How Can We Efficiently Generate Long, Non-Repeating Random Number Sequences?

Generating Random Number Sequences with No Repeats

In computer programming, generating random number sequences with no repetitions is a common task. The problem arises when the range of numbers to generate becomes large, making it inefficient to shuffle the entire range or check for duplicates.

One approach to this problem is to use a linear feedback shift register (LFSR). An LFSR is a shift register where some of the bits are XORed and fed back to the input. By carefully selecting the taps (positions of the bits that are fed back), an LFSR can produce a sequence that is as long as the register size, with no repeats.

For example, a 16-bit LFSR can generate a sequence 65535 long without any repetitions. This is a statistically random sequence, but it is also eminently repeatable, which may not be desirable in some applications.

If a non-repeating random sequence of large numbers is required, a different approach is necessary. One option is to use a hashing function to map the input range to a smaller output range. By generating a random number within the smaller range and hashing it, a unique output number can be obtained. This process can be repeated until a sequence of the desired length is generated.

Another approach is to use a pseudorandom number generator (PRNG) to generate a sequence of random numbers and then filter out any duplicates. This can be done efficiently using a data structure such as a hash table or a set. The drawback of this approach is that it requires storing the generated numbers in memory, which can become a limitation for large sequences.

The above is the detailed content of How Can We Efficiently Generate Long, Non-Repeating Random Number Sequences?. For more information, please follow other related articles on the PHP Chinese website!