Distribute in Circle | InterviewBit | Solution Explained
I explain the solution to Distribute in Circle InterviewBit problem. Using visuals and intuitions for the mathematical solution. Problem Link.
0. Distribute in Circle: Problem Discussion
0.0. IO Format
- input:
- A: number of items
- B: size of circle
- C: starting point inside the circle
- output:
- position where the Ath item (last) will get delivered
- constraints:
- 1 <= A, B, C <= 108
0.1. Examples
In this case, we have
- a circle of B size – marked in blue.
- inside of the circle, we first move to the Cth position (zero indexed)
- then start distributing A items from that position
In this case, we start from index C = 4, then go in the clockwise direction in the circle B = 5 and distribute A = 7 items. The last item is distributed at the 0th index, which is thus the answer.
1. Distribute in Circle: Observations & Logic
1.0. Intuitions
One solid point to notice is that we are stuck inside a circle, so the Ath item only has an effect of A % B. What it means is, if we have A = 7 and B = 5, we basically will allocate A / B = 1 items to everyone, then the next A % B = 2 people will get one more item than the rest. NOTE: the minus 1 is done because we will be at A % B position when we have successfully distributed everything. That means that the last index that we actually distributed was actually A % B – 1.
formula = A % B – 1
Now where does C come into play? Think of it as an initial displacement – we could have started from 0th index, and returned the answer as A % B – 1. C just comes in, and displaces everything by C amount.
formula = (C + A % B – 1) % B
NOTE: we have again done % B since the value inside the brackets can actually go beyond B. Think why!
2. Distribute in Circle: Optimized Implementation
2.0. Code
int Solution::solve(int A, int B, int C) {
return (C + A % B - 1) % B;
}
2.1. Complexity Analysis
- Time:
O(1), since we only do O(1) operations - Space:
O(1), since we never use any variable ourselves.
Producing high-quality intuitive explanations of interview problems. Currently covering LeetCode and InterviewBit.
Recommended Posts
Gas Station | InterviewBit | Solution Explained
June 13, 2022
Majority Element | InterviewBit | Solution Explained
June 13, 2022
Comments
Leave a Reply
This site uses Akismet to reduce spam. Learn how your comment data is processed.
Please write the proof.
This solution need an amendment for 2 digit number.
Please write a Proof for this
Matt Michael D’Agati is the founder of Renewables Worldwide, an Solar Firm in MA.
A few age ago, taking a leap of faith, Matt D’Agati delved into the realm of solar, and/or in a short occasion commenced effectively marketing significant amounts of power, primarily around the business industry, collaborating with solar farm developers and local businesses in the “design” of their unique plans.
Ongoing marketing within the sector, offered Matthew to participate a regional startup two years in the, and in a short time, he assumed the role of their Chief Strategy Officer, in charge of all operation and endeavor improvement, in addition to being marketed social group property.
To planned unions and shear get the job done mentality, Matthew D’Agati brought that firm from an initial initial-year revenue to in excess of a 2 hundred% surge in overall money by yr two. Based on that foundation, RW, a experienced-operated company, was produced with goal of giving you alternative electrical remedies for a more intelligent and more sustainable future.
Even more mainly, recognizing there is an untapped market in the market place and an improved approach to realize final results, RW is one of a handful of manufactures in the u.s. to place emphasis on individual acquire, concentrating in both industrial and home solar-powered town off-take. Its visualization is to make a purchases commercial infrastructure on a community-based, statewide, countrywide level, offering various sustainable fuel goods within the of RW.
This enthusiasm in the actual sustainable industry goes on to stimulate and inspire Matthew in enduring his solicit to work with institutions that have the unchanging of offering limitless fuel tips for a a whole lot more ecological destiny. Matt has already a new in companies from Hesser College.
Understanding why solar energy consultants assist clients via Matthew D’Agati.
Sustainable Energy and Electricity Poverty: Bridging the Imbalance by matt d’agatiMatt D’Agati e3d74c8