Question.java

package Q17_06_Count_of_2s;

public class Question {	
	public static int count2sInRangeAtDigit(int number, int d) {
		int powerOf10 = (int) Math.pow(10, d);
		int nextPowerOf10 = powerOf10 * 10;
		int right = number % powerOf10;
		
		int roundDown = number - number % nextPowerOf10;
		int roundUp = roundDown + nextPowerOf10;
		
		int digit = (number / powerOf10) % 10; 
		if (digit < 2) { // if the digit in spot digit is 
			return roundDown / 10;
		} else if (digit == 2) {
			return roundDown / 10 + right + 1;
		} else {
			return roundUp / 10;
		}
	}
	
	public static int count2sInRange(int number) {
		int count = 0;
		int len = String.valueOf(number).length();
		for (int digit = 0; digit < len; digit++) {
			count += count2sInRangeAtDigit(number, digit);
		}
		return count;
	}
	
	public static int count2sR(int n) {	
		/* Alternate, messier, solution */
		
		// Example: n = 513
		
		// Base case
		if (n == 0) {
			return 0;
		}
		
		// Split apart 513 into 5 * 100 + 13.
		// [Power = 100; First = 5; Remainder = 13]
		int power = 1;
		while (10 * power < n) {
			power *= 10;
		}
		int first = n / power;
		int remainder = n % power;
		
		// Counts 2s from first digit
		int nTwosFirst = 0;
		if (first > 2) {
			nTwosFirst += power; 
		} else if (first == 2) {
			nTwosFirst += remainder + 1;
		}
		
		// Count 2s from all other digits
		int nTwosOther = first * count2sR(power - 1) + count2sR(remainder);
		
		return nTwosFirst + nTwosOther;
	}
	
	public static void main(String[] args) {
		for (int i = 0; i < 10000; i++) {
			int v1 = count2sR(i);
			int v2 = count2sInRange(i);	
			System.out.println("Between 0 and " + i + ": " + v1 + " " + v2);
		}
	}

}