Given an array nums of integers, return how many of them contain an even number of digits.
Example 1:
Input: nums = [12,345,2,6,7896]
Output: 2
Explanation:
12 contains 2 digits (even number of digits).
345 contains 3 digits (odd number of digits).
2 contains 1 digit (odd number of digits).
6 contains 1 digit (odd number of digits).
7896 contains 4 digits (even number of digits).
Therefore only 12 and 7896 contain an even number of digits.
Example 2:
Input: nums = [555,901,482,1771]
Output: 1
Explanation:
Only 1771 contains an even number of digits.
Constraints:
1 <= nums.length <= 500
1 <= nums[i] <= 10^5
Solution: Math
Time complexity: O(n * log(max(num))) Space complexity: O(1)
Median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value. So the median is the mean of the two middle value.
Examples:
[2,3,4] , the median is 3
[2,3], the median is (2 + 3) / 2 = 2.5
Design a data structure that supports the following two operations:
void addNum(int num) – Add a integer number from the data stream to the data structure.
double findMedian() – Return the median of all elements so far.
Given N items, w[i] is the weight of the i-th item and v[i] is value of the i-th item. Given a knapsack with capacity W. Maximize the total value. Each item can be use 0 or 1 time.
We have a sorted set of digits D, a non-empty subset of {'1','2','3','4','5','6','7','8','9'}. (Note that '0' is not included.)
Now, we write numbers using these digits, using each digit as many times as we want. For example, if D = {'1','3','5'}, we may write numbers such as '13', '551', '1351315'.
Return the number of positive integers that can be written (using the digits of D) that are less than or equal to N.
Example 1:
Input: D = ["1","3","5","7"], N = 100Output: 20Explanation:
The 20 numbers that can be written are:
1, 3, 5, 7, 11, 13, 15, 17, 31, 33, 35, 37, 51, 53, 55, 57, 71, 73, 75, 77.
Example 2:
Input: D = ["1","4","9"], N = 1000000000Output: 29523Explanation:
We can write 3 one digit numbers, 9 two digit numbers, 27 three digit numbers,
81 four digit numbers, 243 five digit numbers, 729 six digit numbers,
2187 seven digit numbers, 6561 eight digit numbers, and 19683 nine digit numbers.
In total, this is 29523 integers that can be written using the digits of D.
Note:
D is a subset of digits '1'-'9' in sorted order.
1 <= N <= 10^9
Solution -1: DFS (TLE)
Time complexity: O(|D|^log10(N))
Space complexity: O(n)
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// Author: Huahua
classSolution{
public:
intatMostNGivenDigitSet(vector<string>& D, int N) {
int ans = 0;
dfs(D,0,N,ans);
returnans;
}
private:
voiddfs(constvector<string>& D, int cur, int N, int& ans) {
if (cur > N) return;
if(cur>0&& cur <= N) ++ans;
for(conststring& d : D)
dfs(D, cur * 10 + d[0] - '0', N, ans);
}
};
Solution 1: Math
Time complexity: O(log10(N))
Space complexity: O(1)
Suppose N has n digits.
less than n digits
We can use all the numbers from D to construct numbers of with length 1,2,…,n-1 which are guaranteed to be less than N.
e.g. n = 52125, D = [1, 2, 5]
format X: e.g. 1, 2, 5 counts = |D| ^ 1
format XX: e.g. 11,12,15,21,22,25,51,52,55, counts = |D|^2
format XXX: counts = |D|^3
format XXXX: counts = |D|^4
exact n digits
if all numbers in D != N[0], counts = |d < N[0] | d in D| * |D|^(n-1), and we are done.
