Merge pull request #1033 from fhlasek/dijkstra

fix: linter for dijkstra

graph/dijkstra.cpp

@@ -1,52 +1,180 @@
-#include <cstdio>
+/**
+ * @file
+ * @brief [Graph Dijkstras Shortest Path Algorithm
+ * (Dijkstra's Shortest Path)]
+ * (https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+ *
+ * @author [Ayaan Khan](http://github.com/ayaankhan98)
+ *
+ * @details
+ * Dijkstra's Algorithm is used to find the shortest path from a source
+ * vertex to all other reachable vertex in the graph.
+ * The algorithm initially assumes all the nodes are unreachable from the
+ * given source vertex so we mark the distances of all vertices as INF
+ * (infinity) from source vertex (INF / infinity denotes unable to reach).
+ *
+ * in similar fashion with BFS we assume the distance of source vertex as 0
+ * and pushes the vertex in a priority queue with it's distance.
+ * we maintain the priority queue as a min heap so that we can get the
+ * minimum element at the top of heap
+ *
+ * Basically what we do in this algorithm is that we try to minimize the
+ * distances of all the reachable vertices from the current vertex, look
+ * at the code below to understand in better way.
+ *
+ */
+#include <cassert>
 #include <iostream>
+#include <limits>
 #include <queue>
+#include <utility>
 #include <vector>
-using namespace std;
+#include <memory>
-#define INF 10000010
-vector<pair<int, int>> graph[5 * 100001];
-int dis[5 * 100001];
-int dij(vector<pair<int, int>> *v, int s, int *dis) {
-    priority_queue<pair<int, int>, vector<pair<int, int>>,
-                   greater<pair<int, int>>>
-        pq;
-    // source distance to zero.
-    pq.push(make_pair(0, s));
-    dis[s] = 0;
-    int u;
-    while (!pq.empty()) {
-        u = (pq.top()).second;
-        pq.pop();
-        for (vector<pair<int, int>>::iterator it = v[u].begin();
-             it != v[u].end(); it++) {
-            if (dis[u] + it->first < dis[it->second]) {
-                dis[it->second] = dis[u] + it->first;
-                pq.push(make_pair(dis[it->second], it->second));
-            }
-        }
-    }
-}
-int main() {
-    int m, n, l, x, y, s;
-    // n--> number of nodes , m --> number of edges
-    cin >> n >> m;
-    for (int i = 0; i < m; i++) {
-        // input edges.
-        scanf("%d%d%d", &x, &y, &l);
-        graph[x].push_back(make_pair(l, y));
-        graph[y].push_back(
-            make_pair(l, x));  // comment this line for directed graph
-    }
-    // start node.
-    scanf("%d", &s);
-    // intialise all distances to infinity.
-    for (int i = 1; i <= n; i++) dis[i] = INF;
-    dij(graph, s, dis);
 
-    for (int i = 1; i <= n; i++)
+constexpr int64_t INF = std::numeric_limits<int64_t>::max();
-        if (dis[i] == INF)
+
-            cout << "-1 ";
+/**
-        else
+ * @namespace graph
-            cout << dis[i] << " ";
+ * @brief Graph Algorithms
-    return 0;
+ */
+
+namespace graph {
+  /**
+   * @brief Function that add edge between two nodes or vertices of graph
+   *
+   * @param u any node or vertex of graph
+   * @param v any node or vertex of graph
+   */
+  void addEdge(std::vector<std::vector<std::pair<int, int>>> *adj, int u, int v,
+      int w) {
+    (*adj)[u - 1].push_back(std::make_pair(v - 1, w));
+    // (*adj)[v - 1].push_back(std::make_pair(u - 1, w));
+  }
+
+  /**
+   * @brief Function runs the dijkstra algorithm for some source vertex and
+   * target vertex in the graph and returns the shortest distance of target
+   * from the source.
+   *
+   * @param adj input graph
+   * @param s source vertex
+   * @param t target vertex
+   *
+   * @return shortest distance if target is reachable from source else -1 in
+   * case if target is not reachable from source.
+   */
+  int dijkstra(std::vector<std::vector<std::pair<int, int>>> *adj, int s, int t) {
+    /// n denotes the number of vertices in graph
+    int n = adj->size();
+
+    /// setting all the distances initially to INF
+    std::vector<int64_t> dist(n, INF);
+
+    /// creating a min heap using priority queue
+    /// first element of pair contains the distance
+    /// second element of pair contains the vertex
+    std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>,
+      std::greater<std::pair<int, int>>>
+        pq;
+
+    /// pushing the source vertex 's' with 0 distance in min heap
+    pq.push(std::make_pair(0, s));
+
+    /// marking the distance of source as 0
+    dist[s] = 0;
+
+    while (!pq.empty()) {
+      /// second element of pair denotes the node / vertex
+      int currentNode = pq.top().second;
+
+      /// first element of pair denotes the distance
+      int currentDist = pq.top().first;
+
+      pq.pop();
+
+      /// for all the reachable vertex from the currently exploring vertex
+      /// we will try to minimize the distance
+      for (std::pair<int, int> edge : (*adj)[currentNode]) {
+        /// minimizing distances
+        if (currentDist + edge.second < dist[edge.first]) {
+          dist[edge.first] = currentDist + edge.second;
+          pq.push(std::make_pair(dist[edge.first], edge.first));
+        }
+      }
+    }
+    if (dist[t] != INF) {
+      return dist[t];
+    }
+    return -1;
+  }
+}  // namespace graph
+
+/** Function to test the Algorithm */
+void tests() {
+  std::cout << "Initiatinig Predefined Tests..." << std::endl;
+  std::cout << "Initiating Test 1..." << std::endl;
+  std::vector<std::vector<std::pair<int, int>>> adj1(
+      4, std::vector<std::pair<int, int>>());
+  graph::addEdge(&adj1, 1, 2, 1);
+  graph::addEdge(&adj1, 4, 1, 2);
+  graph::addEdge(&adj1, 2, 3, 2);
+  graph::addEdge(&adj1, 1, 3, 5);
+
+  int s = 1, t = 3;
+  assert(graph::dijkstra(&adj1, s - 1, t - 1) == 3);
+  std::cout << "Test 1 Passed..." << std::endl;
+
+  s = 4, t = 3;
+  std::cout << "Initiating Test 2..." << std::endl;
+  assert(graph::dijkstra(&adj1, s - 1, t - 1) == 5);
+  std::cout << "Test 2 Passed..." << std::endl;
+
+  std::vector<std::vector<std::pair<int, int>>> adj2(
+      5, std::vector<std::pair<int, int>>());
+  graph::addEdge(&adj2, 1, 2, 4);
+  graph::addEdge(&adj2, 1, 3, 2);
+  graph::addEdge(&adj2, 2, 3, 2);
+  graph::addEdge(&adj2, 3, 2, 1);
+  graph::addEdge(&adj2, 2, 4, 2);
+  graph::addEdge(&adj2, 3, 5, 4);
+  graph::addEdge(&adj2, 5, 4, 1);
+  graph::addEdge(&adj2, 2, 5, 3);
+  graph::addEdge(&adj2, 3, 4, 4);
+
+  s = 1, t = 5;
+  std::cout << "Initiating Test 3..." << std::endl;
+  assert(graph::dijkstra(&adj2, s - 1, t - 1) == 6);
+  std::cout << "Test 3 Passed..." << std::endl;
+  std::cout << "All Test Passed..." << std::endl << std::endl;
+}
+
+/** Main function */
+int main() {
+  // running predefined tests
+  tests();
+
+  int vertices = int(), edges = int();
+  std::cout << "Enter the number of vertices : ";
+  std::cin >> vertices;
+  std::cout << "Enter the number of edges : ";
+  std::cin >> edges;
+
+  std::vector<std::vector<std::pair<int, int>>> adj(
+      vertices, std::vector<std::pair<int, int>>());
+
+  int u = int(), v = int(), w = int();
+  while (edges--) {
+    std::cin >> u >> v >> w;
+    graph::addEdge(&adj, u, v, w);
+  }
+
+  int s = int(), t = int();
+  std::cin >> s >> t;
+  int dist = graph::dijkstra(&adj, s - 1, t - 1);
+  if (dist == -1) {
+    std::cout << "Target not reachable from source" << std::endl;
+  } else {
+    std::cout << "Shortest Path Distance : " << dist << std::endl;
+  }
+  return 0;
 }