Implement a suffix tree

While it took me awhile to implement, this exercise was definitely worth
doing. I think there should be a more elegant way to construct the tree using
maybe a stack, but I couldn't find it.

All of this was part of a larger effort to search a string for a variety of
patterns. The solution is to compile the string into a suffix tree and then
search the suffix tree for each of the patterns.

I'm glad I didn't gloss over this exercise.

scratch/facebook/hard/suffix-tree.py

@@ -0,0 +1,64 @@
+import random
+
+def exists(pattern, tree):
+    """
+    Return true if `pattern` exists in `tree`.
+    """
+    if len(pattern) == 0:
+        return True
+    if len(pattern) == 1:
+        for branch in tree:
+            if branch[0] == pattern[0]:
+                return True
+        return False
+    for branch in tree:
+        if branch[0] == pattern[0]:
+            return exists(pattern[1:], branch[1])
+    return False
+
+# Branch :: (Char, [Branch])
+# SuffixTree :: [Branch]
+
+def suffix_tree(xs):
+    """
+    Create a suffix tree from the input string, `xs`.
+    """
+    root = []
+    for i in range(len(xs)):
+        curr = xs[i:]
+        parent = root
+        for c1 in curr:
+            grafted = False
+            for c2, children in parent:
+                if c1 == c2:
+                    grafted = True
+                    parent = children
+            if grafted:
+                continue
+            else:
+                children = []
+                child = (c1, children)
+                parent.append(child)
+                parent = children
+    return root
+
+
+################################################################################
+# Tests
+################################################################################
+
+x = random.choice(["burrito", "pizza", "guacamole"])
+tree = suffix_tree(x)
+for branch in tree:
+    print(branch)
+
+for _ in range(3):
+    n = len(x)
+    i, j = random.randint(0, n), random.randint(0, n)
+    pattern = x[min(i, j):max(i, j)]
+    print("Checking \"{}\" for \"{}\" ...".format(x, pattern))
+    print("Result: {}".format(exists(pattern, tree)))
+    pattern = random.choice(["foo", "bar", "baz"])
+    print("Checking \"{}\" for \"{}\" ...".format(x, pattern))
+    print("Result: {}".format(exists(pattern, tree)))
+    print()