giải bằng thuật toán c++ C. Partitioning the Array,time limit per test: 3 seconds,memory limit per test: 256 megabytes,input: standard input,output: standard output,Allen has an array $a_1,a_2,...,a_n.$ For every positive integer & that is a divisor of n., Allen does the following:,He partitions the array into $\frac nk$ disjoint subarrays of length k. In other words, he partitions the array into the following subarrays: $k$,$[a_1,a_2,...,a_k],[a_{k+1},a_{k+2},...,a_{2k}],...,[a_{n-k+1},a_{n-k+2},...,a_n]$,Allen earns one point if there exists some positive integer m $(m\geq2)$ such that if he replaces every element in the array wwth its,remainder when divided by m, then all suuarrays will be identicall,Help Allen find the number of points he will earn.,Input,Each test consists of multiple test cases. The first line contains a single integer t $(1\leq t\leq10^4)-$ the number of test cases. The,description of the test cases follows.,The first line of each test case contains a single integer n $(1\leq n\leq2.10^5)-$ the length of the array a.,The second line of each test case contains n integers $a_1,a_2,...,a_n(1\leq a_i\leq n)-$ the elements of the array a.,It is guaranteed that the sum of n over all test cases does not exceed 2 $10^5$,Output,For each test case, output a single integer ---the numebb o points Allll wlllaernn,Example,

Question

giải bằng thuật toán c++ C. Partitioning the Array,time limit per test: 3 seconds,memory limit per test: 256 megabytes,input: standard input,output: standard output,Allen has an array $a_1,a_2,...,a_n.$ For every positive integer & that is a divisor of n., Allen does the following:,He partitions the array into $\frac nk$ disjoint subarrays of length k. In other words, he partitions the array into the following subarrays: $k$,$[a_1,a_2,...,a_k],[a_{k+1},a_{k+2},...,a_{2k}],...,[a_{n-k+1},a_{n-k+2},...,a_n]$,Allen earns one point if there exists some positive integer m $(m\geq2)$ such that if he replaces every element in the array wwth its,remainder when divided by m, then all suuarrays will be identicall,Help Allen find the number of points he will earn.,Input,Each test consists of multiple test cases. The first line contains a single integer t $(1\leq t\leq10^4)-$ the number of test cases. The,description of the test cases follows.,The first line of each test case contains a single integer n $(1\leq n\leq2.10^5)-$ the length of the array a.,The second line of each test case contains n integers $a_1,a_2,...,a_n(1\leq a_i\leq n)-$ the elements of the array a.,It is guaranteed that the sum of n over all test cases does not exceed 2 $10^5$,Output,For each test case, output a single integer ---the numebb o  points Allll  wlllaernn,Example,<img src=https://minio.ftech.ai/cvdata/fqa/prod/public/illustration_images/2d9c728926f4469c8a225e66e5cc4992.jpg />

Accepted Answer

Goal: Calculate the number of points Allen earns for each test case.
Conditions for a point:
Partition the array into n/k disjoint subarrays of length k (where k is a divisor of n).
Find a positive integer m (≥2) such that replacing elements with their remainders when divided by m makes all subarrays identical.
Key Steps:

Iterate through divisors of n:
For each divisor k, create subarrays of length k.
Check for potential m values:
Start with m = 2 and increment.
Replace elements with remainders when divided by m.
Verify identical subarrays:
If all subarrays are identical, Allen earns a point.
Count and output points:
Keep track of the total points for each test case.
Output the count for each test case as specified in the output format.
Example:

For n = 4 and a = [1, 2, 1, 4]:
Divisors of n: 1, 2, 4
For k = 1: All subarrays are already identical, so 1 point.
For k = 2: No m value works, so 0 points.
For k = 4: The entire array is a subarray, and m = 2 works, so 1 point.
Total points: 2
Addressing Issues and Incorporating Feedback:

Clarity:
Provide a clear overview of the problem and steps involved.
Explain the conditions for earning a point in more detail.
Use examples to illustrate concepts.
Completeness:
Include essential details like input and output formats.
Address edge cases and potential issues.
Provide a more complete solution, potentially with code examples.
Accuracy:
Ensure the solution is correct and aligns with the problem statement.
Verify the provided example output.
Additional Considerations:

Algorithm efficiency: Explore optimized algorithms for finding divisors and checking subarrays.
Code implementation: Provide code examples in a specific programming language if needed.
Testing: Test the solution with various input cases to ensure correctness.