Abstract / Summary

Given an array of positive integers and a threshold, repeatedly combine the two smallest elements and add their sum back until the total exceeds the threshold.

Note

The full problem description, including helpful examples, can be found on LeetCode.

This problem is ranked as

and has an acceptance rate of about 87% (100k+ submissions).

Typical patterns to solve this problem:

• Array

Every single line of code was written by me, 100% from scratch, between August 2023 and August 2024.
However, two years later I set up this website and used various AI tools to generate most of the walkthrough / explanations below.

See this dedicated page for more details.

Overview

The provided implementation defines a single method minOperations inside a Solution class. Its purpose is to determine how many elements in the input list nums are strictly less than a given threshold k. The method accomplishes this in a single expression by leveraging Python’s generator syntax together with the built-in sum function.

Key Steps

Iteration over the input collection

The core of the algorithm is a generator expression that walks through each element of nums. This lazy iteration means that each element is processed one at a time without constructing an auxiliary data structure.

for n in nums

Evaluation of the comparison predicate

For every element n encountered, the expression checks whether it satisfies the condition n < k. The result of this comparison is a Boolean value that is implicitly converted to an integer (True becomes 1, False becomes 0) when used in arithmetic contexts.

n < k

Accumulation of qualifying elements

The generator yields a 1 for each element that meets the predicate and nothing for those that do not. The surrounding sum call aggregates these 1s, producing the total count of elements less than k.

sum(1 for n in nums if n < k)

Edge Cases Handled

When nums is an empty list, the generator produces no values, and sum returns 0, correctly indicating that no elements are less than k. If every element in nums is greater than or equal to k, the predicate never succeeds, and the result is again 0. Conversely, when all elements are smaller than k, the generator yields a 1 for each entry, and sum returns the length of nums. The comparison works uniformly for positive, zero, and negative integers, so the method gracefully handles scenarios where k itself is negative or zero.

Performance Optimizations

The implementation avoids the creation of intermediate lists by using a generator expression. This design choice reduces memory consumption, especially for large input arrays, because only one element is held in memory at any point during the iteration. Additionally, the direct use of sum with a generator eliminates the overhead of explicit loop constructs and manual counter increments, allowing the Python interpreter to execute the counting in a tight, C-level loop inside the built-in sum function. This results in a fast, low-overhead traversal of the input data.

Imagine a box filled with numbered building blocks. Each block has a different number written on its side. A special rule says that every block must have a number at least as high as the secret target number called k. Some of the blocks are too small and have numbers smaller than the target. The code looks at every single block in the box one by one. If it finds a block with a number smaller than the target, it keeps track of it. By the time the code finishes checking every block, it counts up all the small ones that need to be replaced.

Several LLMs ranked my code quality on a scale from 1 (very poor) to 10 (outstanding):

Time: linear
As a rule of thumb, the maximum input size for one second execution time is

• factorial: up to 10 elements
• exponential: up to 20 elements
• polynomial: a few thousand elements
• loglinear: up to 100,000 elements
• linear: a few million elements
• logarithmic: a billion elements
• constant: practically unlimited

I wrote a basic crawler to find other solutions to that problem.
Obviously, I did that after I solved the problem myself.

In general, AlgoMonster and WalkCCC solutions are high-quality and always worth a look.
I haven't checked most of the other solutions, but they might be helpful as well.

And of course, the LeetCode forum is always a good place (or even the best) to look for alternative approaches.

(click on a column header to sort the table)

	author
author	solutions
www	AlgoMonster	Java		C++		Python	TS
	WalkCCC	Java		C++		Python
	leetcode.ca	Java		C++	Go	Python	TS
	Progiez	Java		C++		Python
github	charles-wangkai	Java
	fsq			C++
	JoshCrozier		JS
	varunu28	Java
AlgoMonster	C++, Python, Java, TypeScript
WalkCCC	C++, Python, Java
leetcode.ca	C++, Go, Java, Python, TypeScript
Progiez	C++, Java, Python
charles-wangkai	Java
fsq	C++
JoshCrozier	JavaScript
varunu28	Java

There are a few extra pages giving you some insights into my setup:

• Tech Stack - my development environment and tools
• AI - how AI helped me create this website (NOT solving the problems)
• Progress - progression over time
• Quality - code quality