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It is known that the dual of the general adversary bound can be used to buildquantum query algorithms with optimal complexity. Despite this result, not manyquantum algorithms have been designed this way. This paper shows anotherexample of such algorithm.  We use the learning graph technique from arXiv:1105.4024 to give a quantumalgorithm for $k$-distinctness problem that runs in $o(n^{3/4})$ queries, for afixed $k$, given some prior knowledge on the structure of the input. The bestknown quantum algorithm for the unconditional problem uses $O(n^{k/(k+1)})$queries.

Quantum Algorithm for k-distinctness with Prior Knowledge on the Input