Largest Time for Given Digits

class Solution {
    private int maxTime = -1;

    public String calculateLargestTime(int[] digits) {
        maxTime = -1;
        generatePermutations(digits, 0);
        if (maxTime == -1)
            return "";
        else
            return String.format("%02d:%02d", maxTime / 60, maxTime % 60);
    }

    protected void generatePermutations(int[] digits, int index) {
        if (index == digits.length) {
            evaluateTime(digits);
            return;
        }
        for (int idx = index; idx < digits.length; ++idx) {
            exchange(digits, idx, index);
            generatePermutations(digits, index + 1);
            exchange(digits, idx, index);
        }
    }

    protected void evaluateTime(int[] permutation) {
        int hours = permutation[0] * 10 + permutation[1];
        int minutes = permutation[2] * 10 + permutation[3];
        if (hours < 24 && minutes < 60)
            maxTime = Math.max(maxTime, hours * 60 + minutes);
    }

    protected void exchange(int[] array, int x, int y) {
        if (x != y) {
            int temporary = array[x];
            array[x] = array[y];
            array[y] = temporary;
        }
    }
}

The Java solution provided is designed to find the largest possible time that can be constructed using the given set of four digits. This task is solved by generating all permutations of the digits and then calculating the maximum valid time.

Here’s a concise breakdown of the process:

• First, the method calculateLargestTime initializes maxTime to -1. This variable is used to store the maximum number of minutes that can be represented by the permutations which form valid time.

• The method generatePermutations recursively generates all permutations of the input array of digits.

• For each permutation, the method evaluateTime calculates the hours and minutes. It then checks if these values form a valid time (i.e., hours less than 24 and minutes less than 60). If the condition is satisfied, it updates maxTime if the current time in minutes is greater than the previously stored maxTime.

• The helper method exchange is used for swapping elements in the array of digits during the generation of permutations.

• If after evaluating all permutations, no valid time is found (maxTime remains -1), the calculateLargestTime method returns an empty string. Otherwise, it formats the time in "HH:MM" format using the maximum minutes calculated.

Implement these steps using recursive permutation generation that efficiently checks and updates the possible maximum valid time. This approach ensures that the final result is the largest possible valid time or an indication that no valid time can be constructed.

class Solution:
    def computeLargestTime(self, digits: List[int]) -> str:

        highest_time = -1

        def calculate_maximum_time(permutation):
            nonlocal highest_time

            hours, min1, min2, sec = permutation
            hour_value = hours*10 + min1
            minute_value = min2*10 + sec
            if hour_value < 24 and minute_value < 60:
                highest_time = max(highest_time, hour_value * 60 + minute_value)

        def exchange_elements(arr, first, second):
            if first != second:
                arr[first], arr[second] = arr[second], arr[first]

        def generate_permutations(arr, initial):
            if initial == len(arr):
                calculate_maximum_time(arr)
                return

            for position in range(initial, len(arr)):
                exchange_elements(arr, position, initial)
                generate_permutations(arr, initial+1)
                exchange_elements(arr, position, initial)

        generate_permutations(digits, 0)
        if highest_time == -1:
            return ""
        else:
            return "{:02d}:{:02d}".format(highest_time // 60, highest_time % 60)

The provided Python function computeLargestTime aims to determine the largest 24-hour format time that can be obtained from a given list of four digits. Follow these steps in the given code to achieve this:

1. Define a function calculate_maximum_time to compute the time from a permutation of digits. The function checks if the constructed hours and minutes fall within valid time boundaries (hours < 24 and minutes < 60). If valid, it updates the highest_time variable to the maximum possible minutes since midnight.

2. Include a helper exchange_elements for swapping elements in the array to facilitate generating permutations by maintaining array integrity.

3. Use the recursive function generate_permutations to create all possible permutations of the input digits. For each complete permutation, call calculate_maximum_time.

4. Inside generate_permutations, iterate through each position in the array to swap the current index with the index of the permutation depth, recursively call to generate further permutations, and subsequently backtrack by reversing the swap.

5. After attempting all permutations, check the highest_time. If no valid time was identified (still -1), return an empty string. Otherwise, format the highest_time (converted back from minutes to hours and minutes) as a string in "HH:MM" format.

This solution effectively utilizes backtracking to explore all possible permutations of the digits and checks each to see if it forms a valid time, keeping track of the maximum.