From 89f15bef0a32e8e2c1c26f773daebfbe4dd3564f Mon Sep 17 00:00:00 2001
From: Bruno Santos <7022432+dunderbruno@users.noreply.github.com>
Date: Sun, 26 May 2019 13:41:46 -0300
Subject: [PATCH] Create prim.py (#397)

---
 Graphs/prim.py | 82 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 82 insertions(+)
 create mode 100644 Graphs/prim.py

diff --git a/Graphs/prim.py b/Graphs/prim.py
new file mode 100644
index 000000000..c9f91d4b0
--- /dev/null
+++ b/Graphs/prim.py
@@ -0,0 +1,82 @@
+"""
+Prim's Algorithm.
+
+Determines the minimum spanning tree(MST) of a graph using the Prim's Algorithm
+
+Create a list to store x the vertices.
+G = [vertex(n) for n in range(x)]
+
+For each vertex in G, add the neighbors:
+G[x].addNeighbor(G[y])
+G[y].addNeighbor(G[x])
+
+For each vertex in G, add the edges:
+G[x].addEdge(G[y], w)
+G[y].addEdge(G[x], w)
+
+To solve run:
+MST = prim(G, G[0])
+"""
+
+import math
+
+
+class vertex():
+    """Class Vertex."""
+
+    def __init__(self, id):
+        """
+        Arguments:
+            id - input an id to identify the vertex
+
+        Attributes:
+            neighbors - a list of the vertices it is linked to
+            edges     - a dict to store the edges's weight
+        """
+        self.id = str(id)
+        self.key = None
+        self.pi = None
+        self.neighbors = []
+        self.edges = {}  # [vertex:distance]
+
+    def __lt__(self, other):
+        """Comparison rule to < operator."""
+        return (self.key < other.key)
+
+    def __repr__(self):
+        """Return the vertex id."""
+        return self.id
+
+    def addNeighbor(self, vertex):
+        """Add a pointer to a vertex at neighbor's list."""
+        self.neighbors.append(vertex)
+
+    def addEdge(self, vertex, weight):
+        """Destination vertex and weight."""
+        self.edges[vertex.id] = weight
+
+
+def prim(graph, root):
+    """
+    Prim's Algorithm.
+
+    Return a list with the edges of a Minimum Spanning Tree
+
+    prim(graph, graph[0])
+    """
+    A = []
+    for u in graph:
+        u.key = math.inf
+        u.pi = None
+    root.key = 0
+    Q = graph[:]
+    while Q:
+        u = min(Q)
+        Q.remove(u)
+        for v in u.neighbors:
+            if (v in Q) and (u.edges[v.id] < v.key):
+                v.pi = u
+                v.key = u.edges[v.id]
+    for i in range(1, len(graph)):
+        A.append([graph[i].id, graph[i].pi.id])
+    return(A)