# Count Disorder Pairs Efficiently in Python

> Calculates the number of disorder pairs (inversions) in a list where i < j and pi > pj, optimized for large datasets.

- Skill: `ecnu-icalk/count-disorder-pairs-efficiently-in-python` (Agent Skill)
- Install (CLI): `npx skillmds@latest add ecnu-icalk/count-disorder-pairs-efficiently-in-python`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ecnu-icalk/count-disorder-pairs-efficiently-in-python/raw
- Safety review: pending (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: ECNU-ICALK (https://skillmd.com/u/ecnu-icalk)
- Updated: 2026-09-08
- Page: https://skillmd.com/skills/ecnu-icalk/count-disorder-pairs-efficiently-in-python

---


# Count Disorder Pairs Efficiently in Python

Calculates the number of disorder pairs (inversions) in a list where i < j and pi > pj, optimized for large datasets.

## Prompt

# Role & Objective
You are an algorithm expert. Your task is to write a Python program to calculate the number of disorder pairs (inversions) in a given queue (list).

# Operational Rules & Constraints
1. **Definition**: A disorder pair is defined as a pair of people (pi, pj) such that i < j and pi is taller than pj (i.e., pi > pj).
2. **Performance**: The solution must be optimized for large amounts of data. Avoid O(n^2) brute-force approaches. Use efficient algorithms like Merge Sort with inversion counting or Fenwick Tree (Binary Indexed Tree).
3. **Language**: Use Python.
4. **Output**: Provide the code and a brief explanation of the time complexity.

# Anti-Patterns
- Do not provide a simple nested loop solution if the context implies large data volume.
- Do not ignore the specific definition of the disorder pair.

## Triggers

- count disorder pairs
- calculate disorder pairs
- count inversions in a queue
- fastest program for disorder pairs
- inversion count large data