Home >Backend Development >C++ >How Can Linear Feedback Shift Registers (LFSRs) Efficiently Generate Unique Random Sequences Without Repetition?
The task of generating pseudo-random numbers without repetitions presents an interesting challenge in programming. While some conventional approaches involve shuffling a range of numbers or checking for repeats in a generated list, these methods may not be optimal for generating large numbers or ensuring efficiency.
For generating large random numbers without storing the entire range, a mathematical technique known as Linear Feedback Shift Registers (LFSRs) offers a more suitable solution. LFSRs are hardware or software implementations that generate sequences of bits using a set of shift registers with some bits fed back to the input.
By carefully selecting the "taps" in the LFSR, it is possible to construct maximal length sequences that are as long as the register size. For instance, a 16-bit LFSR can produce a sequence 65535 long without any repetitions.
For proper construction of an LFSR, the following guidelines are recommended:
Utilizing LFSRs for generating random numbers with no repeats offers several benefits:
LFSRs are particularly advantageous in scenarios where generating large random numbers without repetitions is essential. Examples include:
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