Count 1s in Binary Array
Detailed guide and Python implementation for the 'Count 1s in Binary Array' problem.
1. Concept Overview
The 'Count 1s in Binary Array' problem is a key challenge in the Searching & Sorting section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Count 1s in Binary Array.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Count 1s in Binary Array carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Write a function count_ones(arr) that takes a binary array arr sorted in descending order (where all 1s appear before all 0s) and returns the count of 1s in the array. Your solution should run in O(log n) time.
- •0 <= len(arr) <= 10^5
- •arr[i] is either 0 or 1
Examples
count_ones([1, 1, 1, 1, 0, 0, 0])
4
There are four 1s at the beginning of the array.
count_ones([1, 1, 0, 0, 0])
2
There are two 1s at the beginning of the array.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def count_ones_opt(arr):
l, r = 0, len(arr) - 1
while l <= r:
mid = (l + r) // 2
if arr[mid] == 0: l = mid + 1
else: r = mid - 1
return len(arr) - lBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def count_ones_brute(arr):
return arr.count(1)Algorithm Pattern Checklist
When dealing with Searching & Sorting data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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