Defuse the Bomb

class Solution {
public:
    vector<int> decrypt(vector<int>& code, int k) {
        vector<int> decrypted(code.size(), 0);
        if (k == 0) return decrypted;
        int lIndex = 1, rIndex = k, currSum = 0;
        if (k < 0) {
            lIndex = code.size() - abs(k);
            rIndex = code.size() - 1;
        }
        for (int i = lIndex; i <= rIndex; i++) currSum += code[i];
        for (int i = 0; i < code.size(); i++) {
            decrypted[i] = currSum;
            currSum -= code[lIndex % code.size()];
            currSum += code[(rIndex + 1) % code.size()];
            lIndex++;
            rIndex++;
        }
        return decrypted;
    }
};

The provided C++ code defines a method decrypt in a class Solution that decrypts a numeric code based on a given integer parameter k. Here’s a concise step-by-step explanation of how the method works:

1. The vector<int> decrypted is initialized with the same size as the input vector code, but with all elements set to zero. This will be the output of the method.
2. If k equals 0, the function returns the decrypted vector immediately, all zeroed out.
3. The variables lIndex and rIndex are initialized based on the value of k. If k is positive, you start directly. If k is negative, start from nearly the end of the code vector, adjusted by k.
4. Before entering the main loop, compute the sum of the values from code[lIndex] to code[rIndex] and store it in currSum.
5. Iterate over each index i in code: assign currSum to decrypted[i], then adjust currSum to simulate a circular array by subtracting the element just left behind (code[lIndex % code.size()]) and adding the next element in the sequence (code[(rIndex + 1) % code.size()]). Increment both lIndex and rIndex to move to the next segment.
6. After iterating over all indices, return the decrypted vector.

This function efficiently calculates the decrypted values for the entire code using modular arithmetic to handle wrapping of indices, which is crucial for maintaining performance when k is negative. The circular buffer simulation is achieved without the need for actual buffer rotation, which also enhances performance.

class Solution {
    
    public int[] decode(int[] sequence, int k) {
        int[] output = new int[sequence.length];
        if (k == 0) return output;
        int begin = 1, finish = k, total = 0;
        if (k < 0) {
            begin = sequence.length - Math.abs(k);
            finish = sequence.length - 1;
        }
        for (int j = begin; j <= finish; j++) total += sequence[j];
        for (int j = 0; j < sequence.length; j++) {
            output[j] = total;
            total -= sequence[(begin) % sequence.length];
            total += sequence[(finish + 1) % sequence.length];
            begin++;
            finish++;
        }
        return output;
    }
}

The Java solution presented is designed to solve the problem of decoding a sequence of numbers with a specific encryption rule represented by an integer k. The method decode receives an array sequence and an integer k and returns a new integer array as the decoded sequence.

The decoding process involves the following steps:

1. Initialize an output array of the same length as the input sequence with all elements set to zero.
2. If k equals 0, immediately return the output array.
3. Calculate the starting index (begin) and ending index (finish) for the summation process. The range depends on whether k is positive or negative:
   • For k > 0, the range starts from index 1 to k.
   • For k < 0, adjust the range to handle negative values by setting begin to sequence.length - |k| and finish at sequence.length - 1.
4. Compute the initial total by summing the elements of the sequence from begin to finish.
5. Iterate through each element in the sequence:
   • Set the current index of the output array to the current total.
   • Adjust total by subtracting the element at the current begin position (modular indexing) and adding the element at finish + 1 position (also modular indexing).
   • Increment both begin and finish.

The method ensures efficient handling of negative and positive k values, adapting the range of summation dynamically based on the direction (forward or backward) indicated by k. The wrap-around of indices (using modulo) avoids out-of-bound errors, thus accommodating cyclic movements through the sequence. This solution effectively decodes the sequence according to the mentioned encoding rules, providing a robust and clear approach to the problem.

class Solution:
    def decode(self, sequence: List[int], offset: int) -> List[int]:
        decoded = [0] * len(sequence)
        if offset == 0:
            return decoded
        # Setting up initial indices and sum for processing
        start_index, end_index, sum_values = 1, offset, 0
        # Adjust start and end for negative offsets
        if offset < 0:
            start_index = len(sequence) + offset
            end_index = len(sequence) - 1
        for j in range(start_index, end_index + 1):
            sum_values += sequence[j]
        # Iterating to update the decoded result
        for j in range(len(sequence)):
            decoded[j] = sum_values
            sum_values -= sequence[start_index % len(sequence)]
            sum_values += sequence[(end_index + 1) % len(sequence)]
            start_index += 1
            end_index += 1
        return decoded

The provided Python code implements a method titled decode in a Solution class designed to decipher a sequence of integers according to a specified offset. This implementation is based on transforming the input values into a new set of values where each element in the output list, decoded, is calculated by aggregating certain elements from the input sequence based on the offset.

Here are the primary operations performed by the decode method:

• It initializes the result list decoded with zeros, with the same length as sequence.
• If the offset parameter is zero, it immediately returns the decoded list filled with zeros, as no calculation is required.
• For positive offsets, the method sums elements starting from index 1 to offset.
• For negative offsets, it adjusts the start and end index to correctly wrap around the sequence.
• An accumulation variable, sum_values, is leveraged to keep the sum of the subarray defined by the current start_index and end_index.
• The method then iterates through the sequence, updating each element in the decoded list by adjusting the sum_values to slide over the right elements based on the updated start_index and end_index using mod operation for wrapping around.

Each step manipulatively moves the window (defined by start_index and end_index) over the sequence list to compute the resulting elements in decoded. This ensures the transformations are applied uniformly despite the rotation-like behavior dictated by the offset. This implementation handles both positive and negative offsets efficiently and ensures that even in sequences that wrap due to negative offsets, the calculation maintains integrity by modulating the sequence indices.