Lamp Clock Times

Easy

A designer clock shows the time with ten lamps in two rows. The top row of 4 lamps is the hour from 0 to 11 in binary, and the bottom row of 6 lamps is the minute from 0 to 59, also in binary. A lit lamp is a one and a dark lamp is a zero, with the lowest bit on the right. For example, if the top row has the lamps worth 2 and 1 lit and the bottom row has 32, 8 and 2 lit, the clock reads 3:42. Right now exactly lit lamps are on. Return every time the clock could be showing. Format each string like this: - the hour has no leading zero: "5:07", not "05:07"; - the minutes always have two digits: "10:03", not "10:3". The times may be listed in any order.

Example 1

lit=0 → ['0:00']

All lamps are off, so the clock shows 0:00.

Example 2

lit=9 → []

The hour row can have at most 3 lamps lit (7 or 11) and the minute row at most 5 (such as 59 or 47): 4 lamps would mean hour 15, and 6 would mean minute 63. So at most 8 lamps can be on, and the answer is empty.

Example 3

lit=1 → ['0:01', '0:02', '0:04', '0:08', '0:16', '0:32', '1:00', '2:00', '4:00', '8:00']

One lamp: either an hour of 1, 2, 4 or 8 with 00 minutes, or 0 hours with 01, 02, 04, 08, 16 or 32 minutes.

Constraints

0 ≤ lit ≤ 10

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Topics

Bit Manipulation Backtracking