Prime Factorization using Sieve O ( log n ) for multiple queries | Javascript program to find prime factorization of a number n in O ( Log n ) time with precomputation allowed . ; stores smallest prime factor for every number ; Calculating SPF ( Smallest Prime Factor ) for every number till MAXN . Time Complexity : O ( nloglogn ) ; marking smallest prime factor for every number to be itself . ; separately marking spf for every even number as 2 ; checking if i is prime ; marking SPF for all numbers divisible by i ; marking spf [ j ] if it is not previously marked ; A O ( log n ) function returning primefactorization by dividing by smallest prime factor at every step ; precalculating Smallest Prime Factor ; calling getFactorization function
let MAXN = 100001 ; let spf = new Array ( MAXN ) ; function sieve ( ) { spf [ 1 ] = 1 ; for ( let i = 2 ; i < MAXN ; i ++ ) spf [ i ] = i ; for ( let i = 4 ; i < MAXN ; i += 2 ) spf [ i ] = 2 ; for ( let i = 3 ; i * i < MAXN ; i ++ ) { if ( spf [ i ] == i ) { for ( let j = i * i ; j < MAXN ; j += i ) if ( spf [ j ] == j ) spf [ j ] = i ; } } } function getFactorization ( x ) { let ret = [ ] ; while ( x != 1 ) { ret . push ( spf [ x ] ) ; x = Math . floor ( x / spf [ x ] ) ; } return ret ; } sieve ( ) ; let x = 12246 ; document . write ( " " + x + " " ) ; let p = getFactorization ( x ) ; for ( let i = 0 ; i < p . length ; i ++ ) document . write ( p [ i ] + " " ) ; document . write ( " " ) ;