orderly backtracking

Author: idf

401 Binary Watch.py

@@ -0,0 +1,73 @@
+"""
+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".
+"""
+__author__ = 'Daniel'
+
+
+class Solution(object):
+    def __init__(self):
+        self.hours = (1, 2, 4, 8)
+        self.minutes = (1, 2, 4, 8, 16, 32)
+
+    def readBinaryWatch(self, num):
+        """
+        orderly backtracking
+
+        :type num: int
+        :rtype: List[str]
+        """
+        def gen():
+            for hour_n in xrange(min(num, 4)+1):
+                for hour in self.hour(hour_n):
+                    for minute in self.minute(num-hour_n):
+                        hour = str(hour)
+                        minute = ('0' + str(minute))[-2:]
+                        yield hour + ':' + minute
+
+        return list(gen())
+
+    def gen(self, n, head, lst, func):
+        if head == len(lst):
+            yield None
+
+        if n == 0:
+            yield 0
+
+        for i in xrange(head, len(lst)):
+            for rest in self.gen(n-1, i+1, lst, func):
+                if rest is not None:
+                    ret = lst[i]+rest
+                    if func(ret):
+                        yield ret
+                    else:
+                        break
+
+    def hour(self, n):
+        return self.gen(n, 0, self.hours, lambda x: x < 12)
+
+    def minute(self, n):
+        return self.gen(n, 0, self.minutes, lambda x: x < 60)
+
+
+if __name__ == "__main__":
+    assert Solution().readBinaryWatch(1) == ['0:01', '0:02', '0:04', '0:08', '0:16', '0:32', '1:00', '2:00', '4:00',
+                                             '8:00']