Add coding exercises for Facebook interviews

Add attempts at solving coding problems to Briefcase.

scratch/facebook/find-duplicate-optimize-for-space.py

@@ -0,0 +1,22 @@
+import random
+
+def find_duplicate(xs):
+    print(xs)
+    # entry point in our cycle is the duplicate
+    i = xs[0]
+    j = xs[xs[0]]
+    while i != j:
+        print(i, xs[i], j, xs[j])
+        i = xs[i]
+        j = xs[xs[j]]
+    # detect cycle
+    j = 0
+    while i != j:
+        i = xs[i]
+        j = xs[j]
+    return xs[i]
+
+n = random.randint(5, 10)
+xs = [random.randint(0, n - 1) for _ in range(n)]
+result = find_duplicate(xs)
+print(xs, result)