Asked in: Amazon
Image of the Question
All Testcases Passed ✔
Solution
def findNumber(numbers):
# Write your code here
length_of_numbers = len(numbers)
while length_of_numbers > 2:
// ... rest of solution available after purchaseExplanation
```
To solve the problem of finding the encrypted number based on the described "Pascal Triangle" encryption scheme, begin by carefully understanding how the transformation works and what is required at each step.
Step 1: Understand the encryption process
- The input is an array of digits.
- At each step, the encryption algorithm sums every pair of adjacent digits.
- For each sum, only the rightmost digit (the least significant digit) is retained to form a new sequence.
- The length of the array reduces by one in each iteration since the sums are formed between adjacent pairs.
- This process repeats until only two digits remain.
- These final two digits together form the encrypted number, which is returned as a string.
Step 2: Visualize the transformation using the example
- Take the array [4, 5, 6, 7].
- First step sums:
- 4 + 5 = 9 → rightmost digit is 9.
- 5 + 6 = 11 → rightmost digit is 1.
- 6 + 7 = 13 → rightmost digit is 3.
- The resulting array is [9, 1, 3].
- Second step sums:
- 9 + 1 = 10 → rightmost digit 0.
- 1 + 3 = 4 → rightmost digit 4.
- The resulting array is [0, 4].
- Since only two digits remain, this is the encrypted number "04".
Step 3: Plan the iterative approach
- Start with the original array of digits.
- Iterate while the length of the array is greater than 2.
- In each iteration:
- Create a new array of length one less than the current array.
- For each adjacent pair in the current array:
- Calculate their sum.
- Extract the last digit (sum modulo 10).
- Store this digit in the new array.
- Replace the current array with this new array.
- Once the length of the array is 2, convert these two digits into a string and return.
Step 4: Consider implementation details
- Ensure to handle the conversion between digits and strings properly.
- When extracting the last digit of a sum, always use modulo 10.
- Work with integers for the sums and then convert to digits as needed.
- Maintain the sequence accurately at each iteration.
Step 5: Analyze complexity and efficiency
- Each iteration reduces the array size by one.
- If the initial array length is n, then the total number of iterations is n-2.
- Each iteration involves summing adjacent pairs, which is O(k) where k is the current length.
- Total complexity is roughly O(n^2) due to repeated iterations shrinking the array by one.
- For typical input sizes, this is acceptable, but if the input is extremely large, optimizations or alternative approaches might be needed.
Step 6: Edge cases and validations
- If the initial array length is 2, return the digits directly as the encrypted number.
- Verify that the input consists of digits (0-9).
- Handle cases with repeated digits correctly.
- Consider inputs with minimal length (e.g., length 2) and maximum length as per constraints.
Step 7: Summary of the problem-solving approach
- The problem is essentially simulating the iterative transformation as defined.
- Each step compresses the array by summing adjacent pairs and taking the last digit.
- Repeating this process until only two digits remain yields the encrypted number.
- The main challenge is understanding the transformation and implementing it iteratively.
- The solution is straightforward once the procedure is clearly understood.
By carefully iterating through the array and applying the described digit summation with modulo operations, you can derive the final encrypted two-digit number efficiently and correctly.
```