cours-exercices/01-data-structures-complexity-exercises.ipynb

+%% Cell type:markdown id:82b57c5e tags:
+
+
+%% Cell type:markdown id:e8a19c58 tags:
+
+# INF TC1 - Algorithmes et structures de données
+
+## Exercices
+
+%% Cell type:markdown id:2968208d tags:
+
+---
+
+%% Cell type:markdown id:a4e4fad3 tags:
+
+# Data Structures and Complexity
+
+%% Cell type:markdown id:a8adef9b tags:
+
+---
+
+%% Cell type:markdown id:827ebb43-1e5d-4756-83ba-97af3e36b6af tags:
+
+_For the following question, if a complexity is needed please pick one in this list_
+
+%% Cell type:code id:b54157fc-f0d5-4689-bf2b-344a608bc5a9 tags:
+
+``` python
+list_complexities = ["O(1)", "O(log(n))", "O(n)", "O(n^2)", "O(nlog(n))", "O(n^3)", "O(2^n)", "O(n!)", "O(n^n)"]
+```
+
+%% Cell type:markdown id:568202fd tags:
+
+### Exercise 1: Identify the complexity
+
+%% Cell type:code id:431fe8c1-91d1-40f3-a7a4-f4a3770a4a01 tags:
+
+``` python
+def nested_loop_example(arr):
+    n = len(arr)
+    for i in range(n):
+        for j in range(n):
+            print(arr[i] + arr[j])
+```
+
+%% Cell type:code id:e68b3e9a-418f-4950-9f27-18bb0fe90794 tags:
+
+``` python
+# nested_loop_example_complexity = ?
+# YOUR CODE HERE
+raise NotImplementedError()
+```
+
+%% Cell type:markdown id:612dc873-419b-42c5-be36-0accd03ffa79 tags:
+
+### Exercise 2: Identify the complexity
+
+%% Cell type:code id:76102853-e1f3-4717-8a59-1091195a19eb tags:
+
+``` python
+def fibonacci_recursive(n):
+    if n <= 1:
+        return n
+    return fibonacci_recursive(n - 1) + fibonacci_recursive(n - 2)
+```
+
+%% Cell type:code id:dead6a52-7996-4eae-9d2a-f75d5d26bbb7 tags:
+
+``` python
+# fibonacci_recursive_complexity = ?
+# YOUR CODE HERE
+raise NotImplementedError()
+```
+
+%% Cell type:markdown id:aa4a6ce7-e542-4b23-8a10-ca0bf93de041 tags:
+
+### Exercise 3: Identify the complexity
+
+%% Cell type:code id:70af3e43-8053-49c9-ba58-346a3e915bdb tags:
+
+``` python
+def binary_search(arr, target):
+    low, high = 0, len(arr) - 1
+    while low <= high:
+        mid = (low + high) // 2
+        if arr[mid] == target:
+            return mid
+        elif arr[mid] < target:
+            low = mid + 1
+        else:
+            high = mid - 1
+    return -1
+```
+
+%% Cell type:code id:9c22866c-b4fc-4228-b0ab-5882d964f5f6 tags:
+
+``` python
+# binary_searche_complexity = ?
+# YOUR CODE HERE
+raise NotImplementedError()
+```
+
+%% Cell type:markdown id:87b4921b-ef55-4083-b4f1-a3ca5bb7b011 tags:
+
+### Additional checks (do not change)
+
+%% Cell type:code id:6e8f2878-ce5f-4cd8-a5a5-7bce8f655ab8 tags:
+
+``` python
+assert nested_loop_example_complexity in list_complexities
+assert fibonacci_recursive_complexity in list_complexities
+assert binary_searche_complexity in list_complexities
+```