A numeric string, , is beautiful if it can be split into a sequence of two or more positive integers, , satisfying the following conditions:
- for any (i.e., each element in the sequence is more than the previous element).
- No contains a leading zero. For example, we can split into the sequence , but it is not beautiful because and have leading zeroes.
- The contents of the sequence cannot be rearranged. For example, we can split into the sequence , but it is not beautiful because it breaks our first constraint (i.e., ).
The diagram below depicts some beautiful strings:
You must perform queries where each query consists of some integer string . For each query, print whether or not the string is beautiful on a new line. If it's beautiful, print
YES x, where is the first number of the increasing sequence. If there are multiple such values of , choose the smallest. Otherwise, print
Complete the separateNumbers function in the editor below. It should print a string as described above.
separateNumbers has the following parameter:
- s: an integer value represented as a string
The first line contains an integer , the number of strings to evaluate.
Each of the next lines contains an integer string to query.
For each query, print its answer on a new line (i.e., either
YES x where is the smallest first number of the increasing sequence, or
Sample Input 0
7 1234 91011 99100 101103 010203 13 1
Sample Output 0
YES 1 YES 9 YES 99 NO NO NO NO
The first three numbers are beautiful (see the diagram above). The remaining numbers are not beautiful:
- For , all possible splits violate the first and/or second conditions.
- For , it starts with a zero so all possible splits violate the second condition.
- For , the only possible split is , which violates the first condition.
- For , there are no possible splits because only has one digit.
Sample Input 1
4 99910001001 7891011 9899100 999100010001
Sample Output 1
YES 999 YES 7 YES 98 NO
Solution in Python
def sequential(s,sub_string): if not s: return True if s.startswith(sub_string): l = len(sub_string) return sequential(s[l:],str(int(sub_string)+1)) return False def separateNumbers(s): for i in range(1,len(s)//2+1): sub_string = s[:i] if sequential(s,sub_string): return "YES "+sub_string return "NO" for _ in range(int(input())): s = input() print(separateNumbers(s))
First we create a recursive function, which I have named as sequential. It accepts two parameters string s and substring.
Basically what is does is check if our string starts with given substring,
Example, s = "101112"
If we take substring as "1".
First it checks if s starts with "1". If it starts with "1", we will increment our substring and "1" becomes "2".
Now using recursion we call the function itself to check if the remaining part of string that is "01112" starts with "2".
If it doesn't our function will return False.
If we take substring as "10".
First it checks if s starts with "10". If it starts with "10", we will increment our substring and "10" becomes "11".
Now using recursion we call the function itself to check if the remaining part of string that is "1112" starts with "11".
Since it starts with "11". We again increment our substring by 1 and it becomes "12"
Again using recursion we call the function itself to check if the remaining part of string that is "12" starts with "12".
Since it starts with "12". We again increment our substring by 1 and it becomes "13"
Again using recursion we call the function itself to check if the remaining part of string that is "" which is an empty string starts with "13".
Notice that now s = "" which is an empty string. Therefore it means we have successfully checked all part of our string and it forms a perfect sequence.
If you may have noticed, we have added the following function
if not s: return True
So when no more substring is left our function will return True
The seperate number function is a simple for loop which initially take the first character of our original string a substring. Then call our helper function sequential, If it returns false we will further take first two character as substring then 3 and so on, upto half of the string
Example if our string is "101112"
We will first take "1" as sub_string, then "10" , then "101".
If for any substring our sequential function returns True, we will break our loop and return "YES"
If none of our substrings returns True we will return "NO"