Suppose there is a set S of d-dimensional vectors, |S| = n. Suppose further that

Question

Suppose there is a set S of d-dimensional vectors, |S| = n. Suppose further that there are two vectors in S that are identical. If comparing any two d-dimensional vectors takes O(d) time, design an efficient algorithm that finds the two identical vectors.
I'm looking for a solution that doesn't use hashmaps Suppose there is a set S of d-dimensional vectors, |S| = n. Suppose further that there are two vectors in S that are identical. If comparing any two d-dimensional vectors takes O(d) time, design an efficient algorithm that finds the two identical vectors.
I'm looking for a solution that doesn't use hashmaps
I'm looking for a solution that doesn't use hashmaps

Explanation / Answer

The following is an algorithm without using a hashmap.

We will need two additional arrays sum and product of size n.

Algorithm:

Summing and multiplying takes O(n*d) time.

Also with very high probability the identical vectors will be segregated out. Then to check identicality if a pair vectors will take O(d) time. Therefore running time of this algorithm is O(n*d).

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