binary search

Author: codebasics

Algorithms/BinarySearch/__init__.py

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+### Binary Search Exercise
+1. When I try to find number 5 in below list using binary search, it doesn't work and returns me -1 index. Why is that?
+
+    ```numbers = [1,4,6,9,10,5,7]```
+    
+1. Find index of all the occurances of a number from sorted list
+
+    ```
+    numbers = [1,4,6,9,11,15,15,15,17,21,34,34,56]
+    number_to_find = 15  
+    ```
+   This should return 5,6,7 as indices containing number 15 in the array
+    
+[Solution]()    

Algorithms/BinarySearch/binary_search_exercise.md

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+############ BINARY SEARCH EXERCISE SOLUTION: CODEBASICS YOUTUBE CHANNEL ####################
+
+################### PROBLEM 1 #######################
+#  When I try to find number 5 in below list using binary search, it doesn't work and returns me -1 index. Why is that?
+#  numbers = [1,4,6,9,10,5,7]
+#  Answer: It is because the list is not sorted! Binary search requires that list has to be sorted
+
+################### PROBLEM 2 #######################
+# Problem: Find index of all the occurances of a number from sorted list
+# Solution here tries to find an index of a number using binary search. Now since the list is sorted,
+# it can do left and right scan from the initial index to find all occurances of a given element
+# This method is not most efficient and I want you to figure out even a better way of doing it. In
+# any case below method is still effective
+
+def binary_search(numbers_list, number_to_find):
+    left_index = 0
+    right_index = len(numbers_list) - 1
+    mid_index = 0
+
+    while left_index <= right_index:
+        mid_index = (left_index + right_index) // 2
+        mid_number = numbers_list[mid_index]
+
+        if mid_number == number_to_find:
+            return mid_index
+
+        if mid_number < number_to_find: # this means number is in right hand side of the list
+            left_index = mid_index + 1
+        else: # number to find is on left hand side of the list
+            right_index = mid_index - 1
+
+    return -1
+
+def find_all_occurances(numbers, number_to_find):
+    index = binary_search(numbers, number_to_find)
+    indices = [index]
+    # find indices on left hand side
+    i = index-1
+    while i >=0:
+        if numbers[i] == number_to_find:
+            indices.append(i)
+        else:
+            break
+        i = i - 1
+
+    # find indices on right hand side
+    i = index + 1
+    while i<len(numbers):
+        if numbers[i] == number_to_find:
+            indices.append(i)
+        else:
+            break
+        i = i + 1
+
+    return sorted(indices)
+
+
+if __name__ == '__main__':
+    numbers = [1,4,6,9,11,15,15,15,17,21,34,34,56]
+    number_to_find = 15
+    indices = find_all_occurances(numbers, number_to_find)
+    print(f"Indices of occurances of {number_to_find} are {indices}")

Algorithms/BinarySearch/binary_search_exercise_solution.py

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+from util import time_it
+
+@time_it
+def linear_search(numbers_list, number_to_find):
+    for index, element in enumerate(numbers_list):
+        if element == number_to_find:
+            return index
+    return -1
+
+@time_it
+def binary_search(numbers_list, number_to_find):
+    left_index = 0
+    right_index = len(numbers_list) - 1
+    mid_index = 0
+
+    while left_index <= right_index:
+        mid_index = (left_index + right_index) // 2
+        mid_number = numbers_list[mid_index]
+
+        if mid_number == number_to_find:
+            return mid_index
+
+        if mid_number < number_to_find:
+            left_index = mid_index + 1
+        else:
+            right_index = mid_index - 1
+
+    return -1
+
+def binary_search_recursive(numbers_list, number_to_find, left_index, right_index):
+    if right_index < left_index:
+        return -1
+
+    mid_index = (left_index + right_index) // 2
+    if mid_index >= len(numbers_list) or mid_index < 0:
+        return -1
+
+    mid_number = numbers_list[mid_index]
+
+    if mid_number == number_to_find:
+        return mid_index
+
+    if mid_number < number_to_find:
+        left_index = mid_index + 1
+    else:
+        right_index = mid_index - 1
+
+    return binary_search_recursive(numbers_list, number_to_find, left_index, right_index)
+
+if __name__ == '__main__':
+    numbers_list = [12, 15, 17, 19, 21, 24, 45, 67]
+    number_to_find = 21
+
+    index = binary_search_recursive(numbers_list, number_to_find, 0, len(numbers_list))
+    print(f"Number found at index {index} using binary search")

Algorithms/BinarySearch/binarysearch.py

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+import time
+def time_it(func):
+    def wrapper(*args, **kwargs):
+        start = time.time()
+        result = func(*args,**kwargs)
+        end = time.time()
+        print(func.__name__ +" took " + str((end-start)*1000) + " mil sec")
+        return result
+    return wrapper