電腦科學中良好的問題解決很大程度上依賴高效的演算法，例如貪婪最佳優先搜尋（GBFS）。 GBFS 已經確立了作為尋路或優化問題的最佳解決方法的可信度。因此，我們在本文中深入討論 GBFS，同時探索其使用 C 的實作方法。
void greedyBestFirstSearch(Graph graph, Node startNode, Node goalNode);
貪心最佳優先搜尋演算法旨在找到圖中從給定起始節點到目標節點的路徑。以下是該演算法的一般步驟 -
初始化一個空的優先權佇列。
將起始節點放入優先權佇列。
建立一個空集合來追蹤造訪過的節點。
當優先權佇列不為空時 -
將優先權最高的節點從佇列中出列。
如果出隊的節點是目標節點，則演算法終止，並找到路徑。
否則，將出隊節點標記為已存取。
將出隊節點的所有未存取的鄰居節點放入優先權佇列中。
如果優先權佇列在到達目標節點之前變空，則不存在路徑。
#include <iostream>
#include <queue>
#include <cmath>
#include <vector>
#include <unordered_set>
using namespace std;
// Structure to represent a node in the graph
struct Node {
int x, y; // Coordinates of the node
int cost; // Cost to reach this node
};
// Euclidean distance heuristic function
double euclideanDistance(int x1, int y1, int x2, int y2) {
return sqrt(pow((x1 - x2), 2) + pow((y1 - y2), 2));
}
// Custom comparison function for nodes in the priority queue
struct NodeCompare {
bool operator()(const Node& node1, const Node& node2) const {
return node1.cost > node2.cost;
}
};
// Greedy Best-First Search function
void greedyBestFirstSearch(vector<vector<int>>& graph, Node start, Node goal) {
int rows = graph.size();
int cols = graph[0].size();
// Priority queue for nodes to be explored
priority_queue<Node, vector<Node>, NodeCompare> pq;
// Visited nodes set
unordered_set<int> visited;
// Add the start node to the priority queue
pq.push(start);
while (!pq.empty()) {
// Get the node with the lowest cost
Node current = pq.top();
pq.pop();
// Check if the current node is the goal node
if (current.x == goal.x && current.y == goal.y) {
cout << "Goal node reached!" << endl;
return;
}
// Mark the current node as visited
int nodeId = current.x * cols + current.y;
visited.insert(nodeId);
// Explore the neighboring nodes
int dx[] = {-1, 1, 0, 0}; // Possible x-direction movements
int dy[] = {0, 0, -1, 1}; // Possible y-direction movements
for (int i = 0; i < 4; i++) {
int newX = current.x + dx[i];
int newY = current.y + dy[i];
// Check if the neighboring node is within the graph boundaries
if (newX >= 0 && newX < rows && newY >= 0 && newY < cols) {
// Calculate the heuristic value for the neighboring node
double heuristicValue = euclideanDistance(newX, newY, goal.x, goal.y);
// Check if the neighboring node has not been visited
if (visited.find(newX * cols + newY) == visited.end()) {
// Create a new node for the neighboring position
Node neighbor;
neighbor.x = newX;
neighbor.y = newY;
neighbor.cost = current.cost + graph[newX][newY];
// Add the neighboring node to the priority queue
pq.push(neighbor);
}
}
}
}
cout << "Goal node not reachable!" << endl;
}
int main() {
// Example graph represented as a 2D vector
vector<vector<int>> graph = {
{3, 5, 1, 2},
{1, 3, 2, 4},
{5, 2, 6, 7},
{4, 3, 1, 2}
};
Node start;
start.x = 0; // Starting x-coordinate
start.y = 0; // Starting y-coordinate
start.cost = 0; // Cost to reach the starting node
Node goal;
goal.x = 3; // Goal x-coordinate
goal.y = 3; // Goal y-coordinate
// Run Greedy Best-First Search algorithm
greedyBestFirstSearch(graph, start, goal);
return 0;
}
Goal node reached!
這段程式碼包含兩個關鍵元素。首先，它包含 Graph 類別的定義，該類別表示使用鄰接表的圖結構。
其次，它引入了 CompareEuclideanDistance - 一個自訂比較器，用於透過使用歐幾里德距離公式估計節點與目標節點的距離來評估節點。
greedyBestFirstSearch 函數實作貪婪最佳優先搜尋演算法。它使用優先權隊列根據節點的啟發值來儲存節點。
此演算法首先將起始節點放入優先權佇列中。
在每次迭代中，它將最高優先順序的節點出隊並檢查它是否是目標節點。
如果找到目標節點，則會顯示「路徑已找到！」訊息被列印。否則，演算法將出隊的節點標記為已訪問，並將其未訪問的相鄰節點放入佇列。
如果優先權佇列變空而沒有找到目標節點，則會顯示「不存在路徑！」訊息已列印。
main函數透過建立圖表、定義起始節點和目標節點以及呼叫greedyBestFirstSearch函數來演示了演算法的用法。
我們解決此問題的策略需要使用依賴曼哈頓距離概念的啟發式函數。這種距離度量有時稱為出租車距離，涉及將節點之間的水平和垂直距離相加。
#include <iostream>
#include <queue>
#include <cmath>
#include <vector>
#include <unordered_set>
using namespace std;
// Structure to represent a node in the graph
struct Node {
int x, y; // Coordinates of the node
int cost; // Cost to reach this node
};
// Manhattan distance heuristic function
int manhattanDistance(int x1, int y1, int x2, int y2) {
return abs(x1 - x2) + abs(y1 - y2);
}
// Custom comparison function for nodes in the priority queue
struct NodeCompare {
bool operator()(const Node& node1, const Node& node2) const {
return node1.cost > node2.cost;
}
};
// Greedy Best-First Search function
void greedyBestFirstSearch(vector<vector<int>>& graph, Node start, Node goal) {
int rows = graph.size();
int cols = graph[0].size();
// Priority queue for nodes to be explored
priority_queue<Node, vector<Node>, NodeCompare> pq;
// Visited nodes set
unordered_set<int> visited;
// Add the start node to the priority queue
pq.push(start);
while (!pq.empty()) {
// Get the node with the lowest cost
Node current = pq.top();
pq.pop();
// Check if the current node is the goal node
if (current.x == goal.x && current.y == goal.y) {
cout << "Goal node reached!" << endl;
return;
}
// Mark the current node as visited
int nodeId = current.x * cols + current.y;
visited.insert(nodeId);
// Explore the neighboring nodes
int dx[] = {-1, 1, 0, 0}; // Possible x-direction movements
int dy[] = {0, 0, -1, 1}; // Possible y-direction movements
for (int i = 0; i < 4; i++) {
int newX = current.x + dx[i];
int newY = current.y + dy[i];
// Check if the neighboring node is within the graph boundaries
if (newX >= 0 && newX < rows && newY >= 0 && newY < cols) {
// Calculate the heuristic value for the neighboring node
int heuristicValue = manhattanDistance(newX, newY, goal.x, goal.y);
// Check if the neighboring node has not been visited
if (visited.find(newX * cols + newY) == visited.end()) {
// Create a new node for the neighboring position
Node neighbor;
neighbor.x = newX;
neighbor.y = newY;
neighbor.cost = current.cost + graph[newX][newY];
// Add the neighboring node to the priority queue
pq.push(neighbor);
}
}
}
}
cout << "Goal node not reachable!" << endl;
}
int main() {
// Example graph represented as a 2D vector
vector<vector<int>> graph = {
{3, 5, 1, 2},
{1, 3, 2, 4},
{5, 2, 6, 7},
{4, 3, 1, 2}
};
Node start;
start.x = 0; // Starting x-coordinate
start.y = 0; // Starting y-coordinate
start.cost = 0; // Cost to reach the starting node
Node goal;
goal.x = 3; // Goal x-coordinate
goal.y = 3; // Goal y-coordinate
// Run Greedy Best-First Search algorithm
greedyBestFirstSearch(graph, start, goal);
return 0;
}
Goal node reached!
程式碼遵循與方法 1 類似的結構，但使用自訂比較器 CompareManhattanDistance，該比較器使用曼哈頓距離公式根據到目標節點的估計距離來比較節點。
greedyBestFirstSearch 函數使用曼哈頓距離啟發式實現貪婪最佳優先搜尋演算法。
main函數示範了演算法的使用，建立一個圖，定義起始節點和目標節點，並呼叫greedyBestFirstSearch函數。
在本文中，我們探討了貪婪最佳優先搜尋演算法及其在 C 中的實作。透過採用這些方法，程式設計師可以有效地找到圖中的路徑並解決最佳化問題。啟發式函數的選擇，例如歐氏距離或曼哈頓距離，可以顯著影響演算法在不同場景下的表現。
以上是貪婪最佳優先搜尋演算法（Greedy Best-First Search Algorithm）在C++中的實現的詳細內容。更多資訊請關注PHP中文網其他相關文章！
