Binary Watch
Desicription
A binary watch has 4 LEDs on the top which represent the hours (011), and the 6 LEDs on the bottom represent the minutes (059).
Each LED represents a zero or one, with the least significant bit on the right.
For example, the above binary watch reads “3:25”.
Given a nonnegative integer n which represents the number of LEDs that are currently on, return all possible times the watch could represent.
Example:
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 Input: n = 1 Return: ["1:00", "2:00", "4:00", "8:00", "0:01", "0:02", "0:04", "0:08", "0:16", "0:32"]

Note:
 The order of output does not matter.
 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”.
Solution
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 class Solution { private: std::vector<std::string> res{}; std::vector<int> path = std::vector<int>(10, 0); void dfs(int index, int left) { if(left < 0  index > path.size()) { return ; }
if(index == path.size()) { if(left > 0) { return ; } else if(left == 0) { int hour = 8 * path[0] + 4 * path[1] + 2 * path[2] + 1 * path[3]; int minute = 32 * path[4] + 16 * path[5] + 8 * path[6] + 4 * path[7] + 2 * path[8] + 1 * path[9]; if(hour > 11  minute > 59) { return ; }
std::string hourString{}; std::string minuteString{}; hourString = std::to_string(hour); minuteString = minute >= 10 ? std::to_string(minute) : "0" + std::to_string(minute);
res.push_back(hourString + ":" + minuteString); return ; } }
dfs(index + 1, left); path[index] = 1  path[index]; dfs(index + 1, left  1); path[index] = 1  path[index]; } public: std::vector<std::string> readBinaryWatch(int num) { dfs(0, num); return res; } };
