## Friday, November 11, 2016

### Nearest prime less than given number n - GeeksforGeeks

Nearest prime less than given number n - GeeksforGeeks
You are given a number n ( 3 <= n < 10^6 ) and you have to find nearest prime less than n?

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).
`// array to store all primes less than 10^6`
`vector<``int``> primes;`

`// Utility function of Sieve of Sundaram`
`void` `Sieve()`
`{`
`    ``int` `n = MAX;`

`    ``// In general Sieve of Sundaram, produces primes`
`    ``// smaller than (2*x + 2) for a number given`
`    ``// number x`
`    ``int` `nNew = ``sqrt``(n);`

`    ``// This array is used to separate numbers of the`
`    ``// form i+j+2ij from others where  1 <= i <= j`
`    ``int` `marked[n/2+500] = {0};`

`    ``// eliminate indexes which does not produce primes`
`    ``for` `(``int` `i=1; i<=(nNew-1)/2; i++)`
`        ``for` `(``int` `j=(i*(i+1))<<1; j<=n/2; j=j+2*i+1)`
`            ``marked[j] = 1;`

`    ``// Since 2 is a prime number`
`    ``primes.push_back(2);`

`    ``// Remaining primes are of the form 2*i + 1 such`
`    ``// that marked[i] is false.`
`    ``for` `(``int` `i=1; i<=n/2; i++)`
`        ``if` `(marked[i] == 0)`
`            ``primes.push_back(2*i + 1);`
`}`

`// modified binary search to find nearest prime less than N`
`int` `binarySearch(``int` `left,``int` `right,``int` `n)`
`{`
`    ``if` `(left<=right)`
`    ``{`
`        ``int` `mid = (left + right)/2;`

`        ``// base condition is, if we are reaching at left`
`        ``// corner or right corner of primes[] array then`
`        ``// return that corner element because before or`
`        ``// after that we don't have any prime number in`
`        ``// primes array`
`        ``if` `(mid == 0 || mid == primes.size()-1)`
`            ``return` `primes[mid];`

`        ``// now if n is itself a prime so it will be present`
`        ``// in primes array and here we have to find nearest`
`        ``// prime less than n so we will return primes[mid-1]`
`        ``if` `(primes[mid] == n)`
`            ``return` `primes[mid-1];`

`        ``// now if primes[mid]<n and primes[mid+1]>n that`
`        ``// mean we reached at nearest prime`
`        ``if` `(primes[mid] < n && primes[mid+1] > n)`
`            ``return` `primes[mid];`
`        ``if` `(n < primes[mid])`
`            ``return` `binarySearch(left, mid-1, n);`
`        ``else`
`            ``return` `binarySearch(mid+1, right, n);`
`    ``}`
`    ``return` `0;`
`}`
Read full article from Nearest prime less than given number n - GeeksforGeeks

#### 2 comments:

1. Hi,

Useful article. Understood the concept. Thanks for sharing.

Cheers,
http://www.flowerbrackets.com/binary-search-program-java/

2. Great explanation!! Your blog has best collection of java programs for interview. Thanks for sharing.

Cheers,
http://www.flowerbrackets.com/java-program-to-find-prime-number/

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