剑指 Offer 49. 丑数

剑指 Offer 49. 丑数

我们把只包含质因子 2、3 和 5 的数称作丑数（Ugly Number）。求按从小到大的顺序的第 n 个丑数。

思路

方法一：堆 + 哈希去重

方法二：动态规划

代码

堆 + 哈希去重

typedef long long ll;
class Solution {
public:
    int nthUglyNumber(int n) {
        ll factors[3] = {2, 3, 5};
        unordered_set<ll> seen;
        priority_queue<ll, vector<ll>, greater<ll>> q;
        q.push(1ll);
        seen.insert(1ll);
        ll cur;
        for (int i = 0; i < n; ++i) {
            cur = q.top();
            q.pop();
            for (int j = 0; j < 3; ++j) {
                ll temp = cur * factors[j];
                if (!seen.count(temp)) {
                    q.push(temp);
                    seen.insert(temp);
                }
            }
        }
        return cur;
    }
};

动态规划

class Solution {
public:
    int nthUglyNumber(int n) {
        int a = 0, b = 0, c = 0;
        int dp[n];
        dp[0] = 1;
        for(int i = 1; i < n; i++) {
            int n2 = dp[a] * 2, n3 = dp[b] * 3, n5 = dp[c] * 5;
            dp[i] = min(min(n2, n3), n5);
            if(dp[i] == n2) a++;
            if(dp[i] == n3) b++;
            if(dp[i] == n5) c++;
        }
        return dp[n - 1];
    }
};