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What are some of the balances and trade offs between different sorting algoritms?

Stability 
  - stable sorts maintain the relative order of items with equal "values"
  - important, obviously, if you value the relative order of your input
  - e.g. merge sort, insertion sort
  
Runtime Analysis
  - represents complexity in terms of time (Big-O analysis)
  - trade-off: some faster algorithms require more space, so choosing a slower one might make sense where space is limited