#
# [401] Binary Watch
#
# https://leetcode.com/problems/binary-watch/description/
#
# algorithms
# Easy (44.76%)
# Total Accepted:    45.2K
# Total Submissions: 100.9K
# Testcase Example:  '0'
#
# 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 = 1Return: ["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".
# 
# 
#
class Solution(object):
    def readBinaryWatch(self, n):
        
        def dfs(n, hours, mins, idx):
            if hours >= 12 or mins > 59: return
            if not n:
                res.append(str(hours) + ":" + "0" * (mins < 10) + str(mins))
                return
            for i in range(idx, 10):
                if i < 4: 
                    dfs(n - 1, hours | (1 << i), mins, i + 1)
                else:
                    k = i - 4
                    dfs(n - 1, hours, mins | (1 << k), i + 1)
        
        res = []
        dfs(n, 0, 0, 0)
        return res
