Interviewers often accept a greedy solution only after you explain why it's correct. "It seems to work on the examples" is the answer that loses points. The exchange argument is a short, reusable way to give a real justification in under a minute.
Greedy: sort by end time and always take the interval that ends first. Exchange: if an optimal schedule starts with a different interval, replace it with the one that ends earliest. It ends no later, so it can't conflict with anything that came after; the count stays the same. Repeat for each position.
Serve jobs shortest first. If an optimal order has a longer job immediately before a shorter one, swapping them reduces the waiting time of the shorter job by more than it increases the longer one's, so the total never goes up. An order with no such "inversion" is exactly sorted order.
Coin change with coins {1, 3, 4} and target 6: greedy takes 4+1+1 (three coins), optimal is 3+3 (two). Try the exchange: you can't swap the 4 into the optimal solution without breaking it. Saying this shows the interviewer you test your greedy before trusting it, and it's the cue to switch to dynamic programming.
Before proving, spend 30 seconds attacking your own rule with small inputs: ties, one huge item, items that are only slightly better on one dimension. Most wrong greedy ideas die on a three-element example.
"Take any optimal answer. Where it first disagrees with my choice, I can swap in mine without making it worse, because my choice ends earliest (or is smallest, or has the best ratio). Repeating the swap turns the optimal answer into mine, so mine is optimal."
Disclosure: I help build Linkjob AI copilot, a tool for coding interview practice. This article is independent study material.