LeetCode Entry

3513. Number of Unique XOR Triplets I

23.07.2026 medium 2026 kotlin rust

Uniq xor of tripplets of 1..n

3513. Number of Unique XOR Triplets I medium substack youtube

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Problem TLDR

Uniq xor of tripplets of 1..n

Intuition

    // for xor order doesnt matter
    // nums are the same 1..n
    // 1 xor 1 = 0
    // 1 ^ 0 = 1
    // 1 ^ 0 ^ 1 = 0
    // 1 ^ 0 ^ 0 = 1
    // 1 ^ 1 ^ 1 = 1
    // 1 ^ 1 ^ 0 = 0
    // uniq?

Order doesnt matter. The maximum value 0b1xxxxx allows to construct any intermediate value by taking 1 xor 1 xor n[i] plus tail bits can construct any value of up to 2*max.

Approach

• simulate and see the results, then derive whats happening

Complexity

• Time complexity: \(O(logn)\)

• Space complexity: \(O(1)\)

Code

    fun uniqueXorTriplets(n: IntArray) =
    if (n.size <3) n.size else 2*n.size.takeHighestOneBit()

    pub fn unique_xor_triplets(n: Vec<i32>) -> i32 {
        let l = n.len() as i32; if l < 3 { l } else { 1 << (32 - l.leading_zeros()) }
    }