From ba0027913467957d08561a012c838e00b313238f Mon Sep 17 00:00:00 2001
From: Ionut Hodoroaga <ionut.hodoroaga20@gmail.com>
Date: Wed, 25 Sep 2024 10:32:40 +0300
Subject: [PATCH] [ENHANCEMENT] Include Time and Space Complexity Information
 #698

Added time and space complexity for Bellman-Ford, find cycle and depth first search implementations
---
 graph/bellmanford.go      | 2 ++
 graph/cycle.go            | 4 ++++
 graph/depthfirstsearch.go | 3 +++
 3 files changed, 9 insertions(+)

diff --git a/graph/bellmanford.go b/graph/bellmanford.go
index f130a4e06..7831df633 100644
--- a/graph/bellmanford.go
+++ b/graph/bellmanford.go
@@ -3,6 +3,8 @@
 // It is slower than Dijkstra but capable of handling negative edge weights.
 // https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm
 // Implementation is based on the book 'Introduction to Algorithms' (CLRS)
+// Worst Case Time Complexity: O(V * E)
+// Auxiliary Space: O(V)
 
 package graph
 
diff --git a/graph/cycle.go b/graph/cycle.go
index cf45d1854..df3572a7f 100644
--- a/graph/cycle.go
+++ b/graph/cycle.go
@@ -5,6 +5,8 @@
 
 package graph
 
+// Worst Case Time Complexity: O(V + E)
+// Auxiliary Space: O(V)
 func (g *Graph) HasCycle() bool {
 	//this implimetation referred as 3-color too
 	all := map[int]struct{}{}
@@ -45,6 +47,8 @@ func (g Graph) hasCycleHelper(v int, all, visiting, visited map[int]struct{}) bo
 }
 
 // this function can do HasCycle() job but it is slower
+// Worst Case Time Complexity: O(V + E)
+// Auxiliary Space: O(V)
 func (g *Graph) FindAllCycles() []Graph {
 	all := map[int]struct{}{}
 	visiting := map[int]struct{}{}
diff --git a/graph/depthfirstsearch.go b/graph/depthfirstsearch.go
index c035c79f5..7d06d0f22 100644
--- a/graph/depthfirstsearch.go
+++ b/graph/depthfirstsearch.go
@@ -1,3 +1,6 @@
+// Worst Case Time Complexity: O(V + E)
+// Auxiliary Space: O(V)
+
 package graph
 
 func GetIdx(target int, nodes []int) int {