Merge pull request #170 from code4tomorrow/dsa-practice

DSA Practice Problems

3_advanced/chapter17/solutions/min_superset.py

@@ -2,6 +2,7 @@
 # of minimum size which is the superset of all the given sets.
 # Implement the following method:
 
+
 # superset calcuated using Principle of Inclusion and Exclusion
 # sets: a vector containing 3 sets
 def findMinSupersetLength(sets):

dsa/chapter1/practice/time_complexity.py

@@ -0,0 +1,25 @@
+"""
+For each of the following time complexities, create
+a function that has that time complexity.
+"""
+
+# time complexity: O(1)
+# your code here
+
+
+# time complexity: O(n)
+# your code here
+
+
+# time complexity: O(n^2)
+# your code here
+
+
+# time complexity: O(log(n))
+# your code here
+
+# time complexity: O(n * log(n))
+# your code here
+
+# time complexity: O(2**n)
+# your code here

dsa/chapter1/practice/time_complexity_questions.py

@@ -0,0 +1,74 @@
+"""
+Classify the following code examples with their
+runtimes. Write your responses as comments.
+"""
+
+
+def do_something():
+    # runtime for do_something() is O(1)
+    pass
+
+
+# what is the runtime for example 1?
+def example_one(n):
+    for i in range(n):
+        do_something()
+
+
+# what is the runtime for example 2?
+def example_two(n):
+    do_something()
+
+
+# what is the runtime for example 3?
+def example_three(n):
+    for i in range(n):
+        for x in range(i):
+            do_something()
+
+
+# what is the runtime for example 4?
+def example_four(n):
+    for i in range(n // 2):
+        do_something()
+
+
+# what is the runtime for example 5?
+def example_five(n):
+    i = 0
+    while i < n:
+        do_something()
+        i *= 2
+
+
+# what is the runtime for example 6?
+def example_six(n):
+    for i in range(10):
+        do_something()
+
+
+# what is the runtime for example 7?
+def example_seven(n):
+    for i in range(2**n):
+        do_something()
+
+
+# what is the runtime for example 8?
+def example_eight(n):
+    for i in range(n):
+        for x in range(7):
+            do_something()
+
+
+# what is the runtime for example 9?
+def example_nine(n):
+    for i in range(n):
+        example_one(n)
+
+
+# what is the runtime for example 10?
+def example_ten(n):
+    i = 0
+    while i < n:
+        do_something()
+        i += 2

dsa/chapter1/solutions/time_complexity.py

@@ -0,0 +1,99 @@
+"""
+For each of the following time complexities, create
+a function that has that time complexity. The following solutions
+are examples and not the only ways to have done this problem.
+"""
+
+
+# time complexity: O(1)
+def double_my_number(number):
+    x = number
+    x *= 2
+    return x
+
+
+# time complexity: O(n)
+def sum_till_n(n):
+    total = 0
+    for i in range(n):
+        total += i
+
+    return total
+
+
+# time complexity: O(n^2)
+def print_triangle(n):
+    for row in range(n):
+        for column in range(row):
+            print("* ", end="")
+        print()
+
+
+# time complexity: O(log(n))
+def sum_powers_of_two(max_number):
+    power_of_two = 1
+    total = 0
+
+    while power_of_two < max_number:
+        total += power_of_two
+        power_of_two *= 2
+
+    return total
+
+
+# time complexity: O(n * log(n))
+def sum_many_powers_of_two(number_of_times):
+    total = 0
+    for i in range(number_of_times):
+        # since sum_powers_of_two is O(log(n))and this for loop is O(n),
+        # the resulting time complexity is O(n * log(n))
+        total += sum_powers_of_two(i)
+
+    return total
+
+
+# time complexity: O(2**n)
+def get_binary_combinations(number_of_digits):
+    """
+    Gets the combinations of binary numbers with number_of_digits digits
+    For example, get_binary_combinations(2) should give
+    ["00", "01", "10", "11"].
+
+    """
+    cur_options = ["0", "1"]
+    next_options = []
+
+    operations = 0
+
+    # In total, this is O(2**n). It may be a bit confusing, but
+    # this is O(2**n) because of the fact that the current options
+    # doubles each time we go through the for loop, so it has to
+    # spend twice as long each time.
+    for i in range(number_of_digits - 1):
+        for option in cur_options:
+            next_options.append(option + "0")
+            next_options.append(option + "1")
+            operations += 1
+        cur_options = next_options
+        next_options = []
+
+    print(f"took {operations} operations")
+    return cur_options
+
+
+# for comparison, here's a very easy to understand
+# function with O(2**n) runtime.
+def regular_o_2_to_the_n(n):
+    operations = 0
+    for i in range(2**n):
+        operations += 1
+    print(f"took {operations} operations")
+
+
+# if you actually don't believe that get_binary_combinations is O(2**n),
+# try running the below.
+# as you can see, they have similar operational cost,
+# meaning that get_binary_combinations really is O(2**n)
+# times = 20
+# get_binary_combinations(times)
+# regular_o_2_to_the_n(times)

dsa/chapter1/solutions/time_complexity_questions.py

@@ -0,0 +1,84 @@
+"""
+Classify the following code examples with their
+runtimes. Write your responses as comments.
+"""
+
+
+def do_something():
+    # runtime for do_something() is O(1)
+    pass
+
+
+# what is the runtime for example 1?
+# runtime is O(n)
+def example_one(n):
+    for i in range(n):
+        do_something()
+
+
+# what is the runtime for example 2?
+# runtime is O(1)
+def example_two(n):
+    do_something()
+
+
+# what is the runtime for example 3?
+# runtime is O(n^2)
+def example_three(n):
+    for i in range(n):
+        for x in range(i):
+            do_something()
+
+
+# what is the runtime for example 4?
+# runtime is O(n)
+def example_four(n):
+    for i in range(n // 2):
+        do_something()
+
+
+# what is the runtime for example 5?
+# runtime is O(log(n))
+def example_five(n):
+    i = 0
+    while i < n:
+        do_something()
+        i *= 2
+
+
+# what is the runtime for example 6?
+# runtime is O(1)
+def example_six(n):
+    for i in range(10):
+        do_something()
+
+
+# what is the runtime for example 7?
+# runtime is O(2**n)
+def example_seven(n):
+    for i in range(2**n):
+        do_something()
+
+
+# what is the runtime for example 8?
+# runtime is O(n)
+def example_eight(n):
+    for i in range(n):
+        for x in range(7):
+            do_something()
+
+
+# what is the runtime for example 9?
+# runtime is O(n^2)
+def example_nine(n):
+    for i in range(n):
+        example_one(n)
+
+
+# what is the runtime for example 10?
+# runtime is O(n)
+def example_ten(n):
+    i = 0
+    while i < n:
+        do_something()
+        i += 2