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:

1. The naive approach is to call isUgly for every number until you reach the n^th one. Most numbers are not ugly. Try to focus your effort on generating only the ugly ones.
2. An ugly number must be multiplied by either 2, 3, or 5 from a smaller ugly number.
3. 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.
4. Assume you have U_k, the k^th ugly number. Then U_k+1 must be Min(L₁ * 2, L₂ * 3, L₃ * 5).

int get_min(int a, int b, int c){
    int min = (a - b) > 0 ? b : a;
    return (min - c) > 0 ? c : min;
}
int nthUglyNumber(int n) {
    int *ugly = malloc(n * sizeof(int));
    int factor2 = 2, factor3 = 3, factor5 = 5;
    int index2 = 0, index3 = 0, index5 = 0;
    int minNum = 0;
    
    ugly[0] = 1;
    
    for(int i = 1; i < n; i++){
        minNum = get_min(factor2, factor3, factor5);
        ugly[i] = minNum;
        
        if(factor2 == minNum)
            factor2 = 2 * ugly[++index2];
        if(factor3 == minNum)
            factor3 = 3 * ugly[++index3];
        if(factor5 == minNum)
            factor5 = 5 * ugly[++index5];
    }
    
    return ugly[n - 1];
    
}

• 每一个ugly的值，都是前面某个值*2,3,5中的一个，而前面每一个值都肯定会被使用到3次