# Convert number to base three

## Problem :

Represent a given numbers in following format   : (with base 3 )

1 = “1”
2 = “2”
3 = “00”
4 = “01”
5 = “02”
6 = “10”
7 = “11”
8 = “12”
09 = “20”
10 = “21”
11 = “22”
12 = “000”
13 = “001”
14 = “002”
15 = “010”
Problem is not that simple as it looks . Its like a trinary number instead of a binary number.

## Solution in java :

/**
* Subtract powers of 3 incrementally till number cannot be further subtracted from.
* Left-pad remaining number with count of numbers subtracted.
*/
private String convert(int num) {
int strLen = 0;
for (int i = 1; i < 1000; i++) {
double pow = Math.pow(3, i);
if (num – pow >= 0) {
num -= pow;
strLen += 1;
} else {
break;
}
}
return createStringRepresentation(num, strLen);
}
private String createStringRepresentation(int num, int strLen) {
String numStr = Integer.toString(num, 3);
return lpad(numStr, strLen + 1);
}
private static String lpad(String text, int size) {
StringBuilder builder = new StringBuilder();
while (builder.length() < size – text.length()) {
builder.append(‘0’);
}
return builder.toString() + text;
}

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