From 620569c4ea9daa0bda183987f657edf311b3c8db Mon Sep 17 00:00:00 2001
From: Alexandre Tolstenko <tolstenko@gmail.com>
Date: Fri, 5 Apr 2024 12:06:57 -0400
Subject: [PATCH] fix: mst typings

---
 docs/algorithms/12-mst/README.md | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/docs/algorithms/12-mst/README.md b/docs/algorithms/12-mst/README.md
index 48142f75..67462c6c 100644
--- a/docs/algorithms/12-mst/README.md
+++ b/docs/algorithms/12-mst/README.md
@@ -571,8 +571,14 @@ There are many implementations for the Minimum Spanning Tree algorithm, here goe
 #include <utility>
 using namespace std;
 
+// rename optional<tuple<int, int, int>> to edge
+typedef optional<tuple<int, int, int>> Edge;
+
+// rename unordered_map<int, unordered_map<int, int>> to Graph
+typedef unordered_map<int, unordered_map<int, int>> Graph;
+
 // source, destination, weight
-optional<tuple<int, int, int>> findMinEdge(const unordered_map<int, unordered_map<int, int>>& graph, const unordered_map<int, unordered_map<int, int>>& mst){
+Edge findMinEdge(const Graph& graph, const Graph& mst){
   if(graph.empty())
     return nullopt;
   if(mst.empty()){
@@ -622,8 +628,8 @@ optional<tuple<int, int, int>> findMinEdge(const unordered_map<int, unordered_ma
 
 // returns the accumulated weight of the minimum spanning tree
 // the graph is represented as [source, destination] -> weight
-int MSP(unordered_map<int, unordered_map<int, int>> graph){
-  unordered_map<int, unordered_map<int, int>> mst;
+int MSP(const Graph& graph){
+  Graph mst;
   int accumulatedWeight = 0;
   while(true){
     auto edge = findMinEdge(graph, mst);