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The greedy choice
Let be greedy's first activity (ends earliest) and be OPT's first activity.
Case : . No change needed. Both agree on the first activity.
Case : . Since ends earliest, . Replace with in OPT to create OPT'. Is OPT' valid? Yes! Since ends no later than , it cannot conflict with OPT's second activity (which starts after P10 ends). OPT' has the same count as OPT.
