Hands Apart

An easy Python interview practice problem on DataDriven. Write the Python and run it against test cases, with instant feedback.

Domain
Python
Difficulty
easy
Seniority
L3
Asked in
phData

Problem

A calendar widget renders an analog clock face and needs to know how far apart the two hands sit. Given a hour (1 to 12) and a minute (0 to 59), return the smaller of the two angles in degrees between the hour and minute hands, remembering that the hour hand drifts continuously toward the next mark as the minutes pass rather than jumping on the hour.

Two hands. One gap. One number.

Example 1

Input:

hour = 3, minute = 0

Output:

90

Example 2

Input:

hour = 3, minute = 30

Output:

75

Worked solution and explanation

What this is really testing

Strip the clock face away and this is a question about whether you believe the hour hand actually moves. Almost everyone nails 3:00 equals 90 degrees, writes hour * 30, and ships it. The candidates who pass remember that by 3:30 the hour hand has already crept a quarter of the way toward 4, so the gap is 75 degrees, not 90. Get that one detail wrong and every non-zero minute is off by up to 15 degrees, with passing visible tests hiding the bug.

Break down the requirements

Step 1: Place the minute hand

Sixty minutes cover the whole face, so each minute is 6 degrees: minute * 6.

Step 2: Place the hour hand

Each hour mark is 30 degrees apart, and the hand drifts 0.5 degrees for every minute past the hour: (hour % 12) * 30 + minute * 0.5. The % 12 is what keeps 12 o'clock at 0 rather than 360.

Step 3: Fold to the smaller arc

Take the absolute difference, then return min(diff, 360 - diff). The face is circular, so the two hands always carve out two arcs that sum to 360; you want the smaller one.

The solution

Continuous hand positions
def clock_angle(hour: int, minute: int) -> float:
    minute_angle = minute * 6
    hour_angle = (hour % 12) * 30 + minute * 0.5
    diff = abs(hour_angle - minute_angle)
    return min(diff, 360 - diff)

Common follow-up questions