Question on the Implementation of Grover Adaptive Search

[ShashankGarag]

In the original Grover Adaptive Search procedure, a random x is selected from the decision space, and f(x) is used as the threshold in the Grover's Search Algorithm segment of the procedure. However, in this program, a probability distribution is created to select the random value, and I was confused to why it was necessary. If you could clarify how the Grover Optimizer program aligns with the original Grover Adaptive Search procedure (or Dürr and Høyer’s Algorithm to be specific), it would be greatly appreciated.

Thank You,
Shashank G.