# Question

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.

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

class Solution:
"""
:type num: int
:rtype: List[str]
"""
if num == 0:
return ["0:00"]
comb = []
self._backtrack(comb, [], 0, num)
res = []
for c in comb:
hour = 8 * c[0] + 4 * c[1] + 2 * c[2] + c[3]
if hour <= 11:
minute = 32 * c[4] + 16 * c[5] + 8 * c[6] + 4 * c[7] + 2 * c[8] + c[9]
if minute <= 9:
res.append("{}:0{}".format(hour, minute))
elif minute <= 59:
res.append("{}:{}".format(hour, minute))

return res

def _backtrack(self, res, partial, idx, remaining):
if remaining == 0:
if idx == 10:
res.append(partial)
else:
res.append(partial + [0] * (10 - idx))
elif 10 - idx == remaining:
res.append(partial + [1] * remaining)
elif 10 - idx > remaining:
self._backtrack(res, partial + [0], idx + 1, remaining)
self._backtrack(res, partial + [1], idx + 1, remaining - 1)