Asked in: AURIGO
Image of the Question
All Testcases Passed ✔
Solution
def encryptData(cls, input1,input2,input3,input4,input5,input6):
final_array = [0 for i in range(input2+1)]
for ops,ln,val in zip(input3,input4,input5):
if ops == 1:
// ... rest of solution available after purchaseExplanation
```
To solve the problem of encrypting a sequence of data packets using a series of operations, it is crucial to carefully analyze the nature of the operations, their impact on the array, and the order in which they should be applied. The problem involves applying Q operations to an array data[] of length N, where each operation modifies either the first few packets or the last few packets by XORing their values with a given number X.
Start by thoroughly understanding the two types of operations and what each one does:
1. **Type 1 Operation:**
This operation modifies the first 'a' elements of the data array, where 'a' is given by numberOfPackets[i] for the current operation. Each of these first 'a' elements is XORed with a corresponding value X[i]. XOR (exclusive OR) is a bitwise operation with properties such as being reversible and working independently on each bit, which means repeated XORing with the same value will toggle bits back and forth.
2. **Type 2 Operation:**
This operation modifies the last 'a' elements of the data array, where 'a' is numberOfPackets[i]. It XORs these last 'a' elements with X[i], starting from the end towards the beginning.
Given these, the problem asks to perform Q such operations sequentially and return the resulting encrypted data array.
**Key Points to Consider and Approach:**
- **Sequential Application:**
The operations must be applied in the order they are given because each operation modifies the current state of data, and subsequent operations build upon these changes.
- **Handling Overlaps:**
Since some operations modify overlapping parts of the array (for example, the first few elements and later the last few elements, or even consecutive operations on the same region), the effects accumulate. XOR operations are cumulative and reversible, so the order and repetition matter.
- **Efficient Updates:**
For each operation, you need to XOR either the first a elements or the last a elements with X[i]. A straightforward approach involves looping through the relevant segment and applying XOR one by one.
- **Data Integrity:**
Remember that XOR is reversible. Applying XOR twice with the same number on the same element restores the original value. So, repeated XORs toggle bits back and forth.
- **Constraints and Performance:**
If Q and N are large, repeatedly applying XOR to potentially large segments for each operation might be inefficient. Thus, thinking about optimizing the process is useful. But for now, focus on understanding the problem and designing a correct and clear approach first.
- **Indexing:**
Pay attention to zero-based indexing of the data array when applying operations to the first or last elements. For Type 1, operate on indices 0 through a-1. For Type 2, operate on indices N-1 down to N-a.
- **Examples and Validation:**
Use given examples to confirm your understanding. For instance, the first example clearly shows that after the first Type 1 operation, the first two elements have been XORed with X[0], updating the data array. The second operation XORs the last element with X[1]. Confirming with examples helps prevent off-by-one errors and misunderstanding which segments to modify.
- **Step-by-Step Thought Process:**
1. Iterate over each operation from 0 to Q-1.
2. Check the type of operation.
3. If Type 1, XOR the first numberOfPackets[i] elements of data with X[i].
4. If Type 2, XOR the last numberOfPackets[i] elements of data with X[i].
5. After completing all operations, return the updated data array.
- **Possible Optimizations (Conceptual):**
If the constraints are large and time complexity matters, think about lazy updates or prefix/suffix XOR arrays that keep track of cumulative XOR values for segments without applying XOR to each element immediately. Then, you can apply all the XORs efficiently in a single pass at the end. However, this is a secondary consideration and depends on constraints.
- **Edge Cases:**
Consider edge cases like:
- Operations where numberOfPackets[i] is zero (meaning no packets modified).
- Operations where numberOfPackets[i] equals N (whole array modified).
- All operations are of one type.
- Large values of X[i] or zero.
- **Final Verification:**
After implementing, always verify with test inputs, especially those where overlapping operations occur, to confirm the correctness.
By approaching the problem step-by-step, clearly understanding the bitwise XOR operation, and carefully applying the modifications sequentially, you can successfully solve the problem and produce the correctly encrypted data array.
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