LeetCode 264

Posted 2020-07-09 Juntaran

Ugly Number II

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

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

Note that 1 is typically treated as an ugly number.

Hint:

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

 

 1 /*************************************************************************
 2     > File Name: LeetCode264.c
 3     > Author: Juntaran
 4     > Mail: [email protected]
 5     > Created Time: Wed 18 May 2016 20:12:58 PM CST
 6  ************************************************************************/
 7 
 8 /*************************************************************************
 9     
10     Ugly Number II
11     
12     Write a program to find the n-th ugly number.
13 
14     Ugly numbers are positive numbers whose prime factors 
15     only include 2, 3, 5. For example, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 is 
16     the sequence of the first 10 ugly numbers.
17 
18     Note that 1 is typically treated as an ugly number.
19 
20     Hint:
21 
22     The naive approach is to call isUgly for every number until you 
23     reach the nth one. Most numbers are not ugly. 
24     Try to focus your effort on generating only the ugly ones.
25     An ugly number must be multiplied by either 2, 3, or 5 
26     from a smaller ugly number.
27     The key is how to maintain the order of the ugly numbers. 
28     Try a similar approach of merging from three sorted lists: L1, L2, and L3.
29     Assume you have Uk, the kth ugly number. 
30     Then Uk+1 must be Min(L1 * 2, L2 * 3, L3 * 5).
31 
32  ************************************************************************/
33 
34 int minofThree( int a, int b, int c )
35 {
36     int min = a>b ? b : a;
37     min = min>c ? c : min;
38     return min;
39 }
40 
41 int nthUglyNumber(int n)
42 {
43     if( n <= 0 )
44         return 0;
45     if(n == 1)
46         return 1;
47     int *uglyArr = (int*)malloc(sizeof(int)*n);
48     int i2=0, i3=0, i5=0;
49     int i;
50     uglyArr[0] = 1;
51     
52     for( i=1; i<n; i++ )
53     {
54         int t2 = uglyArr[i2]*2;
55         int t3 = uglyArr[i3]*3;
56         int t5 = uglyArr[i5]*5;
57         int min = minofThree( t2, t3, t5 );
58         uglyArr[i] = min;
59         if(min == t2)
60             i2++;
61         if(min == t3)
62             i3++;
63         if(min == t5)
64             i5++;
65     }
66     return uglyArr[n-1];
67 }
68 
69 int main()
70 {
71     int n = 7;
72     int ret = nthUglyNumber(n);
73     printf("%d\n", ret);
74 }