401. Binary Watch-二进制手表

A binary watch has 4 LEDs on the top which represent the hours (0-11), and the 6 LEDs on the bottom represent the minutes (0-59).

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 non-negative integer n which represents the number of LEDs that are currently on, return all possible times the watch could represent.

Example:
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 in python:

class Solution:
    def readBinaryWatch(self, num: int) -> List[str]:
        def backtrack(alist, count, path, result):
            for item in alist:
                if item in path:
                    continue
                length = len(alist)
                summary = sum(path)
                if (length == 4) and (summary >= 12):
                    return 
                if (length == 6) and (summary >= 60):
                    return 
                if count == 0:
                    result.append(path)
                    return 
                path.append(item)
                backtrack(alist, count-1, path[::], result)
                path.pop()

        hlist = [1, 2, 4, 8]
        mlist = [1, 2, 4, 8, 16, 32]
        times = []
        for k in range(min(4, num+1)):
            path1, path2 = [], []
            result1, result2 = [], []
            backtrack(hlist, k, path1, result1)
            backtrack(mlist, num-k, path2, result2)
            for item1 in result1:
                for item2 in result2:
                    times.append(str(sum(item1))+":"+(str(sum(item2)) if (sum(item2)) > 9 else ("0"+str(sum(item2)))))
        return set(times)