Create OBST_dp.py

Author: careermonk

dynamic-programming/OBST_dp.py

@@ -0,0 +1,58 @@
+# Copyright (c) June 02, 2017 CareerMonk Publications and others.
+# E-Mail           		: [email protected]
+# Creation Date    		: 2017-06-02 06:15:46
+# Last modification		: 2017-06-02
+# Modified by		        : Narasimha Karumanchi
+# Book Title			: Algorithm Design Techniques
+# Warranty         		: This software is provided "as is" without any
+# 				 warranty; without even the implied warranty of
+# 				 merchantability or fitness for a particular purpose.
+
+def OBST(A, F, get_bst=False):
+    n = len(A)
+    table = [[None] * n for _ in xrange(n)]
+    for i in xrange(n):
+        table[i][i] = (F[i], i)
+    # let optimal BST for subproblem A[i..j] be T
+    # if table[i][j] = (cost, keyidx)
+    # then cost is the cost of T, keyidx is index of the root key of T
+    for s in xrange(1, n):
+        for i in xrange(n-s):
+            # compute cost for A[i..i+s]
+            minimal, root = float('inf'), -1
+            # search root with minimal cost
+            freq_sum = sum(F[x] for x in xrange(i, i+s+1))
+            for r in xrange(i, i+s+1):
+                left = 0 if r == i else table[i][r-1][0]
+                right = 0 if r == i+s else table[r+1][i+s][0]
+                cost = left + right + freq_sum
+                if cost < minimal:
+                    minimal = cost
+                    root = r
+            table[i][i+s] = (minimal, root)
+    if get_bst:
+        tree = {}
+        stack = [(0, n-1)]
+        while stack:
+            i, j = stack.pop()
+            root = table[i][j][1]
+            left, right = None, None
+            if root != i:
+                stack.append((i, root-1))
+                left = table[i][root-1][1]
+            if root != j:
+                stack.append((root+1, j))
+                right = table[root+1][j][1]
+            if left is None and right is None:
+                tree[root] = None
+            else:
+                tree[root] = (left, right)
+        return (table[0][n-1][0], tree)
+
+    return table[0][n-1][0]
+
+if __name__ == '__main__':
+    assert OBST([0, 1], [30, 40]) == 100
+    assert OBST(['a', 'b', 'c'], [30, 10, 40]) == 130
+    assert OBST([0, 1], [0.6, 0.4]) == 1.4
+    assert OBST(range(1, 8), [0.05, 0.4, 0.08, 0.04, 0.1, 0.1, 0.23]) == 2.18