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Update knuth-optimization.md#1438

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mhayter merged 2 commits intocp-algorithms:mainfromFloppaInspector:patch-1
Apr 12, 2025

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In time complexity proof cancellation explanation, j=N -> j=N-1

In time complexity proof cancellation explanation, j=N -> j=N-1
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This is technically true probably should say something showing how when j=N-1 the second argument is N to be more thorough.

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FloppaInspector commentedApr 12, 2025
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This is technically true probably should say something showing how when j=N-1 the second argument is N to be more thorough.

Well, it should be clear that since the term j=N-1 remains, and i iterates range [1, N], opt(k, N) form should make clear sense. Saying j=N is a lot more confusing, since the positive term is "opt(i+1, j+1)", not "opt(i, j)", where j=N makes sense, but it isn't the positive term and people can easily misinterpret for the negative term. Though I don't think more explanation is needed, since positive term should clearly refer to "opt(i+1, j+1)" where j=N-1 is correct. Plus j cannot be N because j iterates range [i, N-1].

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mhayter commentedApr 12, 2025
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You're right. I guess I'd prefer to add an additional line but surely it's not more wrong than what's already there.

@mhaytermhayter merged commit862a10b intocp-algorithms:mainApr 12, 2025
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github-actionsbot added a commit that referenced this pull requestApr 12, 2025
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