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
.
Example:
Input: n = 10
Output: 12
Explanation: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 is the sequence of the first 10 ugly numbers.
Note:
1
is typically treated as an ugly number.n
does not exceed 1690.
int nthUglyNumber(int n) { // time: O(n); space: O(n)
if (n <= 0) return 0;
if (n == 1) return 1;
vector<int> dp(n, 0);
dp[0] = 1;
int t2 = 0, t3 = 0, t5 = 0;
for (int i = 1; i < n; ++i) {
dp[i] = min({dp[t2] * 2, dp[t3] * 3, dp[t5] * 5});
if (dp[i] == dp[t2] * 2) ++t2;
if (dp[i] == dp[t3] * 3) ++t3;
if (dp[i] == dp[t5] * 5) ++t5;
}
return dp.back();
}
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