401. Binary Watch
1. Description
A binary watch has 4 LEDs on the top to represent the hours (0-11), and 6 LEDs on the bottom to represent the minutes (0-59). Each LED represents a zero or one, with the least significant bit on the right.
- For example, the below binary watch reads “4:51”.
Given an integer turnedOn which represents the number of LEDs that are currently on (ignoring the PM), return all possible times the watch could represent. You may return the answer in any order.
The hour must not contain a leading zero.
- For example, “01:00” is not valid. It should be “1:00”.
The minute must be consist of two digits and may contain a leading zero.
- For example, “10:2” is not valid. It should be “10:02”.
2. Example
Example 1:
Input: turnedOn = 1
Output: [“0:01”,“0:02”,“0:04”,“0:08”,“0:16”,“0:32”,“1:00”,“2:00”,“4:00”,“8:00”]
Example 2:
Input: turnedOn = 9
Output: []
3. Constraints
- 0 <= turnedOn <= 10
4. Solutions
Bit Manipulation
Time complexity: O(1)
Space complexity: O(1)
// since the space of turnedOn is very small, we can just loop every case
class Solution {
public:
vector<string> readBinaryWatch(int turnedOn) {
vector<string> result;
for (int i = 0; i < hours_; ++i) {
int hour_digits = get_digits_(i);
for (int j = 0; j < minutes_; ++j) {
int minute_digits = get_digits_(j);
int sum_digits = hour_digits + minute_digits;
if (sum_digits == turnedOn) {
result.emplace_back(
to_string(i) + string(":") + (j < 10 ? string("0") : string("")) +
to_string(j));
}
}
}
return result;
}
private:
const int hours_ = 12;
const int minutes_ = 60;
inline int get_digits_(int number) {
int digits = 0;
for (; number > 0; number >>= 1) {
if (number & 1 == 1) {
++digits;
}
}
return digits;
}
};