(pal)
            if ipal < 9:
                results.append(int(pal) + 1)
            else:
                results.append(11) # for 9 next palindrome will be 11
        else:
            pal = list(pal)
            pl = l = mid - 1
            pr = r = mid + 1
            flag =  n  # represents left and right half of input string are same
            while pl >= 0:
                if pal[pl] > pal[pr]:
                    flag =  r  # 123483489 in this case pal[pl] = 4 and pal[pr] = 3 so we just need to copy left half in right half
                    break      # 123484321 will be the answer
                elif pal[pl] < pal[pr]:
                    flag =  m  # 123487489 in this case pal[pl] = 4 and pal[pr] = 9 so copying left half in right half will make number smaller
                    break # in this case we need to take left half increment by 1 and the copy in right half 123494321 will be the anwere
                else:
                    pl = pl -1
                    pr = pr + 1
            if flag ==  m  or flag ==  n : # increment left half by one and copy in right half
                if pal[mid] !=  9 : # if mid element is < 9 the we can simply increment the mid number only and copy left in right half
                        pal[mid] = str(int(pal[mid]) + 1)
                        while r < palen:
                            pal[r] = pal[l]
                            r = r + 1
                            l = l - 1
                        results.append(  .join(pal))
                else: # if mid element is 9 this will effect entire left half because of carry
                    pal[mid] =  0  # we need to take care of large inputs so we can not just directly add 1 in left half
                    pl = l
                    while pal[l] ==  9 :
                        pal[l] =  0 
                        l = l - 1
                    if l >= 0:
                        pal[l] = str(int(pal[l]) + 1)
                    while r < palen:
                        pal[r] = pal[pl]
                        r = r + 1
                        pl = pl - 1
                    if l < 0:
                        pal[0] =  1 
                        pal[palen - 1] =  01 
                    results.append(  .join(pal))
            else:
                while r < palen: # when flag is  r 
                    pal[r] = pal[l]
                    r = r + 1
                    l = l - 1
                results.append(  .join(pal))
    else: # even length almost similar concept here with flags having similar significance as in case of odd length input
        pal = list(pal)
        pr = r = mid
        pl = l = mid - 1
        flag =  n 
        while pl >= 0:
            if pal[pl] > pal[pr]:
                flag =  r 
                break
            elif pal[pl] < pal[pr]:
                flag =  m 
                break
            else:
                pl = pl -1
                pr = pr + 1
        if flag ==  r :
            while r < palen:
                    pal[r] = pal[l]
                    r = r + 1
                    l = l - 1
            results.append(  .join(pal))
        else:
            if pal[l] !=  9 :
                pal[l] = str(int(pal[l]) + 1)
                while r < palen:
                    pal[r] = pal[l]
                    r = r + 1
                    l = l - 1
                results.append(  .join(pal))
            else:
                pal[mid] =  0 
                pl = l
                while pal[l] ==  9 :
                    pal[l] =  0 
                    l = l - 1
                if l >= 0:
                    pal[l] = str(int(pal[l]) + 1)
                while r < palen:
                    pal[r] = pal[pl]
                    r = r + 1
                    pl = pl - 1
                if l < 0:
                    pal[0] =  1 
                    pal[palen - 1] =  01 
                results.append(  .join(pal))

for xx in results:
    print(xx) 

我们可以找到下面的棕榈树。

private void findNextPalindrom(int i) {
    i++;
    while (!checkPalindrom(i)) {
        i++;
    }
    Log.e(TAG, "findNextPalindrom:next palindrom is===" + i);
}


private boolean checkPalindrom(int num) {
    int temp = num;
    int rev = 0;
    while (num > 0) {
        int rem = num % 10;
        rev = rev * 10 + rem;
        num = num / 10;
    }
    return temp == rev;
}

简单编码和测试产出:

class NextPalin
{
public static void main( String[] args )
{
    try {
        int[] a = {2, 23, 88, 234, 432, 464, 7887, 7657, 34567, 99874, 7779222, 2569981, 3346990, 229999, 2299999 };
        for( int i=0; i<a.length; i++)
        {
            int add = findNextPalin(a[i]);
            System.out.println( a[i] + "  +  "  + add +  "  = "  + (a[i]+add)  );
        }
    }
    catch( Exception e ){}
}

static int findNextPalin( int a ) throws Exception
{
    if( a < 0 ) throw new Exception();
    if( a < 10 ) return a;

    int count = 0, reverse = 0, temp = a;
    while( temp > 0 ){
        reverse = reverse*10 + temp%10;
        count++;
        temp /= 10;
    }

    //compare  half  value
    int halfcount = count/2;
    int base = (int)Math.pow(10, halfcount );
    int reverseHalfValue = reverse % base;
    int currentHalfValue = a % base;

    if( reverseHalfValue == currentHalfValue ) return 0;
    if( reverseHalfValue > currentHalfValue )  return  (reverseHalfValue - currentHalfValue);

    if(  (((a-currentHalfValue)/base)%10) == 9 ){
        //cases like 12945 or 1995
        int newValue = a-currentHalfValue + base*10;
        int diff = findNextPalin(newValue);
        return base*10 - currentHalfValue + diff;
    }
    else{
        return (base - currentHalfValue + reverseHalfValue );
    }
}
}

$ java NextPalin
2  +  2  = 4
23  +  9  = 32
88  +  0  = 88
234  +  8  = 242
432  +  2  = 434
464  +  0  = 464
7887  +  0  = 7887
7657  +  10  = 7667
34567  +  76  = 34643
99874  +  25  = 99899
7779222  +  555  = 7779777
2569981  +  9771  = 2579752
3346990  +  443  = 3347433
229999  +  9933  = 239932
2299999  +  9033  = 2309032




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