Algorithmic & Greedy Constructions
Describe a procedure, then prove it terminates and works.
Many 'show that such an arrangement exists' problems are answered by giving an explicit algorithm: repeatedly apply a local fix, and argue with a monovariant that it must stop.
The proof has two halves people forget to separate: termination (some non-negative integer strictly decreases) and correctness (the stopped state has the required property).
Greedy arguments belong here too — take the largest available piece, then prove an exchange argument shows greedy is optimal.
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Find your levelMore techniques
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