Collision problem

The r-to-1 collision problem is an important theoretical problem in complexity theory, quantum computing, and computational mathematics. The collision problem most often refers to the 2-to-1 version: given $n$ even and a function $f:\,\{1,\ldots,n\}\rightarrow\{1,\ldots,n\}$ , we are promised that f is either 1-to-1 or 2-to-1. We are only allowed to make queries about the value of $f(i)$ for any $i\in\{1,\ldots,n\}$ . The problem then asks how many such queries we need to make to determine with certainty whether f is 1-to-1 or 2-to-1.

单词	Collision problem
释义	Collision problem 英语百科 Collision problem The r-to-1 collision problem is an important theoretical problem in complexity theory, quantum computing, and computational mathematics. The collision problem most often refers to the 2-to-1 version: given $n$ even and a function $f:\,\{1,\ldots,n\}\rightarrow\{1,\ldots,n\}$ , we are promised that f is either 1-to-1 or 2-to-1. We are only allowed to make queries about the value of $f(i)$ for any $i\in\{1,\ldots,n\}$ . The problem then asks how many such queries we need to make to determine with certainty whether f is 1-to-1 or 2-to-1.
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