Amazon Interview Question

Country: United States
Interview Type: Phone Interview

Comment hidden because of low score. Click to expand.
3
of 3 vote

I. At first find found all primes <= N (sieve of Eratosthenes). Getting the sum will be easy then.
Follow-up:
Cache the sums for any given N to save time. {N:SUM}
Optimization: Don't have to store sums for every N.
When N = 7, N = 8, N = 9, N = 10, the prime sum remains 17.
For N between 11 to 12, the prime sum is 28.
For N between 13 to 16, the sum is 41.
Use a BST structure as the cache. For N = 16, cache:
{2:3, 4:6, 6:11, 10:17, 12:28, 16:41}
For a given N, call cache.ceilingKey(N) to find the bucket for N.
N/log(n) * log(N)

Complexity
Time:
sieve of Eratosthenes takes O(NloglogN) time.
Insert an element into BST takes O(logN), there are N/logN primes in total to be added.
So building the cache takes logN * N / LogN = O(N) time
requesting primeSum(N) takes O(logN)

Space:
sieve of Eratosthenes takes O(N) extra space which will later be release after the cache is created.
Cache: O(N/logN)

public class PrimeSum {

TreeMap sums;

public PrimeSum(int n) { //input the upper limit for all Ns
sums = new TreeMap<>();
// init an array to track prime numbers
boolean[] primes = new boolean[n + 1];
for (int i = 2; i < n; i++)
primes[i] = true;
for (int i = 2; i <= Math.sqrt(n); i++) {
if (primes[i]) {
for (int j = i + i; j < n; j += i)
primes[j] = false;
}
}
// insert sums into cache
int sum = 0;
for(int i = 2; i <= n; i++) {
if(primes[i]) {
sums.put(i - 1, sum);
sum += i;
}
}
if(primes[n]) {
sums.put(n, sum);
}
}

public int primeSum(int N) {
Integer ceiling = sums.ceilingKey(N);
//if(ceiling == null) {
//Exception("input value overflows");
//}
return sums.get(ceiling);
}
}

Looking for interview experience sharing and mentors?
Visit A++ Coding Bootcamp at aonecode.com.

Taught by experienced engineers/interviewers from FB, Google and Uber,
our ONE TO ONE courses cover everything in an interview including
latest interview questions sorted by companies,
SYSTEM DESIGN Courses (highly recommended for people interviewing with FLAG)
ALGORITHMS (conquer DP, Graph, Greed and other advanced algo problems),
and mock interviews.

Our students got offers from Google, Uber, Facebook, Amazon and other top companies after a few weeks of training.

Welcome to email us with any questions. Thanks for reading.

Name:

Writing Code? Surround your code with {{{ and }}} to preserve whitespace.

Books

is a comprehensive book on getting a job at a top tech company, while focuses on dev interviews and does this for PMs.

Videos

CareerCup's interview videos give you a real-life look at technical interviews. In these unscripted videos, watch how other candidates handle tough questions and how the interviewer thinks about their performance.