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Divide & Conquer

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Divide & Conquer

Binary Search — Decision Tree

Each comparison is a node in the decision tree — go left if target is smaller, right if larger. Eliminated branches fade out.

(✓ in array)

Speed

Step 1/0

Sorted Array

2

0

5

1

8

2

12

3

16

4

23

5

38

6

56

7

72

8

91

9

Decision Tree

Comparing

Found

Not Found

Active range

Eliminated

…

Result

Searching…

Array size10

Target23

Comparisons0

Max possible4

Active Recall1/3

What is the time complexity of binary search?