Dijkstras algorithm (#161)

* Renaming files according to naming convention

* Added Dijkstra's Algorithm

Algorithms/Dijkstra's.js

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+/**
+ * Author: Samarth Jain
+ * Dijkstra's Algorithm implementation in JavaScript
+ * Dijkstra's Algorithm calculates the minimum distance between two nodes.
+ * It is used to find the shortes path.
+ * It uses graph data structure.
+ */
+
+function createGraph (V, E) {
+  // V - Number of vertices in graph
+  // E - Number of edges in graph (u,v,w)
+  const adjList = [] // Adjacency list
+  for (let i = 0; i < V; i++) {
+    adjList.push([])
+  }
+  for (let i = 0; i < E.length; i++) {
+    adjList[E[i][0]].push([E[i][1], E[i][2]])
+    adjList[E[i][1]].push([E[i][0], E[i][2]])
+  }
+  return adjList
+}
+
+function djikstra (graph, V, src) {
+  const vis = Array(V).fill(0)
+  const dist = []
+  for (let i = 0; i < V; i++) dist.push([10000, -1])
+  dist[src][0] = 0
+
+  for (let i = 0; i < V - 1; i++) {
+    let mn = -1
+    for (let j = 0; j < V; j++) {
+      if (vis[j] === 0) {
+        if (mn === -1 || dist[j][0] < dist[mn][0]) mn = j
+      }
+    }
+
+    vis[mn] = 1
+    for (let j = 0; j < graph[mn].length; j++) {
+      const edge = graph[mn][j]
+      if (vis[edge[0]] === 0 && dist[edge[0]][0] > dist[mn][0] + edge[1]) {
+        dist[edge[0]][0] = dist[mn][0] + edge[1]
+        dist[edge[0]][1] = mn
+      }
+    }
+  }
+
+  return dist
+}
+
+const V = 9
+const E = [
+  [0, 1, 4],
+  [0, 7, 8],
+  [1, 7, 11],
+  [1, 2, 8],
+  [7, 8, 7],
+  [6, 7, 1],
+  [2, 8, 2],
+  [6, 8, 6],
+  [5, 6, 2],
+  [2, 5, 4],
+  [2, 3, 7],
+  [3, 5, 14],
+  [3, 4, 9],
+  [4, 5, 10]
+]
+
+const graph = createGraph(V, E)
+const distances = djikstra(graph, V, 0)
+
+/**
+ * The first value in the array determines the minimum distance and the
+ * second value represents the parent node from which the minimum distance has been calculated
+ */
+
+console.log(distances)

Algorithms/SieveOfEratosthenes.js

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+function sieveOfEratosthenes (n) {
+  /*
+     * Calculates prime numbers till a number n
+     * :param n: Number upto which to calculate primes
+     * :return: A boolean list contaning only primes
+     */
+  const primes = new Array(n + 1)
+  primes.fill(true) // set all as true initially
+  primes[0] = primes[1] = false // Handling case for 0 and 1
+  const sqrtn = Math.ceil(Math.sqrt(n))
+  for (let i = 2; i <= sqrtn; i++) {
+    if (primes[i]) {
+      for (let j = 2 * i; j <= n; j += i) {
+        primes[j] = false
+      }
+    }
+  }
+  return primes
+}
+
+function main () {
+  const n = 69 // number till where we wish to find primes
+  const primes = sieveOfEratosthenes(n)
+  for (let i = 2; i <= n; i++) {
+    if (primes[i]) {
+      console.log(i)
+    }
+  }
+}
+
+main()