Minimum Total Cost

Clarify first

Minimum Total Cost alone is not a complete problem. Ask what is being chosen or transformed, how each cost is computed, whether choices affect one another, and the input limits. Restate the confirmed objective before coding.

Build from a baseline

Start with exhaustive choices or a direct simulation so correctness is visible. Then look for structure: independent choices often reduce to a linear minimum scan; ordered choices may need sorting or dynamic programming; graph-like dependencies may need shortest paths or a minimum spanning structure. State the invariant that each transition or greedy choice preserves. Test empty or singleton input, ties, negative costs if allowed, overflow, and impossible states. Do not invent a fixed bound from the title: after clarification, give time and extra space in terms of the confirmed input size, for example O(n) time and O(1) space for one independent minimum scan.