implement 8.7 and 8.8 python

Author: Alex Hagiopol

README.md

@@ -51,7 +51,7 @@ I need help on this project! PRs are very welcome. Here are some ways you can he
 5. Chapter 5 - Bit Manipulation: `7 / 7`  complete.
 6. Chapter 6 - Math and Logic: `0 / 10` complete.
 7. Chapter 7 - Object Oriented Design: `0 / 12` complete. 
-8. Chapter 8 - Recursion and Dynamic Programming: `7 / 14`  complete.
+8. Chapter 8 - Recursion and Dynamic Programming: `9 / 14`  complete.
 9. Chapter 9 - System Design and Scalability: N/A
 10. Chapter 10 - Sorting and Searching: `0 / 11` complete.
 11. Chapter 11 - Testing: N/A
@@ -62,7 +62,7 @@ I need help on this project! PRs are very welcome. Here are some ways you can he
 16. Chapter 16 - Moderate: `1 / 26` complete.
 17. Chapter 17 - Hard: `3 / 26` complete.
 
-Total: `51 / 148`
+Total: `53 / 148`
 
 #### C++ Solutions:
 1. Chapter 1 - Arrays and Strings: `1 / 9`  complete.    

python_solutions/chapter_08_recursion_and_dynamic_programming/problem_08_07_permutations_no_dups.py

@@ -1,2 +1,18 @@
-def permutations_no_dups():
-    pass
+def permutations_no_dups(string):
+    if len(string) <= 0:
+        return None
+    if len(string) == 1:
+        return [string[0]]
+    subproblem_permutations = permutations_no_dups(string[1:])
+    new_permutations = []
+    for subproblem_permutation in subproblem_permutations:
+        new_permutations.extend(create_permutations(subproblem_permutation, string[0]))
+    return new_permutations
+
+
+def create_permutations(string, inserted_character):
+    permutations = []
+    for index in range(0, len(string)):
+        permutations.append(string[0:index] + inserted_character + string[index:])
+    permutations.append(string + inserted_character)
+    return permutations

python_solutions/chapter_08_recursion_and_dynamic_programming/problem_08_08_permutations_with_dups.py

@@ -1,2 +1,23 @@
-def permutations_with_dups():
-    pass
+def permutations_with_dups(string):
+    hash_table = {}
+    permutations = []
+    for character in string:
+        if character in hash_table:
+            hash_table[character] += 1
+        else:
+            hash_table[character] = 1
+    helper('', hash_table, permutations)
+    return permutations
+
+
+def helper(string, hash_table, permutations):
+    if sum(hash_table.values()) <= 0:
+        permutations.append(string)
+    else:
+        for character in hash_table:
+            local_hash_table = hash_table.copy()
+            if local_hash_table[character] <= 1:
+                local_hash_table.pop(character, None)
+            else:
+                local_hash_table[character] -= 1
+            helper(string + character, local_hash_table, permutations)

tests.py

@@ -827,10 +827,25 @@ def test_problem_8_6(self):
         self.assertEqual(tower2.disks, [5, 4, 3, 2, 1])
 
     def test_problem_8_7(self):
-        pass
+        self.assertEqual(set(p_8_7.permutations_no_dups('a')), {'a'})
+        self.assertEqual(set(p_8_7.permutations_no_dups('al')), {'al', 'la'})
+        self.assertEqual(set(p_8_7.permutations_no_dups('ale')), {'ela', 'lea', 'lae', 'eal', 'ael', 'ale'})
+        self.assertEqual(set(p_8_7.permutations_no_dups('alex')), {'xela', 'exla', 'elxa', 'elax',
+                                                                   'xlea', 'lxea', 'lexa', 'leax',
+                                                                   'xlae', 'lxae', 'laxe', 'laex',
+                                                                   'xeal', 'exal', 'eaxl', 'ealx',
+                                                                   'xael', 'axel', 'aexl', 'aelx',
+                                                                   'xale', 'axle', 'alxe', 'alex'})
 
     def test_problem_8_8(self):
-        pass
+        self.assertEqual(set(p_8_8.permutations_with_dups('ala')), {'ala', 'laa', 'aal'})
+        self.assertEqual(set(p_8_8.permutations_with_dups('alaa')), {'aala', 'alaa', 'alaa', 'laaa',  'aala', 'aaal'})
+        self.assertEqual(set(p_8_8.permutations_with_dups('alex')), {'xela', 'exla', 'elxa', 'elax',
+                                                                   'xlea', 'lxea', 'lexa', 'leax',
+                                                                   'xlae', 'lxae', 'laxe', 'laex',
+                                                                   'xeal', 'exal', 'eaxl', 'ealx',
+                                                                   'xael', 'axel', 'aexl', 'aelx',
+                                                                   'xale', 'axle', 'alxe', 'alex'})
 
     def test_problem_8_9(self):
         pass