Discard what can never help, then combine

A one-line filter that makes the rest of the problem trivial, and the argument for why it is safe.

Why it works

A tuple exceeding the target anywhere is poison

Because combining only ever raises components and never lowers them, any tuple with a component larger than the target's can never be part of a solution. Including it makes that component permanently too large.

So discard those first. What remains cannot overshoot in any component, which means combining all of them is safe and gives the largest reachable value in every component simultaneously.

That is the argument: filtering is safe because the operation is monotone, and after filtering there is no reason to be selective, so take everything.

The filter is the whole difficulty, so here it is on its own, with each tuple judged against the target.

1tuples = [(2, 5, 3), (1, 8, 4), (1, 7, 5)]2target = (2, 7, 5)3 4for candidate in tuples:5    overshoots = [value for value, goal in zip(candidate, target) if value > goal]6    verdict = f"poison, exceeds by {overshoots}" if overshoots else "safe to combine"7    print(candidate, "->", verdict)

One component too large rules a tuple out forever, because combining never lowers anything.

Predict the output· 5 min

Predict the output: why one bad component is fatal

Combining two tuples takes the larger value in each position. A tuple that already exceeds the target somewhere is combined anyway, to see what happens. Type the three lines it prints.

Python

1target = (2, 7, 5)2poison = (1, 8, 4)3helpful = (2, 5, 3)4 5combined = tuple(max(a, b) for a, b in zip(poison, helpful))6print("poison combined with a good one:", combined)7print("still within the target?", all(v <= t for v, t in zip(combined, target)))8print("can any later combination lower the 8?", False)

Printed output

Problem· 22 min

Merge Triplets To Form Target Triplet

Read the constraints first and let them tell you what complexity is expected. Derive the approach, implement it, run the tests, and submit when it passes.

1tuples = [(2, 5, 3), (1, 8, 4), (1, 7, 5)]2target = (2, 7, 5)3 4for candidate in tuples:5 overshoots = [value for value, goal in zip(candidate, target) if value > goal]6 verdict = f"poison, exceeds by {overshoots}" if overshoots else "safe to combine"7 print(candidate, "->", verdict)

1target = (2, 7, 5)2poison = (1, 8, 4)3helpful = (2, 5, 3)4 5combined = tuple(max(a, b) for a, b in zip(poison, helpful))6print("poison combined with a good one:", combined)7print("still within the target?", all(v <= t for v, t in zip(combined, target)))8print("can any later combination lower the 8?", False)