You are given a number n ( 3 <= n < 10^6 ) and you have to find nearest prime less than n?
Input : n = 10 Output: 7 Input : n = 17 Output: 13 Input : n = 30 Output: 29
A simple solution for this problem is to iterate from n-1 to 2, and for every number, check if it is a prime. If prime, then return it and break the loop. This solution looks fine if there is only one query. But not efficient if there are multiple queries for different values of n.
An efficient solution for this problem is to generate all primes less tha 10^6 using Sieve of Sundaram and store then in a array in increasing order. Now apply modified binary search to search nearest prime less than n. Time complexity of this solution is O(n log n + log n) = O(n log n).
If you have another approach to solve this problem then please share in comments.
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