264. 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, and n does not exceed 1690.
本题使用DP方法来做的,看了答案才了解,状态方程不是很好想,思路是做三个索引,分别表示2的倍数,3的倍数和5的倍数,然后再做三个factor值,分别记录*2,*3,*5;min为factor三个值的最小值,然后判断这个最小值是哪个factor的,将那个factor=对应的倍数*索引值的数组值,代码如下:
1 public class Solution { 2 public int nthUglyNumber(int n) { 3 int[] num = new int[n]; 4 int index2 = 0,index3 = 0,index5 = 0; 5 int factor2 = 2,factor3 = 3,factor5 = 5; 6 num[0] = 1; 7 for(int i=1;i<n;i++){ 8 int min = Math.min(Math.min(factor2,factor3),factor5); 9 num[i] =min; 10 if(min==factor2){ 11 factor2 = 2*num[++index2]; 12 } 13 if(min==factor3){ 14 factor3 = 3*num[++index3]; 15 } 16 if(min==factor5){ 17 factor5 = 5*num[++index5]; 18 } 19 } 20 return num[n-1]; 21 } 22 }