Special Array II

class Solution {
public:
    vector<bool> checkSpecialArray(vector<int>& elements,
                                   vector<vector<int>>& inquiry) {
        int length = elements.size();
        vector<int> reachExtent(length);

        // Initialize reach for the last element
        reachExtent[length - 1] = length - 1;
        for (int i = length - 2; i >= 0; i--) {
            // Compare parities of adjacent elements
            if ((elements[i] % 2) != (elements[i + 1] % 2)) {
                reachExtent[i] = reachExtent[i + 1]; // Extend reachability
            } else {
                reachExtent[i] = i; // Limit to current index
            }
        }

        vector<bool> results(inquiry.size());

        // Evaluate each of the inquiries
        for (int j = 0; j < inquiry.size(); j++) {
            int startIndex = inquiry[j][0];
            int endIndex = inquiry[j][1];

            // Validate if end index is within the reachable extent from start index
            results[j] = endIndex <= reachExtent[startIndex];
        }

        return results;
    }
};

This C++ solution implements a checkSpecialArray function designed to determine if parts of an array meet specific conditions based on the parity (odd or even nature) of its elements and user-defined inquiries. Here’s how the solution progresses:

1. First, ensure the reachExtent vector, which has the same length as the input elements, is initialized. This vector keeps track of the furthest index each element can reach without encountering an element of the same parity right next to it.

2. Starting from the second last element of the elements array, compare its parity with the next element. If they have different parities, the current element can extend its reach to the reach of the next element, otherwise, its reach is limited to its own index.

3. After constructing the reachExtent, prepare a results vector to store boolean values corresponding to each inquiry. Each inquiry consists of a start and end index, and you need to check if the start index's reach includes the end index.

4. For each inquiry in the inquiry vector, extract the start and end indexes. Refer to the reachExtent vector using the start index to verify if it covers the end index. The result (true or false) is stored in the results vector.

5. Finally, the results vector is returned, which contains the evaluation of each inquiry based on whether an uninterrupted path of alternating parities exists between the start and end indexes specified in each query.

This detailed setup ensures each inquiry is answered efficiently, leveraging pre-computed reachability to minimize repetitive checks and offer a quick lookup time for results based on varying start and end points.

class Solution {

    public boolean[] checkSpecialArray(int[] elements, int[][] ranges) {
        int len = elements.length;
        int[] furthestReach = new int[len];

        // Initialize furthest reach for each index from right to left
        furthestReach[len - 1] = len - 1; // furthest reachable index for the last element is itself
        for (int indx = len - 2; indx >= 0; indx--) {
            // Adjacent elements with different parity
            if ((elements[indx] % 2) != (elements[indx + 1] % 2)) {
                furthestReach[indx] = furthestReach[indx + 1]; // Can reach further as defined by next index
            } else {
                furthestReach[indx] = indx; // Only reachable to itself
            }
        }

        boolean[] results = new boolean[ranges.length];

        // Evaluate the queries using precomputed reachability
        for (int q = 0; q < ranges.length; q++) {
            int startPoint = ranges[q][0];
            int endPoint = ranges[q][1];

            // True if the endPoint lies within the furthestReach of startPoint
            results[q] = endPoint <= furthestReach[startPoint];
        }

        return results;
    }
}

The Java solution for the problem involves determining if specific subarrays within given ranges consist of elements with alternate parities (odd and even). The process involves first precomputing the furthest index that can be reached from each starting index without breaking the parity alternation condition. Then, it evaluates each query by checking if the furthest reach from the start of any given range includes the end point of that range. This is accomplished through the following steps:

1. Calculate the length of the elements array.
2. Initialize an array furthestReach where each index initially points to itself, indicating the furthest it can go preserving the alternate parity condition.
3. Starting from the second-to-last element to the first, update furthestReach for each element based on its next element. If the current element and the next have different parities, the current element can reach as far as the next can. If they're the same, it can only reach itself.
4. Initialize a boolean array results to store the results of the queries.
5. For each query in ranges, check if the end point of the range is within the furthestReach of the start point of the range. Set the corresponding value in results.

The approach efficiently uses precomputation of possible reaches, which allows answering each query in constant time, while the space complexity remains linear to the size of the input array. This makes the solution very efficient for handling multiple queries on the array.

class Checker:
    def isSpecialArray(self, array: List[int], requests: List[List[int]]) -> List[bool]:
        lenA = len(array)
        maxIndexReach = [0] * lenA
        maxIndexReach[-1] = lenA - 1  # The last element can only reach itself
        for idx in range(lenA - 2, -1, -1):
            if array[idx] % 2 != array[idx + 1] % 2:
                maxIndexReach[idx] = maxIndexReach[idx + 1]  # Extend reach
            else:
                maxIndexReach[idx] = idx  # Reach is limited to self

        result = [False] * len(requests)
        for idx, request in enumerate(requests):
            startIdx, endIdx = request
            result[idx] = endIdx <= maxIndexReach[startIdx]

        return result

The Python code defines a class named Checker with a method isSpecialArray designed to check if subarrays specified by a list of requests from an input array conform to a special condition. In this scenario, the condition evaluates if the subarray can be contiguous while maintaining a property based on the oddness or evenness of the array elements.

• The code initializes by determining the length of the array (lenA) and setting up an array maxIndexReach of the same size. Each index in maxIndexReach represents the furthest index that can be reached from the current index while maintaining the special condition.
• For the last element of the array, it sets its reach to itself since it can't extend beyond its position.
• The method sets the reachability of each index, based on the parity (odd or even) of the elements. If consecutive elements have different parity, the reach extends to as far as the previous element's reach. If not, the reach is confined to the element itself.
• For each request, represented by a start and end index, the method checks if the end index of the subarray is within the range defined by the reachability from the start index.
• The result is a list of boolean values where each boolean corresponds to a request, indicating whether the subarray meets the special condition based on reachability.

In summary, the isSpecialArray method efficiently determines if sections of an array meet a specified reachability condition based on the parity of consecutive elements, returning this information for multiple subarray requests.