mediumLeetCode#minimum-spanning-tree#prim

Min Cost to Connect All Points

Connect every point with minimum total Manhattan-distance edge cost.

The Runtime Theory TeamSeptember 25, 202625 min read

Solve it

Solving happens on the judge — come back and mark it done

Sample cases

inpoints=[[0,0],[2,2],[3,10],[5,2],[7,0]]

out20

inpoints=[[3,12],[-2,5],[-4,1]]

out18

inpoints=[[1,1],[1,1]]

out0

Connect every point with minimum total Manhattan-distance edge cost.

A good solution should

State the invariant or decision rule that makes the approach correct.
Explain time and space costs in terms of input size and required output.
Handle empty, minimal, duplicate, and boundary-shaped inputs.

Reasoning prompt

Model points as a complete weighted graph, but avoid materializing every edge if using Prim’s algorithm.

Use the linked judge for the canonical challenge. The examples above are compact TRT checks; create additional tests around the boundary most likely to break your invariant.

One dispatch a week

The trace behind each problem, the tradeoff that explains it, and one technical dispatch per week — no noise.

One technical dispatch per week. No noise.

Not started

A good solution should

Reasoning prompt

More practice in this topic

One dispatch a week