Add coding exercises for Facebook interviews

Add attempts at solving coding problems to Briefcase.

scratch/facebook/dijkstras.py

@@ -0,0 +1,38 @@
+from heapq import heappush, heappop
+import random
+
+# Dijkstra's algorithm will traverse a directed graph with weighted edges. If
+# the edges aren't weighted, we can pretend that each edges weighs 1. The
+# algorithm will find the shortest path between points A and B.
+
+def dijkstra(a, b, graph):
+    h = []
+    seen = set()
+    heappush(h, (0, a, [a], []))
+    while h:
+        km, x, path, steps = heappop(h)
+
+        if x == b:
+            for a, b, d in steps:
+                print("{} -> {} => {}".format(a, b, d))
+            return path, km
+
+        seen.add(x)
+        for c, dist in graph[x]:
+            if c not in seen:
+                heappush(h, (km + dist, c, path + [c], steps + [(x, c, dist)]))
+    return [], float('inf')
+
+graph = {
+    1: [(3, 9), (2, 7), (6, 14)],
+    2: [(1, 7), (3, 10), (4, 15)],
+    3: [(1, 9), (6, 2), (4, 11), (2, 10)],
+    4: [(5, 6), (2, 15), (3, 11)],
+    5: [(4, 6), (6, 9)],
+    6: [(5, 9), (3, 2), (1, 14)],
+}
+
+beg = random.choice(list(graph.keys()))
+end = random.choice(list(graph.keys()))
+print("Searching for the shortest path from {} -> {}".format(beg, end))
+print(dijkstra(beg, end, graph))