UVa290 - Palindroms <---> smordnilaP(进制转换、回文)

 Palindroms  smordnilaP 

The following problem deals with Palindroms composed of digits. A number is a palindrom, if the sequence of signs (digits or characters) read from left to right and read from right to left are identical. Now, given the number 65 with base 10, adding the number read from right to left , that means 56, leads to 121. By definition 121 is a palindrom. With another number you might have to repeat this step until the sum is of the required palindrom form. eg. 87:

    87 + 78 = 165    165 + 561 = 726    726 + 627 = 1353    1353 + 3531 = 4884

The number of steps is 4.

This works in any base with any number. Naturally the number of steps increases incredibly fast, so there exist numbers in base 10 that requires more than 10,000 steps. You will have to find the numbers of steps of a given number in all the bases 15 down to 2. When a Number is in an illegal form in a base, the number of Steps will be represented by a ``?".

Example

Base 15 87 + 78 = 110110 + 011 = 121 2 stepsBase 14 87 + 78 = 111 1 stepBase 13 87 + 78 = 132132 + 231 = 363 2 stepsBase 12 87 + 78 = 143143 + 341 = 484 2 stepsBase 11 87 + 78 = 154154 + 451 = 5A5 2 stepsBase 10 87 + 78 = 165165 + 561 = 726726 + 627 = 13531353 + 3531 = 4884 4 stepsBase 9 87 + 78 = 176176 + 671 = 857857 + 758 = 17261762 + 2671 = 75437543 + 3457 = 1211112111 + 11121 = 23232 6 stepsBase 8 illegal ? stepsBase 7 illegal ? stepsBase 6 illegal ? stepsBase 5 illegal ? stepsBase 4 illegal ? stepsBase 3 illegal ? stepsBase 2 illegal ? steps

Input and Output

The input contains several lines, each of them having a legal base 15 integer.

For each line of the input print a single line containing the 14 number of steps in all bases 15 down to 2 separated by a blank space. The number of steps will never be bigger than 100.

Sample Input

87ED

Sample Output

2 1 2 2 2 4 6 ? ? ? ? ? ? ?19 ? ? ? ? ? ? ? ? ? ? ? ? ?

import java.io.FileInputStream;import java.io.BufferedReader;import java.io.InputStreamReader;import java.io.PrintWriter;import java.io.OutputStreamWriter;import java.io.StreamTokenizer;public class Main {private static final boolean DEBUG = false;private BufferedReader cin;private PrintWriter cout;private StreamTokenizer tokenizer;private String s;public void init() {try {if (DEBUG) {cin = new BufferedReader(new InputStreamReader(new FileInputStream("e:\\uva_in.txt")));} else {cin = new BufferedReader(new InputStreamReader(System.in));}tokenizer = new StreamTokenizer(cin);tokenizer.resetSyntax();tokenizer.wordChars('a', 'z');tokenizer.wordChars('A', 'Z');tokenizer.wordChars('0', '9');tokenizer.wordChars(128 + 32, 255);tokenizer.whitespaceChars(0, ' ');tokenizer.commentChar('/');tokenizer.quoteChar('"');tokenizer.quoteChar('\'');cout = new PrintWriter(new OutputStreamWriter(System.out));} catch (Exception e) {e.printStackTrace();}}private String next() {try { tokenizer.nextToken();  if (tokenizer.ttype == StreamTokenizer.TT_EOF) return null;  else if (tokenizer.ttype == StreamTokenizer.TT_NUMBER) {  return String.valueOf((int)tokenizer.nval); } else return tokenizer.sval;} catch (Exception e) {e.printStackTrace();return null;}}public boolean input() {s = next();if (s == null) return false;return true;}private boolean isPalindrom(String s){int len = s.length();for (int i = 0; i < len / 2; i++) {if (s.charAt(i) != s.charAt(len - 1 - i)) return false;}return true;}private String add(String a, int base){StringBuilder sb = new StringBuilder();int len = a.length();String b = new StringBuilder(a).reverse().toString();int carry = 0;for (int i = 0; i < len; i++) {char ch1 = a.charAt(len - 1 - i);char ch2 = b.charAt(len - 1 - i);int num1 = 0, num2 = 0, sum = 0;if (Character.isDigit(ch1)) {num1 = ch1 - '0';} else if (Character.isLetter(ch1)) {ch1 = Character.toLowerCase(ch1);num1 = ch1 - 'a' + 10;}if (Character.isDigit(ch2)) {num2 = ch2 - '0';} else if (Character.isLetter(ch2)) {ch2 = Character.toLowerCase(ch2);num2 = ch2 - 'a' + 10;}sum = num1 + num2 + carry;carry = sum / base;sum %= base;char ans;if (sum < 10) ans = (char)('0' + sum);else ans = (char)('A' + (sum - 10));sb.append(ans);}if (carry != 0) {char ans;if (carry < 10) ans = (char)('0' + carry);else ans = (char)('A' + (carry - 10));sb.append(ans);}return sb.reverse().toString();}private int check(String s, int base){int len = s.length();for (int i = 0; i < len; i++) {char ch = s.charAt(i);if (Character.isDigit(ch)) {int tmp = ch - '0';if (tmp >= base) return -1;} else if (Character.isLetter(ch)) {ch = Character.toLowerCase(ch);int tmp = ch - 'a' + 10;if (tmp >= base) return -1;} else return -1;}int step = 0;while (!isPalindrom(s)) {s = add(s, base);step++;}return step;}public void solve() {boolean first = true;for (int i = 15; i >= 2; i--) {int ans = check(s, i);if (first) first = false;else cout.print(" ");if (ans == -1) cout.print("?");else cout.print(ans);}cout.println();cout.flush();}public static void main(String[] args) {Main solver = new Main();solver.init();while (solver.input()) {solver.solve();}}}