2683. Neighboring Bitwise XOR
Approach
XOR of all derived values must equal 0 for a valid original array to exist.
Key Techniques
Array problems involve manipulating elements stored in a contiguous block of memory. Key techniques include two-pointer traversal, prefix sums, sliding windows, and in-place partitioning. In C#, arrays are zero-indexed and fixed in size — use List<T> when you need dynamic resizing.
Bit manipulation uses bitwise operators (&, |, ^, ~, <<, >>) for compact and fast solutions. Key tricks: x & (x-1) clears lowest set bit, x ^ x = 0 (XOR cancellation), and bitmask DP represents subsets as integers. In C#, use int (32-bit) or long (64-bit) for bitmasking.
A prefix sum array pre-computes cumulative values so any range query is answered in O(1). The classic sum of range [l, r] = prefix[r+1] - prefix[l]. 2D prefix sums extend this to matrix sub-rectangle queries. Combine with a hash map for "subarray sum equals k" problems.
// Approach: XOR of all derived values must equal 0 for a valid original array to exist.
// Time: O(n) Space: O(1)
public class Solution
{
public bool DoesValidArrayExist(int[] derived)
{
int n = derived.Length;
int ans = 0;
for (int i = 0; i < n - 1; i++)
{
if (derived[i] == 1)
ans ^= 1;
}
if (derived[n - 1] == 1)
return ans != 0;
else
return ans == 0;
}
}