Decode Ways

Problem

A message of digits was made from letters with A = 1, B = 2, ..., Z = 26. Read the digit string and print in how many ways it can be decoded back to letters. A part like 06 is not valid. Print 0 if there is no way.

Constraints

  • 1 <= length <= 45
  • digits only

Examples

Input

226

Output

3

Solutions

Best approachTime O(n)Space O(n)

This is like climbing stairs with rules: one digit step needs a non-zero digit, a two digit step needs a value from 10 to 26. For long digit strings the answer is a Fibonacci-like number. The inputs here stay within 2^53 so JavaScript is exact.

Same code works in Java810172125Basic features only, so nothing changes between versions.
/*
 * Problem : Process text.
 * Input   : One line of text.
 * Output  : The number of ways.
 * Approach: ways[i] from ways[i-1] and ways[i-2].
 * Time    : O(n)
 * Space   : O(n)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static long solve(String s) {
        // Step 1: ways[i] = the number of ways to decode the first i digits. An empty text has 1 way.
        int n = s.length();
        long[] ways = new long[n + 1];
        ways[0] = 1;

        for (int i = 1; i <= n; i++) {
            // Step 2: The last digit alone is a letter if it is not 0.
            if (s.charAt(i - 1) != '0') {
                ways[i] += ways[i - 1];
            }

            // Step 3: The last two digits together are a letter if they are from 10 to 26.
            if (i > 1) {
                int two = Integer.parseInt(s.substring(i - 2, i));
                if (two >= 10 && two <= 26) {
                    ways[i] += ways[i - 2];
                }
            }
        }
        return ways[n];
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String s = scanner.hasNextLine() ? scanner.nextLine() : "";
        System.out.println(solve(s));
    }
}
Hints (1)
  1. Which digit can never be decoded alone?