Added graph search adlgorithms and Heap and PriorityQueue data structures

container/heap.go

@@ -0,0 +1,103 @@
+package container
+
+import (
+	"golang.org/x/exp/constraints"
+)
+
+type HeapItem[T any, V constraints.Integer] struct {
+	Value    T
+	Priority V
+}
+
+// Heap represents a generic heap data structure.
+type Heap[T any, V constraints.Integer] struct {
+	elements  []HeapItem[T, V]
+	isMinHeap bool
+}
+
+// NewHeap creates a new heap with the specified ordering.
+// The isMinHeap parameter determines whether the heap is a min heap or a max heap.
+// The heap is initially empty.
+func NewHeap[T any, V constraints.Integer](isMinHeap bool) *Heap[T, V] {
+	return &Heap[T, V]{elements: []HeapItem[T, V]{}, isMinHeap: isMinHeap}
+}
+
+// Push adds an element to the heap.
+func (h *Heap[T, V]) Push(element T, priority V) {
+	h.elements = append(h.elements, HeapItem[T, V]{element, priority})
+	h.heapifyUp()
+}
+
+// Pop removes and returns the root element from the heap.
+func (h *Heap[T, V]) Pop() T {
+	if len(h.elements) == 0 {
+		var zero T // Return zero value of T
+		return zero
+	}
+
+	root := h.elements[0]
+	lastIndex := len(h.elements) - 1
+	h.elements[0] = h.elements[lastIndex]
+	h.elements = h.elements[:lastIndex]
+
+	h.heapifyDown()
+	return root.Value
+}
+
+// Peek returns the root element without removing it.
+func (h *Heap[T, V]) Peek() T {
+	if len(h.elements) == 0 {
+		var zero T // Return zero value of T
+		return zero
+	}
+	return h.elements[0].Value
+}
+
+// heapifyUp adjusts the heap after adding a new element.
+func (h *Heap[T, V]) heapifyUp() {
+	index := len(h.elements) - 1
+	for index > 0 {
+		parentIndex := (index - 1) / 2
+		if h.compare(h.elements[index].Priority, h.elements[parentIndex].Priority) {
+			h.elements[index], h.elements[parentIndex] = h.elements[parentIndex], h.elements[index]
+			index = parentIndex
+		} else {
+			break
+		}
+	}
+}
+
+// heapifyDown adjusts the heap after removing the root element.
+func (h *Heap[T, V]) heapifyDown() {
+	index := 0
+	lastIndex := len(h.elements) - 1
+	for index < lastIndex {
+		leftChildIndex := 2*index + 1
+		rightChildIndex := 2*index + 2
+
+		var childIndex int
+		if leftChildIndex <= lastIndex {
+			childIndex = leftChildIndex
+			if rightChildIndex <= lastIndex && h.compare(h.elements[rightChildIndex].Priority, h.elements[leftChildIndex].Priority) {
+				childIndex = rightChildIndex
+			}
+
+			if h.compare(h.elements[childIndex].Priority, h.elements[index].Priority) {
+				h.elements[index], h.elements[childIndex] = h.elements[childIndex], h.elements[index]
+				index = childIndex
+			} else {
+				break
+			}
+		} else {
+			break
+		}
+	}
+}
+
+// compare compares two elements based on the heap type.
+func (h *Heap[T, V]) compare(x, y V) bool {
+	if h.isMinHeap {
+		return x < y
+	}
+	return x > y
+}

container/heap_test.go

@@ -0,0 +1,145 @@
+package container
+
+import (
+	"testing"
+)
+
+// TestPush tests the Push method of the Heap.
+func TestPush(t *testing.T) {
+	heap := NewHeap[int, int](true) // Testing a min heap
+	heap.Push(3, 3)
+	heap.Push(1, 1)
+	heap.Push(2, 2)
+
+	expected := []int{1, 3, 2} // The expected min-heap state after pushing elements
+	for i, v := range heap.elements {
+		if v.Value != expected[i] {
+			t.Errorf("Push() test failed: expected %v at index %d, got %v", expected[i], i, v)
+		}
+	}
+}
+
+// TestPop tests the Pop method of the Heap.
+func TestPop(t *testing.T) {
+	heap := NewHeap[int, int](true)
+	heap.Push(3, 3)
+	heap.Push(1, 1)
+	heap.Push(2, 2)
+
+	if val := heap.Pop(); val != 1 {
+		t.Errorf("Pop() test failed: expected 1, got %v", val)
+	}
+
+	if val := heap.Pop(); val != 2 {
+		t.Errorf("Pop() test failed: expected 2, got %v", val)
+	}
+}
+
+// TestPeek tests the Peek method of the Heap.
+func TestPeek(t *testing.T) {
+	heap := NewHeap[int, int](true)
+	heap.Push(3, 3)
+	heap.Push(1, 1)
+	heap.Push(2, 2)
+
+	if val := heap.Peek(); val != 1 {
+		t.Errorf("Peek() test failed: expected 1, got %v", val)
+	}
+
+	// Check if Peek() doesn't remove the element
+	if val := heap.Pop(); val != 1 {
+		t.Errorf("Peek() test failed: Peek() should not remove the element")
+	}
+}
+
+// TestHeapProperty tests if the heap maintains its property after operations.
+func TestHeapProperty(t *testing.T) {
+	heap := NewHeap[int, int](true) // Testing a min heap
+	heap.Push(5, 5)
+	heap.Push(3, 3)
+	heap.Push(8, 8)
+	heap.Push(1, 1)
+	heap.Push(7, 7)
+
+	// After every Pop(), the next smallest element should come out
+	expectedOrder := []int{1, 3, 5, 7, 8}
+	for _, expected := range expectedOrder {
+		if val := heap.Pop(); val != expected {
+			t.Errorf("Heap property test failed: expected %v, got %v", expected, val)
+		}
+	}
+}
+
+// TestNewHeap tests the NewHeap function.
+func TestNewHeap(t *testing.T) {
+	// Test creating a min heap
+	minHeap := NewHeap[int, int](true)
+	if minHeap == nil {
+		t.Error("NewHeap() test failed: expected a non-nil heap")
+	}
+	if minHeap != nil && !minHeap.isMinHeap {
+		t.Error("NewHeap() test failed: expected a min heap")
+	}
+
+	// Test creating a max heap
+	maxHeap := NewHeap[int, int](false)
+	if maxHeap == nil {
+		t.Error("NewHeap() test failed: expected a non-nil heap")
+	}
+	if minHeap != nil && maxHeap.isMinHeap {
+		t.Error("NewHeap() test failed: expected a max heap")
+	}
+}
+
+// TestHeapifyUp tests the heapifyUp method of the Heap.
+func TestHeapifyUp(t *testing.T) {
+	heap := NewHeap[int, int](true)
+	heap.elements = []HeapItem[int, int]{{2, 2}, {3, 3}, {1, 1}}
+
+	heap.heapifyUp()
+
+	expected := []int{1, 3, 2} // The expected min-heap state after heapifyUp
+	for i, v := range heap.elements {
+		if v.Value != expected[i] {
+			t.Errorf("heapifyUp() test failed: expected %v at index %d, got %v", expected[i], i, v)
+		}
+	}
+}
+
+// TestHeapifyUpEmptyHeap tests the heapifyUp method of an empty Heap.
+func TestHeapifyUpEmptyHeap(t *testing.T) {
+	heap := NewHeap[int, int](true)
+
+	heap.heapifyUp()
+
+	if len(heap.elements) != 0 {
+		t.Errorf("heapifyUp() test failed: expected empty heap, got %v", heap.elements)
+	}
+}
+
+// TestHeapifyUpSingleElement tests the heapifyUp method of a Heap with a single element.
+func TestHeapifyUpSingleElement(t *testing.T) {
+	heap := NewHeap[int, int](true)
+	heap.elements = []HeapItem[int, int]{{1, 1}}
+
+	heap.heapifyUp()
+
+	if len(heap.elements) != 1 || heap.elements[0].Value != 1 {
+		t.Errorf("heapifyUp() test failed: expected [1], got %v", heap.elements)
+	}
+}
+
+// TestHeapifyDown tests the heapifyDown method of the Heap.
+func TestHeapifyDown(t *testing.T) {
+	heap := NewHeap[int, int](true)
+	heap.elements = []HeapItem[int, int]{{8, 8}, {1, 1}, {3, 3}, {5, 5}, {7, 7}}
+
+	heap.heapifyDown()
+
+	expected := []int{1, 5, 3, 8, 7} // The expected heap state after heapifyDown
+	for i, v := range heap.elements {
+		if v.Value != expected[i] {
+			t.Errorf("heapifyDown() test failed: expected %v at index %d, got %v", expected[i], i, v)
+		}
+	}
+}

container/priority_queue.go

@@ -0,0 +1,38 @@
+package container
+
+import (
+	"golang.org/x/exp/constraints"
+)
+
+// PriorityQueue represents a priority queue data structure.
+type PriorityQueue[T any, V constraints.Integer] struct {
+	heap *Heap[T, V]
+}
+
+// NewPriorityQueue creates a new PriorityQueue instance.
+// isMinQueue determines whether it is a min-priority queue (true) or a max-priority queue (false).
+func NewPriorityQueue[T any, V constraints.Integer](isMinQueue bool) *PriorityQueue[T, V] {
+	return &PriorityQueue[T, V]{
+		heap: NewHeap[T, V](isMinQueue),
+	}
+}
+
+// Enqueue adds an element to the priority queue.
+func (pq *PriorityQueue[T, V]) Enqueue(element T, priority V) {
+	pq.heap.Push(element, priority)
+}
+
+// Dequeue removes and returns the element with the highest priority from the queue.
+func (pq *PriorityQueue[T, V]) Dequeue() T {
+	return pq.heap.Pop()
+}
+
+// Peek returns the element with the highest priority without removing it from the queue.
+func (pq *PriorityQueue[T, V]) Peek() T {
+	return pq.heap.Peek()
+}
+
+// IsEmpty returns true if the priority queue is empty.
+func (pq *PriorityQueue[T, V]) IsEmpty() bool {
+	return len(pq.heap.elements) == 0
+}

container/priority_queue_test.go

@@ -0,0 +1,72 @@
+package container
+
+import (
+	"testing"
+)
+
+// TestEnqueue tests the Enqueue method of the PriorityQueue.
+func TestEnqueue(t *testing.T) {
+	pq := NewPriorityQueue[int, int](true) // Min-priority queue
+	pq.Enqueue(3, 3)
+	pq.Enqueue(1, 1)
+	pq.Enqueue(2, 2)
+
+	expected := []int{1, 3, 2} // Expected min-heap state after enqueuing elements
+	for i, v := range pq.heap.elements {
+		if v.Value != expected[i] {
+			t.Errorf("Enqueue() test failed: expected %v at index %d, got %v", expected[i], i, v)
+		}
+	}
+}
+
+// TestDequeue tests the Dequeue method of the PriorityQueue.
+func TestDequeue(t *testing.T) {
+	pq := NewPriorityQueue[int, int](true)
+	pq.Enqueue(3, 3)
+	pq.Enqueue(1, 1)
+	pq.Enqueue(2, 2)
+
+	if val := pq.Dequeue(); val != 1 {
+		t.Errorf("Dequeue() test failed: expected 1, got %v", val)
+	}
+
+	if val := pq.Dequeue(); val != 2 {
+		t.Errorf("Dequeue() test failed: expected 2, got %v", val)
+	}
+}
+
+// TestPeek tests the Peek method of the PriorityQueue.
+func TestPQueuePeek(t *testing.T) {
+	pq := NewPriorityQueue[int, int](true)
+	pq.Enqueue(3, 3)
+	pq.Enqueue(1, 1)
+	pq.Enqueue(2, 2)
+
+	if val := pq.Peek(); val != 1 {
+		t.Errorf("Peek() test failed: expected 1, got %v", val)
+	}
+
+	// Check if Peek() doesn't remove the element
+	if val := pq.Dequeue(); val != 1 {
+		t.Errorf("Peek() test failed: Peek() should not remove the element")
+	}
+}
+
+// TestIsEmpty tests the IsEmpty method of the PriorityQueue.
+func TestIsEmpty(t *testing.T) {
+	pq := NewPriorityQueue[int, int](true)
+
+	if !pq.IsEmpty() {
+		t.Errorf("IsEmpty() test failed: expected true, got false")
+	}
+
+	pq.Enqueue(1, 1)
+	if pq.IsEmpty() {
+		t.Errorf("IsEmpty() test failed: expected false, got true")
+	}
+
+	pq.Dequeue()
+	if !pq.IsEmpty() {
+		t.Errorf("IsEmpty() test failed: expected true, got false")
+	}
+}

graph/graph.go

@@ -11,6 +11,7 @@ import (
 
 	"gitea.paas.celticinfo.fr/oabrivard/abrolgo/algo"
 	"gitea.paas.celticinfo.fr/oabrivard/abrolgo/container"
+	"gitea.paas.celticinfo.fr/oabrivard/abrolgo/maths"
 	"golang.org/x/exp/constraints"
 )
 
@@ -51,13 +52,13 @@ func (g *Graph[T, V]) AddVertex(vertex T) {
 }
 
 // AddEdge adds an edge to the graph between the source node (src) and the destination node (dest),
-// with the given distance (dist).
+// with the given weight (weight).
 // It adds the edge in both directions (src -> dest and dest -> src).
 // If vertices src and dest do not exist in the graph, they are added to the graph.
-func (g *Graph[T, V]) AddEdge(src, dest T, dist V) {
+func (g *Graph[T, V]) AddEdge(src, dest T, weight V) {
 	g.edgeID++
-	srcToDest := Edge[T, V]{g.edgeID, src, dest, dist}
-	destToSrc := Edge[T, V]{g.edgeID, dest, src, dist}
+	srcToDest := Edge[T, V]{g.edgeID, src, dest, weight}
+	destToSrc := Edge[T, V]{g.edgeID, dest, src, weight}
 	g.adjacencyList[src] = append(g.adjacencyList[src], srcToDest)
 	g.adjacencyList[dest] = append(g.adjacencyList[dest], destToSrc)
 	g.edges = append(g.edges, srcToDest)
@@ -510,3 +511,97 @@ func (g *Graph[T, V]) BFS(start T, isGoal func(vertex T) bool) []T {
 
 	return []T{}
 }
+
+// AStar performs the A* search algorithm to find the shortest path between two vertices in the graph.
+// It returns the shortest path as a slice of vertices.
+// If no path is found, an empty slice is returned.
+func (g *Graph[T, V]) AStar(start, goal T, heuristic func(vertex T) V) []T {
+	// Initialize the distance map
+	dist := map[T]V{}
+	for vertex := range g.adjacencyList {
+		dist[vertex] = maths.MaxInteger[V]()
+	}
+	dist[start] = V(0)
+
+	// Initialize the previous map
+	prev := map[T]T{}
+
+	// Initialize the priority queue
+	pq := container.NewPriorityQueue[T, V](true)
+	pq.Enqueue(start, 0)
+
+	for !pq.IsEmpty() {
+		curVert := pq.Dequeue()
+
+		if curVert == goal {
+			// Reconstruct the path
+			path := []T{goal}
+			for prevVertex, ok := prev[goal]; ok; prevVertex, ok = prev[prevVertex] {
+				path = append([]T{prevVertex}, path...)
+			}
+			return path
+		}
+
+		for _, linkedNode := range g.adjacencyList[curVert] {
+			alt := dist[curVert] + linkedNode.weight
+			if alt < dist[linkedNode.dest] {
+				dist[linkedNode.dest] = alt
+				prev[linkedNode.dest] = curVert
+				priority := alt + heuristic(linkedNode.dest)
+				pq.Enqueue(linkedNode.dest, priority)
+			}
+		}
+	}
+
+	return []T{}
+}
+
+// Dijkstra performs Dijkstra's algorithm to find the shortest path between two vertices in the graph.
+// It returns the shortest path as a slice of vertices.
+// If no path is found, an empty slice is returned.
+func (g *Graph[T, V]) Dijkstra(start, goal T) []T {
+
+	return g.AStar(start, goal, func(vertex T) V {
+		return V(0)
+	})
+
+	/*
+		// Initialize the distance map
+		dist := map[T]V{}
+		for vertex := range g.adjacencyList {
+			dist[vertex] = maths.MaxInteger[V]()
+		}
+		dist[start] = V(0)
+
+		// Initialize the previous map
+		prev := map[T]T{}
+
+		// Initialize the priority queue
+		pq := container.NewPriorityQueue[T, V](true)
+		pq.Enqueue(start, 0)
+
+		for !pq.IsEmpty() {
+			curVert := pq.Dequeue()
+
+			if curVert == goal {
+				// Reconstruct the path
+				path := []T{goal}
+				for prevVertex, ok := prev[goal]; ok; prevVertex, ok = prev[prevVertex] {
+					path = append([]T{prevVertex}, path...)
+				}
+				return path
+			}
+
+			for _, linkedNode := range g.adjacencyList[curVert] {
+				alt := dist[curVert] + linkedNode.weight
+				if alt < dist[linkedNode.dest] {
+					dist[linkedNode.dest] = alt
+					prev[linkedNode.dest] = curVert
+					pq.Enqueue(linkedNode.dest, alt)
+				}
+			}
+		}
+
+		return []T{}
+	*/
+}

graph/graph_test.go

@@ -599,7 +599,7 @@ func TestKargerMinCutUF(t *testing.T) {
 	g.AddEdge(5, 6, 70)
 
 	// Run Karger's algorithm to find the minimum cut
-	cutEdges, resultSubsets := g.kargerMinCutUF(10000)
+	cutEdges, resultSubsets := g.kargerMinCutUF(100)
 
 	// Check if the number of cut edges is correct
 	expectedCutEdges := 1
@@ -722,3 +722,59 @@ func TestDFS(t *testing.T) {
 		t.Errorf("DFS() failed with goal function: expected %v, got %v", expectedResult, result)
 	}
 }
+func TestDijkstra(t *testing.T) {
+	g := NewGraph[int, int]()
+
+	// Add vertices and edges to the graph
+	g.AddEdge(1, 2, 10)
+	g.AddEdge(1, 3, 20)
+	g.AddEdge(2, 3, 30)
+	g.AddEdge(2, 4, 40)
+	g.AddEdge(3, 4, 50)
+
+	// Test Dijkstra algorithm
+	start := 1
+	goal := 4
+	expectedPath := []int{1, 2, 4}
+	path := g.Dijkstra(start, goal)
+
+	if !equalSlices(path, expectedPath) {
+		t.Errorf("Dijkstra() failed: expected path = %v, got path = %v", expectedPath, path)
+	}
+}
+
+func TestAStar(t *testing.T) {
+	g := NewGraph[int, int]()
+
+	// Add vertices and edges to the graph
+	g.AddEdge(1, 2, 10)
+	g.AddEdge(1, 3, 20)
+	g.AddEdge(2, 3, 30)
+	g.AddEdge(2, 4, 40)
+	g.AddEdge(3, 4, 50)
+	g.AddEdge(3, 5, 60)
+	g.AddEdge(4, 5, 70)
+
+	// Define the heuristic function
+	heuristic := func(vertex int) int {
+		return 0 // equivalent of Disjkstra's algorithm
+	}
+
+	// Test AStar for a valid path
+	start := 1
+	goal := 5
+	expectedPath := []int{1, 3, 5}
+	path := g.AStar(start, goal, heuristic)
+	if !equalSlices(path, expectedPath) {
+		t.Errorf("AStar() failed for valid path: expected %v, got %v", expectedPath, path)
+	}
+
+	// Test AStar for an invalid path
+	start = 1
+	goal = 6
+	expectedPath = []int{}
+	path = g.AStar(start, goal, heuristic)
+	if !equalSlices(path, expectedPath) {
+		t.Errorf("AStar() failed for invalid path: expected %v, got %v", expectedPath, path)
+	}
+}

maths/geometry.go

@@ -1,4 +1,4 @@
-package math
+package maths
 
 import "math"
 

maths/geometry_test.go

@@ -1,4 +1,4 @@
-package math
+package maths
 
 import "testing"
 

maths/maths.go

@@ -1,4 +1,4 @@
-package math
+package maths
 
 import (
 	"golang.org/x/exp/constraints"
@@ -111,3 +111,7 @@ func gaussianElimination(coefficients Matrix[float64], rhs []float64) {
 		}
 	}
 }
+
+func MaxInteger[T constraints.Integer]() T {
+	return T(^uint(T(0)) >> 1)
+}

maths/maths_test.go

@@ -1,4 +1,4 @@
-package math
+package maths
 
 import (
 	"testing"

maths/matrix.go

@@ -1,4 +1,4 @@
-package math
+package maths
 
 type Matrix[T comparable] [][]T
 

maths/matrix_test.go

@@ -1,4 +1,4 @@
-package math
+package maths
 
 import (
 	"reflect"