Minimum Spanning Tree Manhattan Distance Problem Solution
"Explore the solution to finding a minimum spanning tree for a set of points based on Manhattan distance in this informative visual guide. Learn about pruning the graph and optimizing algorithms for efficient computation."
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Presentation Transcript
PS Bonus Debrief By Le Beier
Problem Given N points(x, y), the weight between each pair of points are given by the manhattan distance. Find a minimum spanning tree(MST) manhattan distance = |X1- X2| + |Y1-Y2|
Constraints 1 <= N <= 100, 000 0 <= (x, y) <= 1000 Remove Duplicates Points are non-distinct edge weight = manhattan distance
For i = 0 n: For k = 0 n: Add edge(point_i, point_k, dist) into Edge List Result = MST(Edge List)
O(N^2) + O(E log N) = O(N^2 log N) * E = N^2 Since N = 100000 100000^2 log 100000 = 166096404744 166096404744
TLE TLE AC Solution
Prune the graph How?
O(XY)+O(XY log XY) = O(XY log XY) Note: 0<= X, Y < 1000 O(1000000 log 1000000) = 19931568
Delaunay Triangulation Using line sweep algorithm which runs in O(n log n)
https://www.topcoder.com/communi ty/data-science/data-science- tutorials/line-sweep-algorithms/
