Title:

Decode Ways

Link to LeetCode:

https://leetcode.com/problems/decode-ways/

Specification:

A message containing letters from A-Z is being encoded to numbers using the following mapping:

'A' -> 1

'B' -> 2

...

'Z' -> 26

Given a non-empty string containing only digits, determine the total number of ways to decode it.

Examples:

Example 1:

Input: "12"

Output: 2

Explanation: It could be decoded as "AB" (1 2) or "L" (12).

Example 2:

Input: "226"

Output: 3

Explanation: It could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6).

Initial Code and Signature:

```
```public interface Decoder {
public int numDecodings(String s);
}

Algorithm:

Main Idea:In some cases F (n) = F (n + 1) + F (n + 2); if char [n] and char [n+1] >= 1 and <= 26.

In some cases F (n) = F (n + 1); if char [n] >= 3 or if char [n] and char [ n+1 ] >= 27.

In some cases F (n) = F (n + 2); if char [n] and char [n+1] = 10 or 20;

In one case F (n) = 0; if char [n] = 0;

- Consider an array of integer, called number of decodings, having the length of the given string.
- Start from the end of the given string, and scan the last character.
- If the number that the last char represents is between 1 and 9 then set the related cell in the number of decodings to 1.
- else if the number is zero then set the related cell to 0.
- Move to the previous char.
- If the number that the current char represents is greater or equal to three or if the current char is 2 and the next char is 7 or higher then number of decodings [i] = number of decodings [ i+1 ], since there is only one way to decode this char, and that way is to remove the current char alone.
- Else if the number the current char represents is 0, then number of decodings [i] = 0, since there is no valid decoding for this char.
- Else if the number that the current char and the next char represent is 10 or is 20, then number of decodings [i] = number of decodings [ i+2 ], since there is only one way to decode the current char and that way is to decode it together with the next char.
- Else if the number the current char and the next char represent is between 1 and 26, then number of decodings [i] = number of decodings [ i+1 ] + number of decodings [ i+2 ], since there are two ways to decode the current char.
- to decode the current char alone and go to the next char , or
- to decode the current char with the next char, and then go to the char after the next char.

- Go to 5- and continue until all of the string is scanned.
- Return number of decodings [0].

Run-Time Complexity Analysis

GitHub Project:

https://github.com/m-h-s/Algorithms-Codes/tree/master/25-DecodeWays

Code:

```
```
/**
*
* @author Mahsa Sadi
*
* @since 2020 - 06 - 17
*
* License: Creative Commons
*
* Copyright by Mahsa Sadi
*
*/
public class DecoderS3 implements Decoder {
/**
* Problem: Decode Ways
*
*
* Description:
*
* A message containing letters from A-Z is being encoded to numbers using the following mapping:
* 'A' -> 1
* 'B' -> 2
* ...
* 'Z' -> 26
*
* Given a non-empty string containing only digits, determine the total number of ways to decode it.
*
*
*
*
* Solution:
*
* Main Idea:
* In some cases F (n) = F (n + 1) + F (n + 2); if char [n] and char [n+1] >= 1 and <= 26.
* In some cases F (n) = F (n + 1); if char [n] >= 3 or if char [n] and char [ n+1 ] >= 27
* In some cases F (n) = F (n + 2); if char [n] and char [n+1] = 10 or 20;
* In one case F (n) = 0; if char [n] = 0;
*
* 1- Consider an array of integer, called number of decodings, having the length of the given string.
*
* 2- Start from the end of the given string, and scan the last character.
*
* 3- If the number that the last char represents is between 1 and 9 then set the related cell in the number of decodings to 1.
*
* 4- else if the number is zero then set the related cell to 0.
*
* 5- Move to the previous char.
*
* 6- If the number that the current char represents is greater or equal to three or if the current char is 2 and the next char is 7 or higher then
* number of decodings [i] = number of decodings [ i+1 ], since there is only one way to decode this char, and that way is to remove the current char alone.
*
* 7- Else if the number the current char represents is 0, then
* number of decodings [i] = 0, since there is no valid decoding for this char.
*
*
* 8- Else if the number that the current char and the next char represent is 10 or is 20, then
* number of decodings [i] = number of decodings [ i+2 ], since there is only one way to decode the current char and that way is to decode it together with the next char.
*
* 9- Else if the number the current char and the next char represent is between 1 and 26, then
* number of decodings [i] = number of decodings [ i+1 ] + number of decodings [ i+2 ], since there are two ways to decode the current char
* 1- to decode the current char alone and go to the next char , or
* 2- to decode the current char with the next char, and then go to the char after the next char.
*
* 10- Go to 5- and continue until all of the string is scanned.
*
* 11- Return number of decodings [0];
*
*/
@Override
public int numDecodings(String s) {
int [] numberOfDecodings = new int [s.length()];
int currentNum, nextNum;
currentNum = Integer.parseInt(s.charAt(s.length() - 1 )+"");
if ( currentNum != 0 )
numberOfDecodings [s.length() - 1 ] = 1;
else
numberOfDecodings [s.length() - 1 ] = 0;
for (int i = s.length() - 2; i >= 0; i--)
{
nextNum = currentNum;
currentNum = Integer.parseInt(s.charAt(i) +"");
if (currentNum == 0)
numberOfDecodings [i] = 0;
else
{
if ( currentNum >= 3 ||
(currentNum == 2 && nextNum >= 7 )
)
numberOfDecodings [i] = numberOfDecodings [i + 1];
else if (
i + 2 <= s.length() - 1 &&
( ( currentNum == 1 || currentNum == 2 ) && nextNum == 0)
)
numberOfDecodings [i] = numberOfDecodings [i + 2];
else
{
if ( i + 2 <= s.length() - 1)
numberOfDecodings [i] = numberOfDecodings [i + 1] + numberOfDecodings [i + 2];
else
{
if ( ( currentNum == 1 || currentNum == 2 ) && nextNum == 0)
numberOfDecodings [i] = 1;
else
numberOfDecodings [i] = 2;
}
}
}
}
return numberOfDecodings [0];
}
}