Maximize the sum of array
Detailed guide and Python implementation for the 'Maximize the sum of array' problem.
1. Concept Overview
The 'Maximize the sum of array' problem is a key challenge in the Greedy 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 Maximize the sum of array.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Maximize the sum of 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 maximize_sum(arr, k) that returns the maximum possible sum of the array after performing exactly k negations. In each negation, you must choose an element and replace it with its negative value. You can negate the same element multiple times.
- •1 <= len(arr) <= 10^5
- •1 <= k <= 10^5
- •-10^4 <= arr[i] <= 10^4
Examples
maximize_sum([-2, 0, 5, -1, 2], 4)
10
Negate -2 to 2, -1 to 1. The remaining 2 negations can be performed on 0. The array becomes [2, 0, 5, 1, 2], summing to 10.
maximize_sum([3, -1, 0, 2], 3)
6
Negate -1 to 1. The remaining 2 negations are performed on 0. Sum is 3 + 1 + 0 + 2 = 6.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
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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
import heapq
def max_sum_opt(arr, k):
heapq.heapify(arr)
for _ in range(k):
val = heapq.heappop(arr)
heapq.heappush(arr, -val)
return sum(arr)Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def max_sum_brute(arr, k):
for _ in range(k):
arr.sort(); arr[0] = -arr[0]
return sum(arr)Algorithm Pattern Checklist
When dealing with Greedy data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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