The best replacement for algorithms is heuristics.

The best alternatives to algorithms are rated as following:
★★★★★  heuristics
★★  logarithms
★  programs
★  pseudo code
★  protocols
  nondeterministic polynomial (np) time algorithms
  genetic programming

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Speaking about algorithms, one probably shouldn't forget about flowcharts.

Other search terms related to algorithms and their ratings are:
★★★★★ flowcharts
You have in mind a companion for algorithms and it is not yet here? Propose!



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algorithms
heuristics
logarithms