263. Ugly number && 264. Ugly number II && 313. Super Ugly Number

263. Ugly Numberwrite A program to check whether a given number was an Ugly number.

Ugly numbers is positive numbers whose prime factors only include 2, 3, 5 . For example, was ugly while was not 6, 8 14 ugly since it includes another prime factor 7 .

Note that's 1 typically treated as an ugly number.

Hide TagsMathHide Similar Problems(e) Happy number (e) Count Primes (M) Ugly number II

 Public classSolution { Public Booleanisugly (intnum) {        if(num = = 0)            return false; Num= Removefactor (num, 2); Num= Removefactor (num, 3); Num= Removefactor (num, 5); returnnum = = 1; }        Private intRemovefactor (intNumintfactor) {         while(num%factor==0) {num= num/factor; }        returnnum; }}

Ugly number II

Write a program to find the n -th ugly number.

Ugly numbers is positive numbers whose prime factors only include 2, 3, 5 . For example, is the sequence of the first 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 10 ugly numbers.

Note that's 1 typically treated as an ugly number.

Hint:

1. The naive approach is to call for isUgly every number until you reach the nth one. Most numbers is not ugly. Try to focus your effort in generating only the ugly ones.
2. An ugly number must is multiplied by either 2, 3, or 5 from a smaller ugly number.
3. The key is what to maintain the order of the ugly numbers. Try A similar approach of merging from three sorted lists:l1, L2, and L3.
4. Assume you have Uk, the kth ugly number. Then uk+1 must is Min (L1 * 2, L2 * 3, L3 * 5).

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Dynamic Programming Heap MathHide Similar Problems(H) Merge K Sorted Lists (E) Count Primes (E) Ugly number (m) Perfect squares (m) Super Ugly number

 Public classSolution { Public intNthuglynumber (intN) {if(n==1)return1; Priorityqueue<Long> q =NewPriorityqueue (); Q.add (1l);  for(LongI=1; i<n; i++) {            LongTMP =Q.poll ();  while(!q.isempty () && Q.peek () ==tmp) TMP =Q.poll (); Q.add (TMP* *); Q.add (TMP*); Q.add (TMPThe); }        returnQ.poll (). Intvalue (); }}

313. Super Ugly Number

Write a program to find the nth super ugly number.

Super ugly numbers is positive numbers whose all prime factors is in the given prime list of primes size k . For example, is the sequence of the first 4 [1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 32]  super ugly numbers given primes = of [2, 7, 13, 19] size.

Note:
(1) is 1 a super ugly number for any given primes .
(2) The given numbers in is in primes ascending order.
(3) 0 < k ≤100, 0 < n ≤106, 0 < primes[i] < 1000.

Hide TagsMath HeapHide Similar Problems(M) Ugly number IISlight modify the solution above would get a timelimitexceeded solutions

 Public classSolution { Public intNthsuperuglynumber (intNint[] primes)        {Arrays.sort (primes); if(n==1)             return1; Priorityqueue<Long> q =NewPriorityqueue (); Q.add (1l);  for(LongI=1; i<n; i++) {            LongTMP =Q.poll ();  while(!q.isempty () && q.peek () = =tmp) TMP=Q.poll ();  for(Integer p:primes) {q.add (TMP*p); }        }        returnQ.poll (). Intvalue (); }}

263. Ugly number && 264. Ugly number II && 313. Super Ugly Number