From 41c6783a2057198d08c75d8b3220cdee5d7bb2df Mon Sep 17 00:00:00 2001
From: kortschak <dan.kortschak@adelaide.edu.au>
Date: Sat, 6 Jun 2015 19:12:45 +0930
Subject: [PATCH] search: add time complexity notes

---
 search/bellman_ford_moore.go | 2 ++
 search/dijkstra.go           | 4 ++++
 search/floydwarshall.go      | 2 ++
 search/johnson_apsp.go       | 2 ++
 4 files changed, 10 insertions(+)

diff --git a/search/bellman_ford_moore.go b/search/bellman_ford_moore.go
index b8339623..30937f21 100644
--- a/search/bellman_ford_moore.go
+++ b/search/bellman_ford_moore.go
@@ -9,6 +9,8 @@ import "github.com/gonum/graph"
 // BellmanFordFrom returns a shortest-path tree for a shortest path from u to all nodes in
 // the graph g, or false indicating that a negative cycle exists in the graph. If weight
 // is nil and the graph does not implement graph.Coster, UniformCost is used.
+//
+// The time complexity of BellmanFordFrom is O(|V|.|E|).
 func BellmanFordFrom(u graph.Node, g graph.Graph, weight graph.CostFunc) (path Shortest, ok bool) {
 	if !g.NodeExists(u) {
 		return Shortest{from: u}, true
diff --git a/search/dijkstra.go b/search/dijkstra.go
index 197276ec..a738a6cf 100644
--- a/search/dijkstra.go
+++ b/search/dijkstra.go
@@ -15,6 +15,8 @@ import (
 // DijkstraFrom returns a shortest-path tree for a shortest path from u to all nodes in
 // the graph g. If weight is nil and the graph does not implement graph.Coster, UniformCost
 // is used. DijkstraFrom will panic if g has a u-reachable negative edge weight.
+//
+// The time complexity of DijkstrFrom is O(|E|+|V|.log|V|).
 func DijkstraFrom(u graph.Node, g graph.Graph, weight graph.CostFunc) Shortest {
 	if !g.NodeExists(u) {
 		return Shortest{from: u}
@@ -73,6 +75,8 @@ func DijkstraFrom(u graph.Node, g graph.Graph, weight graph.CostFunc) Shortest {
 // DijkstraAllPaths returns a shortest-path tree for shortest paths in the graph g.
 // If weight is nil and the graph does not implement graph.Coster, UniformCost is used.
 // DijkstraAllPaths will panic if g has a negative edge weight.
+//
+// The time complexity of DijkstrAllPaths is O(|V|.|E|+|V|^2.log|V|).
 func DijkstraAllPaths(g graph.Graph, weight graph.CostFunc) (paths ShortestPaths) {
 	var (
 		from   = g.Neighbors
diff --git a/search/floydwarshall.go b/search/floydwarshall.go
index df36d5ad..deaab2b6 100644
--- a/search/floydwarshall.go
+++ b/search/floydwarshall.go
@@ -14,6 +14,8 @@ import (
 // FloydWarshall returns a shortest-path tree for the graph g or false indicating
 // that a negative cycle exists in the graph. If weight is nil and the graph does not
 // implement graph.Coster, UniformCost is used.
+//
+// The time complexity of FloydWarshall is O(|V|^3).
 func FloydWarshall(g graph.Graph, weight graph.CostFunc) (paths ShortestPaths, ok bool) {
 	var (
 		from   = g.Neighbors
diff --git a/search/johnson_apsp.go b/search/johnson_apsp.go
index 63bdb666..78280ea0 100644
--- a/search/johnson_apsp.go
+++ b/search/johnson_apsp.go
@@ -14,6 +14,8 @@ import (
 
 // JohnsonAllPaths returns a shortest-path tree for shortest paths in the graph g.
 // If weight is nil and the graph does not implement graph.Coster, UniformCost is used.
+//
+// The time complexity of JonsonAllPaths is O(|V|.|E|+|V|^2.log|V|).
 func JohnsonAllPaths(g graph.Graph, weight graph.CostFunc) (paths ShortestPaths, ok bool) {
 	jg := johnsonWeightAdjuster{
 		g:      g,