Some more examples
Beginner: Linked list reversal, Mergesort, Sieve of Eratosthenes, Red-black tree algorithms (insertion and removal)
Intermediate: Simplex, Miller-Rabin primality test, Huffman coding, Kruskal's algorithm
Advanced: Viterbi Algorithm, Cooley–Tukey FFT, Simulated Annealing, Hindley–Milner type inference
I tried to find links that had at least some pseudocode and/or good explanation. But the thing about advanced algorithms is that they have many variations. So, you can explain the basic outline of a "genetic algorithm", but there are actually many algorithms that goes by that name. (The same for the FFT; I linked a named variant of it)
This text about numerical integration, for a gaming audience, describes two algorithms for numerical integration: a simpler, straightforward algorithm (the Euler integrator), and a more advanced one (the Runge-Kutta order 4 integrator). It may be a good for seeing "basic vs. advanced". You can use integrators for simulating physics, and the Euler integrator leads to enormous errors, so he recommends RK4 instead. But they are arguably variations of the "same" algorithm: Euler is first-order RK.