Question

Given four digits, count how many valid times can be displayed on a digital clock (in 24-hour format) using those digits. The earliest time is 00:00 and the latest time is 23:59. Write a function: int solution(int A, int B, int c, int D); that, given four integers A, B, C and D (describing the four digits), returns the number of valid times that can be displayed on a digital clock. Examples: 1. Given A = 1, B = 8, C = 3, D = 2, the function should return 6. The valid times are: 12:38, 13:28, 18:23, 18:32, 21:38 and 23:18. 2. Given A = 2, B = 3, C = 3, D = 2, the function should return 3. The valid times are: 22:33, 23:23 and 23:32. = 3. Given A = 6, B = 2, C = 4, D = 7, the function should return O. It is not possible to display any valid time using the given digits. Assume that: • A, B, C and D are integers within the range [0..9).

Answer 1

To find the number of valid times on a digital clock using four digits, generate all unique permutations of the digits, check if they are within the 24-hour clock limits, and return a count of the valid times.

Step-by-step explanation:

To find the number of valid times that can be displayed on a digital clock using four given digits, we must consider the constraints of a 24-hour clock format. The function int solution(int A, int B, int C, int D) should establish the rules: the first two digits must form a number between 00 and 23 (hours), and the last two between 00 and 59 (minutes). The process involves generating all permutations of the four digits and then counting the ones that satisfy these time constraints.

Here is a step-by-step outline of how you could program this solution:

1. Generate all unique permutations of the four digits.
2. For each permutation, split it into two parts; the first part represents hours, and the second part represents minutes.
3. Check if the hours part is less than 24 and the minutes part is less than 60.
4. If the condition is met, increment a counter.
5. Once all permutations are checked, return the counter's value.

For the given example A = 1, B = 8, C = 3, D = 2, the function would return 6 as there are 6 valid permutations that satisfy the digital clock's constraints.

Answer 2

The task requires the construction of a function to compute the number of valid digital clock times from four digits. It's a problem involving permutation counting within constraints specific to time formatting. Using examples, it's shown how the function should give the count based on these criteria.

Step-by-step explanation:

Creating a function to count the number of valid times that can be displayed on a digital clock is a problem that involves both permutations and conditions. The function we are looking at is int solution(int A, int B, int C, int D), and it takes four integers that are used to form the digits of potential times. In order to be a valid time, the first two digits must form a number between 00 and 23 (since the clock is 24-hour format) and the last two digits must be between 00 and 59.

To solve this, you would generate all possible permutations of the four given digits and then count those permutations that result in valid times. It's also important to take into account the special handling of leading zeros and the fact that certain permutations may result in identical times, which means we must ensure we count every valid time once.

For example, given A = 1, B = 8, C = 3, D = 2, the function should return 6. Here are the valid times you could form: 12:38, 13:28, 18:23, 18:32, 21:38, and 23:18. For the second example, A = 2, B = 3, C = 3, D = 2, you're able to form three valid times: 22:33, 23:23, and 23:32. The final example demonstrates that sometimes no valid times can be constructed; with A = 6, B = 2, C = 4, D = 7, the function should return 0, since none of the permutations of these digits form a valid 24-hour time.