Add Minimum Spanning Tree in PowerShell (TheRenegadeCoder#4858)

Author: rzuckerm

archive/p/powershell/MinimumSpanningTree.ps1

@@ -0,0 +1,144 @@
+function Show-Usage() {
+    Write-Host "Usage: please provide a comma-separated list of integers"
+    Exit(1)
+}
+
+function Parse-IntList([string]$Str) {
+    @($Str.Split(",") | ForEach-Object { [int]::Parse($_) })
+}
+
+class NodeItem {
+    [int]$Index
+    [int]$Weight
+
+    NodeItem([int]$index, [int]$weight) {
+        $this.Index = $index
+        $this.Weight = $weight
+    }
+}
+
+class Node {
+    [int]$Index
+    [NodeItem[]]$Children
+
+    Node([int]$index) {
+        $this.Index = $index
+        $this.Children = @()
+    }
+
+    [void] AddChild([int]$index, [int]$weight) {
+        $this.Children += [NodeItem]::new($index, $weight)
+    }
+}
+
+function Create-Graph([array]$Weights, [int]$NumVertices) {
+    # Initialize nodes
+    $nodes = 0..($NumVertices - 1) | ForEach-Object { [Node]::new($_) }
+
+    # Get neighbors for this node based on weights
+    $index = 0
+    for ($row = 0; $row -lt $NumVertices; $row++) {
+        for ($col = 0; $col -lt $NumVertices; ($col++), ($index++)) {
+            if ($Weights[$index] -gt 0) {
+                $nodes[$row].AddChild($col, $Weights[$index])
+            }
+        }
+    }
+
+    $nodes
+}
+
+class MstItem {
+    [int]$SrcIndex
+    [int]$DestIndex
+    [int]$Weight
+
+    MstItem([int]$srcIndex, [int]$destIndex, [int]$weight) {
+        $this.SrcIndex = $srcIndex
+        $this.DestIndex = $destIndex
+        $this.Weight = $weight
+    }
+}
+
+# Prim's Minimum Spanning Tree (MST) Algorithm based on C implementation of
+# https://www.geeksforgeeks.org/prims-minimum-spanning-tree-mst-greedy-algo-5/
+function Invoke-PrimMst([Node[]]$Graph) {
+    $numVertices = $Graph.Length
+
+    # Array to store constructed MST. Indicate no parents yet
+    $parents = @(-1) * $numVertices
+
+    # Key values used to pick minimum weight edge. Initialize to infinity
+    $keys = @([int]::MaxValue) * $numVertices
+
+    # Indicate nothing in MST yet
+    $mstSet = @($false) * $numVertices
+
+    # Include first vertex in MST
+    $keys[0] = 0
+
+    # The MST will include all vertices
+    for ($i = 1; $i -lt $numVertices; $i++) {
+        # Pick index of the minimum key value not already in MST
+        $u = Find-MinKey $keys $mstSet
+
+        # Add picked vertex to MST
+        $mstSet[$u] = $true
+
+        # Update key values and parent indices of picked adjacent
+        # vertices. Only consider vertices not yet in MST
+        foreach ($child in $Graph[$u].Children) {
+            $v = $child.Index
+            $w = $child.Weight
+            if (-not $mstSet[$v] -and $w -lt $keys[$v]) {
+                $parents[$v] = $u
+                $keys[$v] = $w
+            }
+        }
+    }
+
+    # Construct MST information to return, skipping over root
+    @(1..($numVertices - 1) | ForEach-Object { [MstItem]::new($parents[$_], $_, $keys[$_]) })
+}
+
+function Find-MinKey([int[]]$Keys, [bool[]]$MstSet) {
+    $minValue = [int]::MaxValue
+    $minIndex = -1
+    for ($v = 0; $v -lt $Keys.Length; $v++) {
+        if ($Keys[$v] -lt $minValue -and -not $MstSet[$v]) {
+            $minValue = $Keys[$v]
+            $minIndex = $v
+        }
+    }
+
+    $minIndex
+}
+
+function Invoke-MstTotalWeight([MstItem[]]$mst) {
+    ($mst.Weight | Measure-Object -Sum).Sum
+}
+
+if ($args.Length -lt 1 -or -not $args[0]) {
+    Show-Usage
+}
+
+try {
+    $weights = Parse-IntList $args[0]
+} catch {
+    Show-Usage
+}
+
+$numVertices = [int][Math]::Floor([Math]::Sqrt($weights.Length))
+if ($weights.Length -ne $numVertices * $numVertices) {
+    Show-Usage
+}
+
+# Create graph from weights
+$graph = Create-Graph $weights $numVertices
+
+# Get MST using Prim's algorithm
+$mst = Invoke-PrimMst $graph
+
+# Calculate total weight of MST
+$totalWeight = Invoke-MstTotalWeight $mst
+Write-Output $totalWeight