Given a number (as string) and two integers a and b, divide the string in two non-empty parts such that the first part is divisible by a and second part is divisible by b. If string can not be divided into two non-empty parts, output “NO”, else print “YES” with the two parts.
Input : str = "123", a = 12, b = 3 Output : YES 12, 3 "12" is divisible by a and "3" is divisible by b. Input : str = "1200", a = 4, b = 3 Output : YES 12, 00 Input : str = "125", a = 12, b = 3 Output : NO
A simple solution is to one by one partition array around all points. For every partition, check if left and right of it are divisible by a and b respectively. If yes, print the left and right parts and return.
An efficient solution is to do some preprocessing and save the division modulo by ‘a’ by scanning the string from left to right and division modulo by ‘b’ from right to left.
If we know the remainder of prefix from 0 to i, when divided by a, then we compute remainder of prefix from 0 to i+1 using below formula.
lr[i+1] = (lr[i]*10 + str[i] -‘0’)%a.
Same way, modulo by b can be found by scanning from right to left. We create another rl to store remainders with b from right to left.
Once we have precomputed two remainders, we can easily find the point that partition string in two parts.
YES 12, 3
Time Complexity : O(len) where len is length of input number string.
This article is contributed by Ekta Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.about the topic discussed above
- Split a number into 3 parts such that none of the parts is divisible by 3
- Split a string in equal parts such that all parts are palindromes
- Find the number of ways to divide number into four parts such that a = c and b = d
- Count number of ways to divide a number in 4 parts
- Break the number into three parts
- Divide a number into two parts
- Divide a big number into two parts that differ by k
- Count number of ways to partition a set into k subsets
- Bell Numbers (Number of ways to Partition a Set)
- Divide number into two parts divisible by given numbers
- Divide a number into two parts such that sum of digits is maximum
- Possible cuts of a number such that maximum parts are divisible by 3
- Number of ways to partition a string into two balanced subsequences
- Break a number such that sum of maximum divisors of all parts is minimum
- Split the number into N parts such that difference between the smallest and the largest part is minimum
Improved By : Mithun Kumar