A star

Greedy/A-Star Shortest Path/README.md

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+# A\* Shortest Path Algorithm
+
+The A\* (A Star) algorithm is a popular and efficient search algorithm used to find the shortest path between nodes in a graph. It is widely used in various applications, such as pathfinding in video games, robotics, and network routing
+
+![](https://www.101computing.net/wp/wp-content/uploads/A-Star-Search-Algorithm-Step-1.png)
+
+## Overview
+A\* combines features of Dijkstra's Algorithm and Greedy Best-First Search. It uses a heuristic to prioritize paths that appear to lead most directly to the goal, which often allows it to find the shortest path more efficiently than Dijkstra's algorithm alone. The algorithm calculates the cost of reaching a node based on the actual cost from the start node and an estimated cost to the goal.
+
+## Key Concepts
+G-Score: The cost of the path from the start node to the current node.
+H-Score (Heuristic): An estimate of the cost from the current node to the goal.
+F-Score: The sum of G-Score and H-Score. A\* selects the node with the lowest F-Score to explore next.
+
+## How It Works
+Initialization: Start with the initial node. The G-Score is 0, and the F-Score is equal to the heuristic value for reaching the goal.
+
+Exploration: For each node, calculate the G-Score and H-Score. Update the F-Score for each adjacent node.
+
+Path Selection: Select the node with the lowest F-Score for exploration. If the goal is reached, the algorithm terminates.
+
+Repeat: Continue exploring nodes, updating scores, and selecting the next node until the goal is found or all possible paths are exhausted.
+
+## References
+trekhleb/javascript-algorithms - A* Implementation
+Wikipedia - A* Search Algorithm
+YouTube - A* Pathfinding by Amit Patel
+YouTube - A* Algorithm by Sebastian Lague

Greedy/A-Star Shortest Path/code.js

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+// import visualization libraries {
+const {
+  Tracer,
+  Array1DTracer,
+  GraphTracer,
+  Randomize,
+  Layout,
+  VerticalLayout,
+} = require("algorithm-visualizer");
+// }
+
+const G = Randomize.Graph({
+  N: 5,
+  ratio: 0.6,
+  directed: false,
+  weighted: true,
+});
+const MAX_VALUE = Infinity;
+const S = []; // S[end] returns the distance from start node to end node
+for (let i = 0; i < G.length; i++) S[i] = MAX_VALUE;
+
+// Heuristic function based on actual distances between nodes
+function heuristic(node, goal) {
+  if (G[node][goal] !== 0) {
+    return G[node][goal]; // Use the direct edge weight if available
+  } else {
+    // Use an alternative if no direct edge exists (optional)
+    let minEdge = MAX_VALUE;
+    for (let i = 0; i < G.length; i++) {
+      if (G[node][i] !== 0 && G[node][i] < minEdge) {
+        minEdge = G[node][i];
+      }
+    }
+    return minEdge !== MAX_VALUE ? minEdge : 1; // Use the smallest edge connected to the node as a fallback heuristic
+  }
+}
+
+// define tracer variables {
+const tracer = new GraphTracer().directed(false).weighted();
+const tracerS = new Array1DTracer();
+Layout.setRoot(new VerticalLayout([tracer, tracerS]));
+tracer.set(G);
+tracerS.set(S);
+Tracer.delay();
+// }
+
+function AStar(start, end) {
+  let minIndex;
+  let minDistance;
+  const D = []; // D[i] indicates whether the i-th node is discovered or not
+  const openSet = []; // Nodes to be evaluated
+  const previous = []; // Array to store the previous node for path reconstruction
+  for (let i = 0; i < G.length; i++) {
+    D.push(false);
+    previous.push(null);
+  }
+  S[start] = 0; // Starting node is at distance 0 from itself
+  openSet.push({ node: start, fCost: heuristic(start, end) });
+
+  // visualize {
+  tracerS.patch(start, S[start]);
+  Tracer.delay();
+  tracerS.depatch(start);
+  tracerS.select(start);
+  // }
+
+  while (openSet.length > 0) {
+    // Find the node in the open set with the lowest fCost (gCost + hCost)
+    minIndex = openSet.reduce((prev, curr, idx, arr) => {
+      return arr[prev].fCost < curr.fCost ? prev : idx;
+    }, 0);
+
+    const current = openSet[minIndex].node;
+
+    if (current === end) {
+      break; // If we reached the goal, stop
+    }
+
+    openSet.splice(minIndex, 1);
+    D[current] = true;
+
+    // visualize {
+    tracerS.select(current);
+    tracer.visit(current);
+    Tracer.delay();
+    // }
+
+    // For every unvisited neighbor of the current node
+    for (let i = 0; i < G.length; i++) {
+      if (G[current][i] && !D[i]) {
+        const tentative_gCost = S[current] + G[current][i];
+        if (tentative_gCost < S[i]) {
+          S[i] = tentative_gCost;
+          previous[i] = current; // Store the previous node
+          const fCost = tentative_gCost + heuristic(i, end);
+          openSet.push({ node: i, fCost });
+
+          // visualize {
+          tracerS.patch(i, S[i]);
+          tracer.visit(i, current, S[i]);
+          Tracer.delay();
+          tracerS.depatch(i);
+          tracer.leave(i, current);
+          Tracer.delay();
+          // }
+        }
+      }
+    }
+    // visualize {
+    tracer.leave(current);
+    Tracer.delay();
+    // }
+  }
+
+  // If end is reached, reconstruct the path
+  if (S[end] !== MAX_VALUE) {
+    let path = [];
+    for (let at = end; at !== null; at = previous[at]) {
+      path.push(at);
+    }
+    path.reverse();
+
+    // visualize the final path
+    for (let i = 0; i < path.length; i++) {
+      tracer.select(path[i]);
+      if (i > 0) {
+        tracer.visit(path[i], path[i - 1]);
+      }
+      Tracer.delay();
+    }
+  }
+}
+
+const s = Randomize.Integer({ min: 0, max: G.length - 1 }); // s = start node
+let e; // e = end node
+do {
+  e = Randomize.Integer({ min: 0, max: G.length - 1 });
+} while (s === e);
+Tracer.delay();
+AStar(s, e);