Graphs/Min Cost to Connect All PointsMedium

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Min Cost to Connect All Points

Graphs·Medium

You are given an array points of n 2-D integer points. The cost to connect two points (x1, y1) and (x2, y2) is their Manhattan distance: |x1 - x2| + |y1 - y2|. Return the minimum cost to connect all points (i.e., build a minimum spanning tree).

Use Prim's algorithm: maintain a minCost array of the cheapest edge connecting each unvisited node to the current MST. At each step, pick the unvisited node with the smallest minCost, add it to the MST, then update neighbors.

Examples

Input: points = [[0,0],[2,2],[3,10],[5,2],[7,0]]

Output: 20

MST edges: (0,0)-(2,2)=4, (2,2)-(5,2)=3, (5,2)-(7,0)=4, (2,2)-(3,10)=9. Total=20.

Input: points = [[3,12],[-2,5],[-4,1]]

Output: 18

Constraints

1 <= points.length <= 1000
-(10^6) <= xi, yi <= 10^6
All pairs (xi, yi) are distinct.

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Tests

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Passed32 ms

First attempt — retry to track metric movement here.

Your approach

Pattern:Graphs
Time:O(N)
Space:O(1)

Complete approach — pattern and complexity both named.

Coach

What you got right

You correctly matched the sorted input requirement and implemented a linear-time scan using two pointers.

Where it diverged

No divergence detected. The code correctly aligns with the stated approach.

Next attempt: focus on

Try solving related sliding window problems to build familiarity with two-pointer variants.

Signals

No signals fired — clean run, you stayed in flow.