We Keep Coding

The smallest Palindrome number is greater N

For a given positive integer N of not more than 1000000 digits, write the value of the smallest palindrome larger than N to output.
Here is my code:
public class Palin {
public static String reverseString(String s) {
String newS = "";
for(int i = s.length() - 1; i >= 0; i--)
newS += s.charAt(i);
return newS;
}
public static String getPalin(String s) {
int lth = s.length();
String left = "", mid = "", right = "", newS = "";
if(lth % 2 != 0) {
left = s.substring(0, lth / 2);
mid = s.substring(lth / 2, lth / 2 + 1);
right = reverseString(left);
newS = left + mid + right;
if(s.compareTo(newS) < 0) return newS;
else {
int temp = Integer.parseInt(mid);
temp++;
mid = Integer.toString(temp);
newS = left + mid + right;
return newS;
}
}
else {
left = s.substring(0, lth / 2 - 1);
mid = s.substring(lth / 2 - 1, lth / 2);
right = reverseString(left);
newS = left + mid + mid + right;
if(s.compareTo(newS) < 0) return newS;
else {
int temp = Integer.parseInt(mid);
temp++;
mid = Integer.toString(temp);
newS = left + mid + mid + right;
return newS;
}
}
}
public static void main(String[] args) throws java.lang.Exception {
Scanner input = new Scanner(System.in);
//Scanner input = new Scanner(System.in);
int k = input.nextInt();
String[] s = new String[k];
for(int i = 0; i < k; i++) {
s[i] = input.next();
}
for(int i = 0; i < k; i++) {
System.out.println(getPalin(s[i]));
}
}
}
My idea is use a String represent for a number. I divide this String into 2 part, coppy first part and reverse it for second part. I think my solve is correct but it not fast enough. I need a more efficient algorithm.
Thanks

EDITED
Since you said that:
For a given positive integer N of not more than 1000000 digits
My previous solution won't work since I have converted them to int and an int can't accommodate 1000000 digits. Thus I have made a new approach, an approach that doesn't need any String to int conversion.
Refer to the code and comment below for details.
CODE:
package main;
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
// Scanner input = new Scanner(System.in);
int k = Integer.parseInt(input.nextLine());
String[] s = new String[k];
for (int i = 0; i < k; i++) {
s[i] = input.nextLine();
}
for (int i = 0; i < k; i++) {
System.out.println(getPalin(s[i]));
}
input.close();
}
public static String getPalin(String s) {
// initialize the result to "" since if input is 1 digit, nothing is printed
String result = "";
// if input is greater than 1000000 digits
if (s.length() >= 1000000) {
// return the highest palindrome less than 1000000
result = "999999";
} else if (s.length() > 1) {
// get the middle index of the string
int mid = s.length() % 2 == 0 ? s.length() / 2 : (s.length() / 2) + 1;
// get the left part of the string
String leftPart = getPalindrome(s.substring(0, mid));
if (s.length() % 2 == 0) {
// attach the left part and the reverse left part
result = leftPart + new StringBuilder(leftPart).reverse().toString();
} else {
// attach the left part and the reverse left part excluding the middle digit
result = leftPart
+ new StringBuilder(leftPart.substring(0, leftPart.length() - 1)).reverse().toString();
}
// check if the new result greater than 1000000 digits
if (result.length() >= 1000000) {
// return the highest palindrome less than 1000000
result = "999999";
}
}
return result;
}
public static String getPalindrome(String param) {
String result = "";
// iterate through the string from last index until index 0
for (int i = param.length() - 1; i >= 0; i--) {
// get the char at index i
char c = param.charAt(i);
/*
* increment char since the next palindrome is the current digit + 1. Example:
* User input is 121, then param will be 12 so the next is 13
*/
c++;
/*
* check if the current character is greater than '9', which means it is not a
* digit after incrementing
*/
if (c > '9') {
// set the current char to 0
c = '0';
// check if index is at index 0
if (i - 1 < 0) {
// if at index 0 then add '1' at start
result = '1' + result;
} else {
// if not then append c at result
result = result + c;
}
} else {
// check if index is at index 0
if (i - 1 < 0) {
// if not then prepend c at result
result = c + result;
} else {
// if not then get the rest of param then append c and result
result = param.substring(0, i) + c + result;
}
break;
}
}
return result;
}
}

how to calculate total number of combinations for 4*3 matrix where 2 elements in matrix are not present

below is the format of the matrix. and no diagonal combinations of letters is allowed ,only vertical and horizontal combinations are allowed.
Can anyone suggest how to calculate the number of combinations required for a particular level.
example: if i say level is 1 then , only 1 letter combination is allowed i.e. A,B,C,D,E,F,G,H,I i.e. 10 combinations
if i say level is 2 then possible combinations are AA,BB,AB,AD,BC,BE,... and so on so total 36 combinations for level 2.
Like that if input is any level number given, then how do i calculate the possible number of combinations ?
A B C
D E F
G H I
J
I tried using this formula :
(n!/(r!(n-r)!)
but it doesnt calculate properly from level 2 onwards.
note : on both sides of J no letter is present.
Please suggest.

#Thientvse
This is the code that i coded... it gives correct output...can you please tell me whether my code is correct and whether it will satisfy all test cases for this scenario
import java.util.ArrayList;
import java.util.Scanner;
public class Game {
public static int combinationCounts(int input1){
ArrayList<String> mainalternatestring = new ArrayList<String>();
ArrayList<String> mainverticalstring = new ArrayList<String>();
String sb = "ABC#DEF#GHI# J ";
String a=null,b=null,c=null,nw=null;
int mainindex = 0,counter,totalcount=10,index=0,mainindex_duplicate=0,count=1;
if(input1 > 1 && input1 <= 4){
while(mainindex != 11){
int level = 0;
counter = 0;
count=1;
char[] strtoworkon = new char[sb.length()];
index=0;
if(mainindex != 0)
mainindex = mainindex+1;
for(int j = mainindex; count!= (sb.length()-mainindex) ; j++){
if(level == input1)
break;
if(sb.charAt(j) == '#'){
level++;
if (counter == 0){
mainindex_duplicate = j;
counter = 1;
}
}
if(level <= input1){
strtoworkon[index] = sb.charAt(j);
index++;
}
count++;
}
mainindex = mainindex_duplicate;
// for sideways combinations
for(int m = 0; m <= strtoworkon.length; m++){
c = null;
if(strtoworkon[m] == ' ')
break;
if(!String.valueOf(strtoworkon).substring(m, m+(input1)).contains("#")){
c = String.valueOf(strtoworkon).substring(m, m+(input1));
if(!c.matches(".*[A-Z].*"))
break;
if(!mainalternatestring.contains(c))
mainalternatestring.add(c);
}
}
//for vertical combinations
nw = "#" + (String.valueOf(strtoworkon));
int counter1=0;
while(counter1 != 3){
c="";
for(int n = 0; n<= strtoworkon.length; n++){
if(nw.charAt(n) == '#'){
Character test = nw.charAt(n+counter1);
a = Character.toString(strtoworkon[n+counter1]).trim();
if(a.contains("#"))
break;
c = a+c;
c.trim();
}
}
if(!mainverticalstring.contains(c) && c.length() == input1)
mainverticalstring.add(c);
counter1++;
}
if(mainindex == 11)
break;
}
totalcount = totalcount + (2*mainalternatestring.size()) + (2*mainverticalstring.size());
}
return totalcount;
}
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
int output = 0;
int ip1 = Integer.parseInt(in.nextLine().trim());
output = combinationCounts(ip1);
System.out.println(String.valueOf(output));
}
}

Find the longest sequence of same characters in a string

This code supposed to output the longest run on which a character in a string has a consecutive runs of itself. Though the problem is that it outputs: 8 (which should be 5 instead). I just would like to ask what seems to be the problem regarding this code.
public class Sample {
public static void main(String[] args) {
String setofletters = "aaakkcccccczz"; /* 15 */
int output = runLongestIndex(setofletters);
System.out.println("Longest run that first appeared in index:" + output);
}
public static int runLongestIndex(String setofletters) {
int ctr = 0;
int ctrstor = 0;
int ii = 0;
int output = 0;
// loops until the last character in the string
for (int i = 0; i < setofletters.length() - 1; i++) {
// checks if the letter is the same to the next
if (setofletters.charAt(i) == setofletters.charAt(i++)) {
ctr++;
ii = i++;
// loops until the letter in the index is no longer equal
while (setofletters.charAt(i) == setofletters.charAt(ii)) {
ii++;
ctr++;
}
if (ctr > ctrstor) {
output = i;
}
// storing purposes
ctrstor = ctr;
}
// resets the counter
ctr = 0;
}
return output;
}
}

UPDATE Sorry, I misunderstood your question a bit, you need to make the following changes in your code to make it work.(lines with comments)
public static int runLongestIndex(String setofletters){
int ctr = 1; // every character is repeated at least once, so you should initialize it to 1, not 0
int ctrstor = 0;
int ii = 0;
int output = 0;
for (int i = 0; i < setofletters.length() - 1; i++) {
if (i < setofletters.length() - 1 && setofletters.charAt(i) == setofletters.charAt(i+1)) { // i++ is not same as i+1
ctr++;
ii = i+1; // i++ is not same as i+1
while (setofletters.charAt(i) == setofletters.charAt(ii)) {
ii++;
ctr++;
}
if (ctr > ctrstor) {
output = i;
}
ctrstor = ctr;
}
ctr = 1; // for the same reason I mentioned above
}
return output;
}
EDIT : the easiest way to write your code is :
public static int runLongestIndex(String setofletters){
int ctr = 1;
int output = 0;
int j=0;
for(int i=0; i<setofletters.length()-1;i++){
j=i;
while(i <setofletters.length()-1 && setofletters.charAt(i)==setofletters.charAt(i+1)){
i++;
ctr++;
}
if(ctr>output){
output=j;
}
ctr = 1;
}
return output;
}
Why are you assigning i to output? You should assign ctr to output.
change
if(ctr>ctrstor){
output=i;
}
to
if(ctr>ctrstor){
output=ctr;
}
and also I think you should change
if(setofletters.charAt(i)==setofletters.charAt(i++))
to
if(i<setofletters.length()-1 && setofletters.charAt(i)==setofletters.charAt(i+1)){
and you should intialize ctr to 1 but not 0 because every character is repeated at least once.

I'll give you a Scala implementation for that problem.
Here it is the automatic test (in BDD style with ScalaTest)
import org.scalatest._
class RichStringSpec extends FlatSpec with MustMatchers {
"A rich string" should "find the longest run of consecutive characters" in {
import Example._
"abceedd".longestRun mustBe Set("ee", "dd")
"aeebceeedd".longestRun mustBe Set("eee")
"aaaaaaa".longestRun mustBe Set("aaaaaaa")
"abcdefgh".longestRun mustBe empty
}
}
Following is the imperative style implementation, with nested loops and mutable variables as you would normally choose to do in Java or C++:
object Example {
implicit class RichString(string: String) {
def longestRun: Set[String] = {
val chunks = mutable.Set.empty[String]
val ilen = string.length
var gmax = 0
for ((ch, curr) <- string.zipWithIndex) {
val chunk = mutable.ListBuffer(ch)
var next = curr + 1
while (next < ilen && string(next) == ch) {
chunk += string(next)
next = next + 1
}
gmax = chunk.length max gmax
if (gmax > 1) chunks += chunk.mkString
}
chunks.toSet.filter( _.length == gmax )
}
}
}
Following is a functional-style implementation, hence no variables, no loops but tail recursion with result accumulators and pattern matching to compare each character with the next one (Crazy! Isn't it?):
object Example {
implicit class RichString(string: String) {
def longestRun: Set[String] = {
def recurse(chars: String, chunk: mutable.ListBuffer[Char], chunks: mutable.Set[String]): Set[String] = {
chars.toList match {
case List(x, y, _*) if (x == y) =>
recurse(
chars.tail,
if (chunk.isEmpty) chunk ++= List(x, y) else chunk += y,
chunks
)
case Nil =>
// terminate recursion
chunks.toSet
case _ => // x != y
recurse(
chars.tail,
chunk = mutable.ListBuffer(),
chunks += chunk.mkString
)
}
}
val chunks = recurse(string, mutable.ListBuffer(), mutable.Set.empty[String])
val max = chunks.map(_.length).max
if (max > 0) chunks.filter( _.length == max ) else Set()
}
}
}
For example, for the given "aeebceeedd" string, both implementations above will build the following set of chunks (repeating characters)
Set("ee", "eee", "dd")
and they will filter those chunks having the maximum length (resulting "eee").

This code should work for any length of string sequence.
public class LongestStringSequqnce {
static String myString = "aaaabbbbcccchhhhiiiiibbbbbbbbbccccccc";
static int largestSequence = 0;
static char longestChar = '\0';
public static void main(String args[]) {
int currentSequence = 1;
char current = '\0';
char next = '\0';
for (int i = 0; i < myString.length() - 1; i++) {
current = myString.charAt(i);
next = myString.charAt(i + 1);
// If character's are in sequence , increase the counter
if (current == next) {
currentSequence += 1;
} else {
if (currentSequence > largestSequence) { // When sequence is
// completed, check if
// it is longest
largestSequence = currentSequence;
longestChar = current;
}
currentSequence = 1; // re-initialize counter
}
}
if (currentSequence > largestSequence) { // Check if last string
// sequence is longest
largestSequence = currentSequence;
longestChar = current;
}
System.out.println("Longest character sequence is of character "
+ longestChar + " and is " + largestSequence + " long");
}
}
Source : http://www.5balloons.info/program-java-code-to-find-longest-character-sequence-in-a-random-string/

if(ctr>ctrstor){
output=i;
}
//storing purposes
ctrstor=ctr;
This looks like the problem. So if you find 8 consecutive characters, it will set output to 8, and proceed. The next time thru, it finds 3 consecutive characters, so doesn't set output, but sets ctrstor. Next time thru it finds 4 consecutive characters, and this will set output to 4

There are few traps in the code that your logic felt in:
Code incorrectly assumes that there is always next character to compare current one.
This fails for string like "a" or the last character in any string.
Code does not store the max count of characters but only the max index (i).
MaxCount is needed to compare the next chars sequence size.
Loop for and loop while repeat the same subset of characters.
Also variable name style makes it harder to understand the code.
After correcting above
public static int runLongestIndex(String setofletters) {
int maxCount = 0;
int maxIndex = 0;
// loops each character in the string
for (int i = 0; i < setofletters.length() - 1; ) {
// new char sequence starts here
char currChar = setofletters.charAt(i);
int count = 1;
int index = i;
while ( (index < setofletters.length() - 1) &&
(currChar == setofletters.charAt(++index)) ) {
count++;
}
if (count > maxCount) {
maxIndex = i;
maxCount = count;
}
i = index;
}
return maxIndex;
}
See Java DEMO

I think you don't need an internal loop:
public static int runLongestIndex(String setofletters) {
if (setofletters == null || setofletters.isEmpty()) {
return -1;
}
int cnt = 1;
char prevC = setofletters.charAt(0);
int maxCnt = 1;
//char maxC = prevC;
int maxRunIdx = 0;
int curRunIdx = 0;
for (int i = 1; i < setofletters.length(); i++){
final char c = setofletters.charAt(i);
if (prevC == c) {
cnt++;
} else {
if (cnt > maxCnt) {
maxCnt = cnt;
//maxC = prevC;
maxRunIdx = curRunIdx;
}
cnt = 1;
curRunIdx = i;
}
prevC = c;
}
if (setofletters.charAt(setofletters.length() - 1) == prevC) {
if (cnt > maxCnt) {
//maxC = prevC;
maxCnt = cnt;
maxRunIdx = curRunIdx;
}
}
return maxRunIdx;
}
and this code:
System.out.println(runLongestIndex("aaakkcccccczz"));
gives you
5

This is how a "colleague" of mine is understanding to write readable code in order to solve this problem, even if this is working :)
public static int count (String str) {
int i = 0;
while(i < str.length()-1 && str.charAt(i)==str.charAt(i+1))
i ++;
return ++i;
}
public static int getLongestIndex(String str){
int output = 0;
for(int i=0, cnt = 1, counter = 0 ; i<str.length() - 1;i += cnt, cnt = count(str.substring(i)), output = (counter = (cnt > counter ? cnt : counter)) == cnt ? i : output);
return output;
}

int indexOfLongestRun(String str) {
char[] ar = str.toCharArray();
int longestRun = 0;
int lastLongestRun = 0;
int index = 0;
for(int i = ar.length-1; i>0; i--){
if(ar[i] == ar[i-1]){
longestRun++;
}else{
if(longestRun > lastLongestRun){
lastLongestRun = longestRun;
longestRun = 0;
index = i;
}
}
}
return index;

Well, the solution a bit depends on the additional requirements. Here is the code which returns the FIRST longest sequence of a repeated character int the given string, meaning if you have a second sequence with the same length you never get it out :(. But still, this is a simple and clear solution here, so good news - it works! :)
string = 'abbbccddddddddeehhhfffzzzzzzzzdddvyy'
longest_sequence = ''
for i in range(len(string)):
is_sequence = True
ch_sequence = ''
while is_sequence:
ch_sequence += string[i]
if i+1 < len(string) and string[i]==string[i+1]:
i += 1
else:
is_sequence = False
if len(ch_sequence) > len(longest_sequence):
longest_sequence = ch_sequence
print (longest_sequence)

#Paolo Angioletti already provided an answer using Scala, but it's more complicated than it needs to be. The idea is not very different from Run-length encoding. Time complexity O(n).
def longestConsecutive(s: String): (Char, Int) = {
Iterator.iterate(('\u0000', 0, 0)) { case (ch, longestRun, i) =>
val run = (i until s.length)
.takeWhile(s(_) == s(i))
.size
if (run > longestRun) (s(i), run, i + run)
else (ch, longestRun, i + run)
}
.dropWhile(i => s.isDefinedAt(i._3))
.take(1)
.map(x => (x._1, x._2))
.next()
}
Tested with:
("s", "ch", "n")
----------------
("", '\u0000', 0),
("a", 'a', 1),
("aabcddbbbea", 'b', 3),
("abcddbbb", 'b', 3),
("cbccca", 'c', 3)

#include <iostream>
#include<algorithm>
using namespace std;
int main() {
string s="abbcccccbbffffffffff";
//cin>>s;
int count=1;
int maxcount=1;
int start=0;
int ps=0;
for (int i=0;i<s.size()-1;i++)
{
if(s.at(i)==s.at(i+1))
{
count +=1;
maxcount=max(maxcount,count);
}
else
{
ps=max(ps,start+count);
count =1;
start=i;
}
}
for(int i=1;i<=maxcount;i++)
{
cout<<s.at(i+ps);
}
// your code goes here
return 0;
}

This is the simplest I can think of and it will print the number of the longest sequenced identical characters in a one line string.
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
String s = scanner.nextLine();
scanner.close();
int count = 0;
int curCount = 1;
for (int i = 0; i < s.length() -1; i++) {
if (s.charAt(i) == s.charAt(i + 1)) {
curCount++;
if (curCount > count) {
count = curCount;
}
}else {
if (curCount > count) {
count = curCount;
}
curCount = 1;
}
}
System.out.println(count);
}

Optimizing the largest palindrome from product of two three digit numbers?

I am working on an interview question which I was asked in which I was supposed to write a program to find the largest palindrome from product of two three digit numbers.
Here is the question
I came up with this brute force approach which starts from bottom.
public class LargestPalindromeQuestion {
public static void main(String[] args) {
int value = 0;
for (int i = 100; i <= 999; i++) {
for (int j = i; j <= 999; j++) {
int value1 = i * j;
if (isPalindrome(value1) && value < value1) {
value = value1;
}
}
}
System.out.println(value);
}
private static boolean isPalindrome(final int product) {
int p = product;
int reverse = 0;
while (p != 0) {
reverse *= 10;
reverse += p % 10;
p /= 10;
}
return reverse == product;
}
}
They asked me what are the optimizations I can do in this program? I mentioned that we can try pruning the search space and optimize checking step for each item in the search space but then I am confuse how would I make this work in my above solution?
What are the optimizations we can do in this program? Right now it is executing 810000 steps to find the largest palindrome.
What is the least number of steps we can execute to find the largest palindrome in two three digit numbers?

The program looks very good to me. I would make the i loop count from 999 down to 100, and I would only check j values that would actually give a larger product than the current maximum.
This program is able to finish surprisingly soon, at i == 952 to be precise. The mathematical reason for this is that once the solution 906609 (993 * 913) is found, it will no longer be possible to find a larger palindrome where the larger factor is less than the square-root of 906609, which is 952.160....
public static void main(String[] args) {
int value = 0;
for (int i = 999; i >= 100; i--) {
int r = value / i;
if (r >= i) {
System.out.println("We broke at i = " + i);
break;
}
for (int j = i; j > r; j--) {
int value1 = i * j;
if (isPalindrome(value1)) {
value = value1;
break;
}
}
}
System.out.println(value);
}

One pretty simple way of optimizing this would be to simply start with the highest 3-digit numbers instead of the smallest. Since the solution will most likely be closer to the pair (999 , 999) than to (100 , 100).

One useful mechanism to prune the search tree is to notice that the highest digit of the product a * b doesn't change often. E.g.
a = 111; b = 112 a*b = 12432
; b = 113 a*b = 12543
; b = 114 a*b = 12654
; ...
; b = 180 a*b = 19980
; b = 181 a*b = 20091 = (19980 + a)
Thus, for all the values in between (a = 111, a < b < 181), one already knows the MSB, which must equal to the LSB or (a % 10) * (b % 10) % 10 == MSB.
e.g.
LSB = 1 --> a % 10 == 1, b % 10 == 1
OR a % 10 == 3, b % 10 == 7
OR a % 10 == 7, b % 10 == 3
OR a % 10 == 9, b % 10 == 9
Most of the time there's either none, or just one candidate in set 'b' to be checked for any pair MSB, a % 10.

The least number of steps I could get to is 375. Consider multiplying the three-digit number, a1a2a3, by the three-digit number, b1b2b3:
JavaScript code:
var modHash = new Array(10);
var iterations = 0;
for (var i=1; i<10; i++){
modHash[i] = {0: [0]}
for (var j=1; j<10; j++){
iterations ++;
var r = i * j % 10;
if (modHash[i][r])
modHash[i][r].push(j);
else
modHash[i][r] = [j];
}
}
var highest = 0;
function multiples(x,y,carry,mod){
for (var i in modHash[x]){
var m = (10 + mod - i - carry) % 10;
if (modHash[y][m]){
for (var j in modHash[x][i]){
for (var k in modHash[y][m]){
iterations ++;
var palindrome = num(9,modHash[y][m][k],x,9,modHash[x][i][k],y);
if (x == 3 && mod == 0){
console.log(x + " * " + modHash[x][i][j] + " + "
+ y + " * " + modHash[y][m][k] + ": " + palindrome);
}
var str = String(palindrome);
if (str == str.split("").reverse().join("") && palindrome > highest){
highest = palindrome;
}
}
}
}
}
}
function num(a1,a2,a3,b1,b2,b3){
return (100*a1 + 10*a2 + a3)
* (100*b1 + 10*b2 + b3);
}
var a3b3s = [[7,7,4],[9,1,0],[3,3,0]];
for (var i in a3b3s){
for (var mod=0; mod<10; mod++){
var x = a3b3s[i][0],
y = a3b3s[i][1],
carry = a3b3s[i][2];
multiples(x,y,carry,mod);
}
}
console.log(highest);
console.log("iterations: " + iterations);
Output:
3 * 0 + 3 * 0: 815409
3 * 7 + 3 * 3: 907809
3 * 4 + 3 * 6: 908109
3 * 1 + 3 * 9: 906609
3 * 8 + 3 * 2: 907309
3 * 5 + 3 * 5: 908209
3 * 2 + 3 * 8: 907309
3 * 9 + 3 * 1: 906609
3 * 6 + 3 * 4: 908109
3 * 3 + 3 * 7: 907809
906609
iterations: 375

First optimize isPalindrome by seperating 6 digits as 3 digits. i.e. N = ABCDEF => a = ABC = N/1000, b = DEF = N%1000; Then reverse b and return a==reversed_b;
Secondly while producing palindromes loop through till max_palindrome_so_far/999 which is the minimum value that you would use. max_palindrome_so_far is initially equals N.
public class Solution {
public static boolean isPalindrome(int n){
int a = n/1000;
int b = n%1000;
int d, r = 0, i = 3;
while(i-- > 0){
d = b%10;
r = r*10 + d;
b = b/10;
}
if (a == r)
return true;
return false;
}
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
int t = in.nextInt();
for(int a0 = 0; a0 < t; a0++){
int n = in.nextInt();
int r=0, m=n;
int i,j;
for(i = 999;i>=100;i--){
for(j = 999;j>=m/999;j--){
if (i*j < n && i*j > 100000 && isPalindrome(i*j)){
r = Math.max(i*j, r);
m = r;
}
}
}
// System.out.println(i + " * " + j + " = " + i*j);
System.out.println(r);
}
}
}

Homework: how to write own multiplication of big numbers?

In my project I have to deal with multiplication of big numbers ( greater then java.long ) stared in my own BigNumber class as int[]. Basically I need to implement something like this :
157 x
121 y
----
157 result1
314 + result2
157 + result3
------
18997 finalResult
But how do I implement it?
I thought about expanding result2,3 with zeros (3140, 15700) and adding them. But first I somehow need to navigate between each digit of y and multiply it by each digit of x.

Use the diagonal approach. Make an array, and multiply each digit by each other digit and fill in the numbers in each cell.
36 x 92
3 6
+-----+-----+
| 2 / | 5 / |
9 | / | / |
| / 7 | / 4 |
+-----+-----+
| 0 / | 1 / |
2 | / | / |
| / 6 | / 2 |
+-----+-----+
Add the numbers on each diagonal. Move from the least-significant digit (at the lower right) to the most (upper left).
2 2 (least-significant)
(6 + 1 + 4) = 11 (make this 1, and carry the 1 to the next digit) 1
(5 + 7 + 0 + 1(carried)) = 13 (make this 3, and carry the 1) 3
2 + 1(carried) = 3 3 (most-significant)
The answer's 3312.
Make a two-dimensional array of your digits. Fill the array with the multiplications of the single digits together.
Write some logic to scrape the diagonals as I did above.
This should work for arbitrarily large numbers (as long as you still have memory left).

Here's the code I had written. Basically same as manual multiplication. Pass the two big numbers as strings to this function, the result is returned as a string.
public String multiply(String num1, String num2){
int product, carry=0, sum=0;
String result = new String("");
String partial = new String("");
ArrayList<String> partialList = new ArrayList<String>();
/* computing partial products using this loop. */
for(int j=num2.length()-1 ; j>=0 ; j--) {
for(int i=num1.length()-1 ; i>=0 ; i--) {
product = Integer.parseInt((new Character(num1.charAt(i))).toString()) *
Integer.parseInt((new Character(num2.charAt(j))).toString()) + carry;
carry = product/10;
partial = Integer.toString(product%10) + partial;
}
if(carry != 0)
partial = Integer.toString(carry) + partial;
partialList.add(partial);
partial = "";
carry = 0;
}
/* appending zeroes incrementally */
for(int i=0 ; i<partialList.size() ; i++)
partialList.set(i, partialList.get(i) + (Long.toString( (long)java.lang.Math.pow(10.0,(double)i))).substring(1) );
/* getting the size of the largest partial product(last) */
int largestPartial = partialList.get(partialList.size()-1).length();
/* prefixing zeroes */
int zeroes;
for(int i=0 ; i<partialList.size() ; i++) {
zeroes = largestPartial - partialList.get(i).length();
if(zeroes >= 1)
partialList.set(i, (Long.toString( (long)java.lang.Math.pow(10.0,(double)zeroes))).substring(1) + partialList.get(i) );
}
/* to compute the result */
carry = 0;
for(int i=largestPartial-1 ; i>=0 ; i--) {
sum = 0;
for(int j=0 ; j<partialList.size() ; j++)
sum = sum + Integer.parseInt(new Character(partialList.get(j).charAt(i)).toString());
sum = sum + carry;
carry = sum/10;
result = Integer.toString(sum%10) + result;
}
if(carry != 0)
result = Integer.toString(carry) + result;
return result;
}

I would avoid the headaches of writing your own and just use the java.math.BigInteger class. It should have everything you need.

Separating out the carrying and the digit multiplication:
def carries(digitlist):
digitlist.reverse()
for idx,digit in enumerate(digitlist):
if digit>9:
newdigit = digit%10
carry = (digit-newdigit)/10
digitlist[idx] = newdigit
if idx+1 > len(digitlist)-1:
digitlist.append(carry)
else:
digitlist[idx+1] += carry
digitlist.reverse()
return True
def multiply(first,second):
digits = [0 for place in range(len(first)+len(second))]
for fid,fdig in enumerate(reversed(first)):
for sid,sdig in enumerate(reversed(second)):
offset = fid+sid
mult = fdig*sdig
digits[offset] += mult
digits.reverse()
carries(digits)
return digits
def prettify(digitlist):
return ''.join(list(`i` for i in digitlist))
Then we can call it:
a = [1,2,3,4,7,6,2]
b = [9,8,7,9]
mult = multiply(a,b)
print prettify(a)+"*"+prettify(b)
print "calc:",prettify(mult)
print "real:",int(prettify(a))*int(prettify(b))
Yields:
1234762*9879
calc: 12198213798
real: 12198213798
Of course the 10s in the carries function and the implicit decimal representation in prettify are the only thing requiring this to be base 10. Adding an argument could make this base n, so you could switch to base 1000 in order to reduce the numbers of blocks and speed up the calculation.

I have implemented this in C++. refer to this for logic...
#include <iostream>
#include <deque>
using namespace std;
void print_num(deque<int> &num) {
for(int i=0;i < num.size();i++) {
cout<<num[i];
}
cout<<endl;
}
deque<int> sum(deque<int> &oppA, deque<int> &oppB) {
if (oppA.size() == 0) return oppB;
if (oppB.size() == 0) return oppA;
deque<int> result;
unsigned int carry = 0;
deque<int>::reverse_iterator r_oppA = oppA.rbegin();
deque<int>::reverse_iterator r_oppB = oppB.rbegin();
while ((r_oppA != oppA.rend()) && (r_oppB != oppB.rend())) {
int tmp = *r_oppA + *r_oppB + carry;
result.push_front(tmp % 10);
carry = tmp / 10;
r_oppB++;
r_oppA++;
}
while (r_oppA != oppA.rend()) {
int tmp = *r_oppA + carry;
result.push_front(tmp % 10);
carry = tmp / 10;
r_oppA++;
}
while (r_oppB != oppB.rend()) {
int tmp = *r_oppB + carry;
result.push_front(tmp % 10);
carry = tmp / 10;
r_oppB++;
}
return result;
}
deque<int> multiply(deque<int>& multiplicand, deque<int>& multiplier) {
unsigned int carry = 0;
deque<int> result;
int deci_cnt = 0;
deque<int>::reverse_iterator r_multiplier = multiplier.rbegin();
deque<int> tmp_result;
while (r_multiplier != multiplier.rend()) {
for (int i=0; i<deci_cnt ;i++) {
tmp_result.push_front(0);
}
deque<int>::reverse_iterator r_multiplicand = multiplicand.rbegin();
while (r_multiplicand != multiplicand.rend()) {
int tmp = (*r_multiplicand) * (*r_multiplier) + carry;
tmp_result.push_front(tmp % 10);
carry = tmp / 10;
r_multiplicand++;
}
if (carry != 0) {
tmp_result.push_front(carry);
carry = 0;
}
result = sum(result, tmp_result);
deci_cnt++;
tmp_result.clear();
r_multiplier++;
}
return result;
}
deque<int> int_to_deque(unsigned long num) {
deque<int> result;
if (num == 0) {
result.push_front(0);
}
while (num > 0) {
result.push_front(num % 10);
num = num / 10;
}
return result;
}
int main() {
deque<int> num1 = int_to_deque(18446744073709551615ULL);
deque<int> num2 = int_to_deque(18446744073709551615ULL);
deque<int> result = multiply(num1, num2);
print_num(result);
return 0;
}
Output: 340282366920928463426481119284349108225

You're going to have to treat each int in the array as a single "digit". Instead of using base 10 where each digit goes from 0 to 9, you'll have to use base 2^32 = 4294967296, where every digit goes from 0 to 4294967295.
I would first implement addition, as your algorithm for multiplication might use addition as an auxiliary.

As this is for homework I'll give a few hints.
You could approach it the same way you show your example, using strings to hold numbers of any length and implementing:
add one number to another
multiply as your example by appending zeroes and calling the addition method per step (so for multiply with 20, append the "0" and addd that number twice
The addition method you can build by retrieving the char[] from the strings, allocate a result char[] that is 1 longer than the longest and add like you would do on paper from the end back to the start of both arrays.
The end result will not be the best performing solution, but it it easy to show it is correct and will handle any length numbers (as long they will fit a Java string.)
Update
Ok, if you solved adding two numbers, you could:
implement multiplication by 10
implement multiplication by repeated addition like in your example
or:
implement multiplication by 2 (left shift)
implement a binary multiplication via the same concept, only this time x 2 and add once
to illustrate the latter,
13
5 x
----
13 x 1
26 x 0
52 x 1
---- +
65
note that the 1 0 1 are the bits in the number (5) you multiply with and 26 = 13 x 2, 52 = 26 x 2. Your get the idea :-)

did it my own way :
int bigger = t1.length;
int smaller = t2.length;
int resultLength = bigger + smaller;
int []resultTemp = new int[resultLength];
int []result = new int[bigger + smaller];
int []temporary = new int[resultLength+1];
int z = resultLength-1;
int zet = z;
int step = 0;
int carry = 0;
int modulo = 0;
for(int i=smaller-1; i>=0; i--){
for(int k = bigger-1; k>= -1; k--){
if(k == -1 && carry != 0 ){
resultTemp[z] = carry;
carry = 0;
break;
}
else if(k == -1 && carry == 0){
resultTemp[z] = 0;
break;
}
resultTemp[z] = carry + t1[k]*t2[i];
carry = 0;
if( resultTemp[z] > 9 ){
modulo = resultTemp[z] % 10;
carry = resultTemp[z]/10;
resultTemp[z] = modulo;
}
else{
resultTemp[z] = resultTemp[z];
}
z--;
}
temporary = add(resultTemp, result);
result = copyArray(temporary);
resultTemp = clear(resultTemp);
z = zet;
step++;
z = z - step;
}
then I check the sign.

Since this is homework... Are you sure using an int array is your best shot?
I tried to implement something similar a year ago for performance in a research
project, and we ended up going with concatenated primitives..
Using this you can take advantage of what's already there, and "only" have to worry about overflows near the ends.. This might prove to be fairly simple when you implement your multiplication with <<'s (bit shift lefts) and additions..
Now if you want a real challenge try to implement a modulo... ;)

You can check the below solution which teaches us both multiplication and addition of bigger numbers. Please comment if it can be improved.
public static void main(String args[]) {
String s1 = "123666666666666666666666666666666666666666666666669999999999999999999999999666666666666666666666666666666666666666666666666666666666666666666";
String s2 = "45688888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888";
System.out.println(multiply(s1, s2));
}
private static String multiply(String s1, String s2) {
int[] firstArray = convert(s1);
int[] secondArray = convert(s2);
//System.out.println(Arrays.toString(firstArray));
//System.out.println(Arrays.toString(secondArray));
// pass the arrays and get the array which is holding the individual
// rows while we multiply using pen and paper
String[] result = doMultiply(firstArray, secondArray);
//System.out.println(Arrays.toString(result));
// Now we are almost done lets format them as we like
result = format(result);
//System.out.println(Arrays.toString(result));
//Add elements now and we are done
String sum="0";
for(String s:result){
sum=add(sum,s);
}
return sum;
}
private static String[] doMultiply(int[] firstArray, int[] secondArray) {
String[] temp = new String[secondArray.length];
for (int i = secondArray.length - 1; i >= 0; i--) {
int result = 0;
int carry = 0;
int rem = 0;
temp[secondArray.length - 1 - i] = "";
for (int j = firstArray.length - 1; j >= 0; j--) {
result = (secondArray[i] * firstArray[j]) + carry;
carry = result / 10;
rem = result % 10;
temp[secondArray.length - 1 - i] = rem
+ temp[secondArray.length - 1 - i];
}
// if the last carry remains in the last digit
if (carry > 0)
temp[secondArray.length - 1 - i] = carry
+ temp[secondArray.length - 1 - i];
}
return temp;
}
public static int[] convert(String str) {
int[] arr = new int[str.length()];
for (int i = 0; i < str.length(); i++) {
arr[i] = Character.digit(str.charAt(i), 10);
}
return arr;
}
private static String[] format(String[] result) {
for (int i = 0; i < result.length; i++) {
int j = 0;
while (j < i) {
result[i] += "0";
j++;
}
}
return result;
}
public static String add(String num1, String num2) {
//System.out.println("First Number :" + num1);
//System.out.println("Second Number :" + num2);
int max = num1.length() > num2.length() ? num1.length() : num2.length();
int[] numArr1 = new int[max];
int[] numArr2 = new int[max];
for (int i = 0; i < num1.length(); i++) {
numArr1[i] = Integer.parseInt(""
+ num1.charAt(num1.length() - 1 - i));
}
for (int i = 0; i < num2.length(); i++) {
numArr2[i] = Integer.parseInt(""
+ num2.charAt(num2.length() - 1 - i));
}
int carry = 0;
int[] sumArr = new int[max + 1];
for (int k = 0; k < max; k++) {
int tempsum = numArr1[k] + numArr2[k] + carry;
sumArr[k] = tempsum % 10;
carry = 0;
if (tempsum >= 10) {
carry = 1;
}
}
sumArr[max] = carry;
/* System.out.println("Sum :"
+ new StringBuffer(Arrays.toString(sumArr)).reverse()
.toString().replaceAll(",", "").replace("[", "")
.replace("]", "").replace(" ", ""));*/
return new StringBuffer(Arrays.toString(sumArr)).reverse().toString()
.replaceAll(",", "").replace("[", "").replace("]", "")
.replace(" ", "");
}

I think this will help you
import java.util.ArrayList;
import java.util.List;
public class Multiply {
static int len;
public static void main(String[] args) {
System.out.println(multiply("123456789012345678901","123456789012345678901");
}
private static ArrayList<Integer> addTheList(List<ArrayList<Integer>> myList) {
ArrayList<Integer> result=new ArrayList<>();
for(int i=0;i<len;i++)
{
result.add(0);
}
int index=0;
for(int i=0;i<myList.size();i++)
{
ArrayList<Integer> a=new ArrayList<>(myList.get(index));
ArrayList<Integer> b=new ArrayList<>(myList.get(index+1));
for (int j = 0; j < a.size()||j < b.size(); i++) {
result.add(a.get(i) + b.get(i));
}
}
return result;
}
private static ArrayList<Integer> multiply(ArrayList<Integer> list1, Integer integer) {
ArrayList<Integer> result=new ArrayList<>();
int prvs=0;
for(int i=0;i<list1.size();i++)
{
int sum=(list1.get(i)*integer)+prvs;
System.out.println(sum);
int r=sum/10;
int m=sum%10;
if(!(r>0))
{
result.add(sum);
}
else
{
result.add(m);
prvs=r;
}
if(!(i==(list1.size()-1)))
{
prvs=0;
}
}
if(!(prvs==0))
{
result.add(prvs);
}
return result;
}
private static ArrayList<Integer> changeToNumber(String str1) {
ArrayList<Integer> list1=new ArrayList<>();
for(int i=0;i<str1.length();i++)
{
list1.add(Character.getNumericValue(str1.charAt(i)));
}
return list1;
}
public static String multiply(String num1, String num2) {
String n1 = new StringBuilder(num1).reverse().toString();
String n2 = new StringBuilder(num2).reverse().toString();
int[] d = new int[num1.length()+num2.length()];
//multiply each digit and sum at the corresponding positions
for(int i=0; i<n1.length(); i++){
for(int j=0; j<n2.length(); j++){
d[i+j] += (n1.charAt(i)-'0') * (n2.charAt(j)-'0');
}
}
StringBuilder sb = new StringBuilder();
//calculate each digit
for(int i=0; i<d.length; i++){
int mod = d[i]%10;
int carry = d[i]/10;
if(i+1<d.length){
d[i+1] += carry;
}
sb.insert(0, mod);
}
//remove front 0's
while(sb.charAt(0) == '0' && sb.length()> 1){
sb.deleteCharAt(0);
}
return sb.toString();
}
}