Appeal Regarding Plagiarism Flag: Submission [351054331]

To the Administration/Judge,

I am writing to formally appeal the plagiarism flag on my submission [351054331] for problem 2170F. While I acknowledge that my solution coincides with a list of other users, I want to state clearly and unequivocally that I wrote this code independently.

The reason so many people (including myself) wrote nearly identical code is that this problem requires a very specific, standard optimization technique known as "Offline Queries with Rightmost Index DP."

Here is a detailed breakdown of exactly why my code ended up looking like others:

1. The "Offline Query" Boilerplate

Since the problem asks about ranges, the standard, most efficient method is to process the queries "offline." This involves iterating through the array once (from index $$$1$$$ to $$$N$$$) and handling all queries ending at the current index $$$R$$$.

My code does exactly this:

vector qryAt[MAXN]; // ... for (int r = 1; r <= n; r++) { ... }

This is not unique logic; it is the standard boilerplate for offline processing. Almost every C++ competitive programmer uses a vector of structs or pairs to store the queries in this manner.

2. The "Rightmost Index" Trick

The core difficulty of this problem is checking if a subset exists within the range $$$[L, R]$$$. The textbook trick for this is to avoid storing a boolean and instead store the rightmost index.

The logic is defined as follows: * $$$dp[k][x]$$$ = the largest index $$$i$$$ such that we can form XOR sum $$$x$$$ using $$$k$$$ elements ending at $$$i$$$.

The validation check then becomes standard: If $$$dp[k][target] \ge L$$$, then the subset is valid.

Once you know this trick, there is essentially only one way to write the if statement. It is not copied; it is a direct implementation of the required logic.

3. The Loop Structure (Knapsack Style)

You will notice my inner loop iterates backwards:

for (int k = 12; k >= 2; k--) { ... }

I wrote it this way because it functions exactly like the 1D Knapsack DP. You must iterate backwards to ensure you do not use the current element $$$a[r]$$$ more than once for the same subset size. This is not a stylistic choice—if I had looped forwards, the logic would be incorrect.

4. Constants and Variables

• 4096 and 13: These are not random numbers. The problem constraints limit values to 4096 and the subset size to 12. I simply defined constants MAXV and MAXK to match the problem statement.
• Variable Names: n, q, l, r, x are simply the variable names provided in the input section of the problem statement.

Conclusion

When a problem has tight constraints and relies on a specific "textbook" optimization (Rightmost Index DP), the solution space is extremely small. There are only so many ways to write three nested loops and a max function.

The similarity is due to "convergent evolution" on a standard algorithm, not plagiarism. I request that you review the code with this context in mind.