Add explanation and solution for LeetCode problem 1515 (Find the Minimum Number of Fibonacci Numbers Whose Sum Is K) #50

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Add explanation and solution for LeetCode problem 1515 (Find the Minimum Number of Fibonacci Numbers Whose Sum Is K) #50

romankurnovskii wants to merge 1 commit into main from pr-problem-1515

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@romankurnovskii romankurnovskii commented Aug 28, 2025 •

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Summary

Add comprehensive explanation and Python solution for LeetCode problem 1515 (Find the Minimum Number of Fibonacci Numbers Whose Sum Is K).

New Features

Add detailed Markdown explanation for problem 1515 following the established rule structure
Implement Python solution using greedy approach with Fibonacci number generation
Use tex instead of text for code blocks as requested

Documentation

Problem 1515: Find the Minimum Number of Fibonacci Numbers Whose Sum Is K [Medium]
Category: Math, Greedy
Approach: Generate Fibonacci numbers and use greedy selection
Time Complexity: O(log k)
Space Complexity: O(log k)

Key Implementation Details

Generates Fibonacci numbers up to the target value k
Uses greedy approach to always select the largest possible Fibonacci number
Works backwards from largest to smallest for optimal efficiency
Handles edge cases including single Fibonacci numbers
Provides clean, well-commented code following repository standards

Files Added

explanations/1515/en.md - Comprehensive problem explanation with strategy and step-by-step walkthrough
solutions/1515/01.py - Clean Python solution with proper documentation

The solution demonstrates an elegant greedy approach to Fibonacci number decomposition, making it an excellent example for learning greedy algorithms and mathematical problem-solving techniques.

Summary by Sourcery

Add comprehensive markdown explanation and Python solution for LeetCode problem 1515 by generating Fibonacci numbers and using a greedy selection to achieve the target sum

New Features:

Implement Python greedy solution for finding the minimum number of Fibonacci numbers summing to k

Documentation:

Add detailed markdown explanation for LeetCode problem 1515, including problem statement, examples, strategy, and complexity analysis

Summary by CodeRabbit

New Features
- Added a solution for "Find the Minimum Number of Fibonacci Numbers Whose Sum Is K," using a greedy approach for efficient performance, including handling k=0 and large inputs.
Documentation
- Introduced a comprehensive explanation page for the problem with the statement, constraints, step-by-step strategy, rationale for the greedy method, edge cases, examples (e.g., k=7, 10, 19), and time/space complexity.

@romankurnovskii


 Add explanation and solution for LeetCode problem 1515 (Find the Mini...

8c5269d

...mum Number of Fibonacci Numbers Whose Sum Is K)

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coderabbitai bot commented Aug 28, 2025 •

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📝 Generate Docstrings

🧪 Generate unit tests

Create PR with unit tests
Post copyable unit tests in a comment
Commit unit tests in branch pr-problem-1515

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sourcery-ai bot commented Aug 28, 2025 •

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Reviewer's Guide

Introduces a comprehensive Markdown explanation and a new Python greedy solution for LeetCode problem 1515, covering problem breakdown, examples, step-by-step strategy, and complexity analysis, all aligned with repository standards.

Class diagram for the greedy Fibonacci decomposition solution

classDiagram
 class Solution {
 +findMinFibonacciNumbers(k)
 }
 class FibonacciGenerator {
 +fib_numbers: List[int]
 +generate_up_to(k)
 }
 Solution --> FibonacciGenerator: uses

Flow diagram for the greedy selection process in Fibonacci decomposition

flowchart TD
 A[Start with target k] --> B[Generate Fibonacci numbers up to k]
 B --> C[Set remaining = k]
 C --> D[Find largest Fibonacci number <= remaining]
 D --> E[Subtract Fibonacci number from remaining]
 E --> F[Increment count]
 F --> G{Is remaining == 0?}
 G -- Yes --> H[Return count]
 G -- No --> D

File-Level Changes

Change	Details	Files
Add comprehensive problem explanation in Markdown	Structured problem description with examples and constraints Outlined greedy strategy with high-level approach and decomposition Walkthrough for sample cases and complexity analysis Switched code blocks to use ```tex fences	`explanations/1515/en.md`
Implement Python greedy solution for Fibonacci sum	Generate Fibonacci numbers up to target k Select largest feasible Fibonacci numbers in descending order Track and return minimum count of terms Include docstring and inline comments per style guide	`solutions/1515/01.py`

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Actionable comments posted: 2

🧹 Nitpick comments (7)

solutions/1515/01.py (3)

14-19: Tighten Fibonacci generation loop.

Remove the redundant loop condition + internal break; compute the predicate once.

Apply:

- # Keep generating Fibonacci numbers until we exceed k
- while fib_numbers[-1] <= k:
- next_fib = fib_numbers[-1] + fib_numbers[-2]
- if next_fib > k:
- break
- fib_numbers.append(next_fib)
+ # Keep generating Fibonacci numbers while next ≤ k
+ while fib_numbers[-1] + fib_numbers[-2] <= k:
+ fib_numbers.append(fib_numbers[-1] + fib_numbers[-2])

25-35: Optional: allow reusing the same Fibonacci number without multiple passes.

Your current single-pass for-loop uses each Fibonacci number at most once (still correct for minimal representation). If you prefer to match the doc phrasing "can be used multiple times," use an inner while to keep subtracting the same term.

Apply:

- for i in range(len(fib_numbers) - 1, -1, -1):
- if fib_numbers[i] <= remaining:
- remaining -= fib_numbers[i]
- count += 1
- 
- # If we've reached the target, we're done
- if remaining == 0:
- break
+ for i in range(len(fib_numbers) - 1, -1, -1):
+ while remaining >= fib_numbers[i]:
+ remaining -= fib_numbers[i]
+ count += 1
+ if remaining == 0:
+ break

1-10: Add type hints and tighten docstring.

Small clarity/consistency boost.

Apply:

-def findMinFibonacciNumbers(k):
+def findMinFibonacciNumbers(k: int) -> int:
 """
- Find the minimum number of Fibonacci numbers whose sum equals k.
+ Compute the minimum count of Fibonacci numbers whose sum equals k.
 
 Args:
- k: int - Target sum to achieve
+ k (int): Target sum to achieve.
 
 Returns:
- int - Minimum number of Fibonacci numbers needed
+ int: Minimum number of Fibonacci numbers needed.
+
+ Notes:
+ Time: O(log k); Space: O(log k) — number of Fibonacci numbers ≤ k.
 """

explanations/1515/en.md (4)

3-3: Fix MD034 (bare URL) and align with corrected problem number.

Wrap the URL in a link label.

Apply:

-https://leetcode.com/problems/find-the-minimum-number-of-fibonacci-numbers-whose-sum-is-k
+[Problem link](https://leetcode.com/problems/find-the-minimum-number-of-fibonacci-numbers-whose-sum-is-k)

16-16: Convert bolded section titles to proper headings (MD036).

Use headings for sections instead of bold emphasis.

Apply (illustrative):

-**Examples**
+## Examples
-**Constraints**
+## Constraints
-**Step 1: Generate Fibonacci numbers up to k**
+#### Step 1: Generate Fibonacci numbers up to k
-**Step 2: Greedy selection process**
+#### Step 2: Greedy selection process
-**Step 3: Result**
+#### Step 3: Result

Also applies to: 36-36, 75-75, 83-83, 97-97

62-67: Minor editorial polish for the numbered list.

Add periods and parallel structure for readability.

Apply:

-1. **Generate Fibonacci numbers**: Create all Fibonacci numbers up to `k`
-2. **Greedy selection**: Always choose the largest Fibonacci number that fits
-3. **Subtract and repeat**: Subtract the chosen number and continue until sum reaches 0
-4. **Count operations**: Track how many Fibonacci numbers were used
+1. **Generate Fibonacci numbers**: Create all Fibonacci numbers up to `k`.
+2. **Greedy selection**: Choose the largest Fibonacci number that fits.
+3. **Subtract and repeat**: Subtract the chosen number; repeat until the sum reaches 0.
+4. **Count operations**: Track how many Fibonacci numbers were used.

101-106: Optional: cite the theorem underpinning the greedy choice.

A brief nod to Zeckendorf’s theorem strengthens the justification for optimality.

Apply:

-3. **Fibonacci properties**: Each Fibonacci number is the sum of the two preceding ones, making the greedy choice optimal
+3. **Fibonacci properties (Zeckendorf’s theorem)**: Every positive integer can be represented as a sum of nonconsecutive Fibonacci numbers, which underpins the optimality of the greedy choice.

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📥 Commits

Reviewing files that changed from the base of the PR and between ad2075f and 8c5269d.

📒 Files selected for processing (2)

explanations/1515/en.md (1 hunks)
solutions/1515/01.py (1 hunks)

🧰 Additional context used

🪛 LanguageTool

explanations/1515/en.md

[style] ~48-~48: As an alternative to the over-used intensifier ‘very’, consider replacing this phrase.
Context: ...ven?** A target integer k that can be very large (up to 109). What is being asked? ...

(EN_WEAK_ADJECTIVE)

[grammar] ~59-~59: There might be a mistake here.
Context: ...onacci numbers High-level approach: The solution involves generating Fibonac...

(QB_NEW_EN)

[grammar] ~62-~62: There might be a mistake here.
Context: ... in the remaining sum. Decomposition: 1. Generate Fibonacci numbers: Create all...

(QB_NEW_EN)

[grammar] ~63-~63: There might be a mistake here.
Context: ...s**: Create all Fibonacci numbers up to k 2. Greedy selection: Always choose the la...

(QB_NEW_EN)

[grammar] ~65-~65: There might be a mistake here.
Context: ...Subtract the chosen number and continue until sum reaches 0 4. Count operations: ...

(QB_NEW_EN)

[grammar] ~70-~70: There might be a mistake here.
Context: ...extremely inefficient. - Optimized: Use greedy approach with pre-generated Fibo...

(QB_NEW_EN)

[grammar] ~72-~72: There might be a mistake here.
Context: ...rs. This takes O(log k) time. ### Steps Let's walk through the solution step by ...

(QB_NEW_EN)

[grammar] ~75-~75: There might be a mistake here.
Context: ...ep 1: Generate Fibonacci numbers up to k** - Start with F1 = 1, F2 = 1 - F3 = F2 + F1...

(QB_NEW_EN)

[grammar] ~77-~77: There might be a mistake here.
Context: ...1 = 1, F2 = 1 - F3 = F2 + F1 = 1 + 1 = 2 - F4 = F3 + F2 = 2 + 1 = 3 - F5 = F4 + F3 ...

(QB_NEW_EN)

[grammar] ~78-~78: There might be a mistake here.
Context: ...1 = 1 + 1 = 2 - F4 = F3 + F2 = 2 + 1 = 3 - F5 = F4 + F3 = 3 + 2 = 5 - F6 = F5 + F4 ...

(QB_NEW_EN)

[grammar] ~79-~79: There might be a mistake here.
Context: ...2 = 2 + 1 = 3 - F5 = F4 + F3 = 3 + 2 = 5 - F6 = F5 + F4 = 5 + 3 = 8 (exceeds 7, sto...

(QB_NEW_EN)

[grammar] ~80-~80: There might be a mistake here.
Context: ... = F5 + F4 = 5 + 3 = 8 (exceeds 7, stop) - Fibonacci numbers up to 7: [1, 1, 2, 3, ...

(QB_NEW_EN)

[grammar] ~83-~83: There might be a mistake here.
Context: ..., 5] Step 2: Greedy selection process - Remaining sum: 7 - **Largest Fibonacci...

(QB_NEW_EN)

[grammar] ~84-~84: There might be a mistake here.
Context: ...lection process** - Remaining sum: 7 - Largest Fibonacci ≤ 7: 5 - Use 5: ...

(QB_NEW_EN)

[grammar] ~85-~85: There might be a mistake here.
Context: ... sum**: 7 - Largest Fibonacci ≤ 7: 5 - Use 5: 7 - 5 = 2 - Count: 1 - **R...

(QB_NEW_EN)

[grammar] ~86-~86: There might be a mistake here.
Context: ...ibonacci ≤ 7**: 5 - Use 5: 7 - 5 = 2 - Count: 1 - Remaining sum: 2 - **L...

(QB_NEW_EN)

[grammar] ~89-~89: There might be a mistake here.
Context: ...2 - Count: 1 - Remaining sum: 2 - Largest Fibonacci ≤ 2: 2 - Use 2: ...

(QB_NEW_EN)

[grammar] ~90-~90: There might be a mistake here.
Context: ... sum**: 2 - Largest Fibonacci ≤ 2: 2 - Use 2: 2 - 2 = 0 - Count: 2 - **R...

(QB_NEW_EN)

[grammar] ~91-~91: There might be a mistake here.
Context: ...ibonacci ≤ 2**: 2 - Use 2: 2 - 2 = 0 - Count: 2 - Remaining sum: 0 - **P...

(QB_NEW_EN)

[grammar] ~94-~94: There might be a mistake here.
Context: ...0 - Count: 2 - Remaining sum: 0 - Process complete Step 3: Result -...

(QB_NEW_EN)

[grammar] ~97-~97: There might be a mistake here.
Context: ...- Process complete Step 3: Result - Total Fibonacci numbers used: 2 - Soluti...

(QB_NEW_EN)

[grammar] ~98-~98: There might be a mistake here.
Context: ...sult** - Total Fibonacci numbers used: 2 - Solution: 5 + 2 = 7 Why this works:...

(QB_NEW_EN)

[grammar] ~101-~101: There might be a mistake here.
Context: ...Solution: 5 + 2 = 7 Why this works: The greedy approach works because: 1. **...

(QB_NEW_EN)

[grammar] ~102-~102: There might be a mistake here.
Context: ...ks:** The greedy approach works because: 1. Optimal substructure: If we can repres...

(QB_NEW_EN)

🪛 markdownlint-cli2 (0.17.2)

explanations/1515/en.md

3-3: Bare URL used

(MD034, no-bare-urls)

16-16: Emphasis used instead of a heading