1. String Patterns

Given the length of a word (wordLen) and the maximum number of consecutive vowels that can be used (maxVowels), determine how many unique words can be generated.

Words will consist of English alphabetic letters a through z only.
Vowels are {a, e, i, o, u}; consonants are the remaining 21 letters.
In the explanations, v and c represent vowels and consonants.

wordLen = 1

maxVowels = 1

Patterns: {v, c}
That means there are 26 possibilities, one for each letter in the alphabet.

V or C
5    21

wordLen = 4

maxVowels = 1

Patterns: {cccc, vccc, cvcc, ccvc, cccv, vcvc, cvcv, cvvc, vccv}
There are 412,776 possibilities – see below:

C  C  C  C      → 21 * 21 * 21 * 21 = 194481
V  C  C  C      → 5 * 21 * 21 * 21 = 46305
C  V  C  C      → 21 * 5 * 21 * 21 = 46305
C  C  V  C      → 21 * 21 * 5 * 21 = 46305
C  C  C  V      → 21 * 21 * 21 * 5 = 46305
                → 4 * 46305 = 185220
V  C  V  C      → (5 * 21 * 5 * 21) = 11025
C  V  C  V      → (21 * 5 * 21 * 5) = 11025
C  V  V  C      → (21 * 5 * 5 * 21) = 11025
V  C  C  V      → (5 * 21 * 21 * 5) = 11025
                → 4 * 11025 = 33075
Total: 194481 + 185220 + 33075 = 412776

wordLen = 4

maxVowels = 2

In this case, all of the combinations from the previous example are still valid.

• There are 5 additional patterns to consider, three with 2 vowels (vvcc, cvvc, ccvv) and two with 3 vowels (vvvc and vccv)
• Their counts are:

3 * (5 * 5 * 21 * 21) = 3 * 11025 = 33075
2 * (5 * 5 * 5 * 21) = 2 * 2625 = 5250

• The total number of combinations then is:

412776 + 33075 + 5250 = 451101

The result may be a very large number, so return the answer modulo (10^9 + 7).

Note

While the answers will be within the limit of a 32-bit integer, interim values may exceed that limit. Within the function, you may need to use a 64-bit integer type to store them.

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2. Work Schedule

An employee has to work exactly as many hours as they are told to each week, scheduling no more than a given daily maximum number of hours. On some days, the number of hours worked will be given. The employee gets to choose the remainder of their schedule, within the given limits.

A completed schedule consists of exactly 7 digits in the range 0 to 8 that represent a day's work hours. A pattern string similar to the schedule is given, but some of its digits are replaced by a question mark, ? (ascii 63 decimal). Given a maximum number of hours that can be worked in a day, replace the question marks with digits so that the sum of scheduled hours is exactly the hours that must be worked in a week.

Determine all possible work schedules that meet the requirements and return them as a list of strings, sorted ascending.

Example

pattern = '08??840'
work_hours = 24
day_hours = 4

There are two days on which they must work
24 - 20 = 4 more hours for the week.
All of the possible schedules are listed below:

0804840  
0813840  
0822840  
0831840  
0840840  

Function Description

Complete the function findSchedules in the editor below.

findSchedules has the following parameter(s):

• int work_hours: the hours that must be worked in the week
• int day_hours: the maximum hours that may be worked in a day
• int pattern: the partially completed schedule

Returns

• string arr[]: represents all possible valid schedules (must be ordered ascending)

Constraints

• 1 <= work_hours <= 56
• 1 <= day_hours <= 8
• |pattern| = 7
• Each character of pattern ∈ {0, ..., 8}
• There is at least one correct schedule.

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Sample Input

STDIN         Function
-----         --------
3             → work_hours = 3
2             → day_hours = 2
??? ??0 0     → pattern = '?????00'

Sample Output

0020100  
0021000  
0120000  
1020000  

Explanation

work_hours = 3  
day_hours = 2  
pattern = '?????00'

They only need to schedule 1 more hour for the week, and it can be on any one of the days in question.

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