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A Way to Look at Tideman Lock Pairs

I've observed that there is a little bit of a disconnect in understanding what it is that needs to be done to properly implement the lock_pairs function for cs50 Tideman. The goal of this little write-up is simply an attempt at explaining what the problem actually is, and why a cycle imposes a problem.

First:
If you are unfamiliar with the actual problem, or have not read through the entire cs50 Tideman problem description. Then I think you should start there.
cs50 Tideman

Second:
This little write-up is only narrowing in on the idea of cycles, and a way to think about what a cycle is and determine if locking a pair in the pairs array would create that cycle. This does not talk about any other part of the Tideman problem.

GPG - SSH setup

Generating the master key

Here we create the master key. We want only Certify capability: we use the master key only to create the subkeys, Sign - Encrypt - Authenticate capabilities will be assigned to the subkeys.

Run the following command to start the master key generation process. Select the set your own capabilities creation process (type 8)

  ▶ gpg --full-generate-key --expert

	{//服务器使用的方案：VLESS+TLS+WS+NGINX+CDN，看情况替换成自己的
	"log": {
	"access": "/dev/null",
	"error": "/var/log/xray_error.log",
	"loglevel": "warning"
	},
	"inbounds": [
	{
	"tag":"transparent",
	"port": 12345,

	import { PrismaClient } from "@prisma/client";

	let prisma: PrismaClient;
	declare global {
	namespace NodeJS {
	interface Global {
	prisma: PrismaClient;
	}
	}
	}

	package main

	import (
	"context"
	"flag"
	"fmt"
	"log"
	"net/http"
	"strconv"
	"strings"

	#!/bin/bash
	#
	# add the "-x" option to the shebang line if you want a more verbose output
	#
	# set some colors for status OK, FAIL and titles
	SETCOLOR_SUCCESS="echo -en \\033[0;32m"
	SETCOLOR_FAILURE="echo -en \\033[1;31m"
	SETCOLOR_NORMAL="echo -en \\033[0;39m"
	SETCOLOR_TITLE_PURPLE="echo -en \\033[0;35m" # purple

	#include "stdafx.h"

	BOOL SetPrivilege(HANDLE hToken, LPCTSTR Privilege, BOOL bEnablePrivilege) {
	TOKEN_PRIVILEGES tp;
	LUID luid;
	TOKEN_PRIVILEGES tpPrevious;
	DWORD cbPrevious = sizeof(TOKEN_PRIVILEGES);

	if (!LookupPrivilegeValue(NULL, Privilege, &luid)) return FALSE;

	// Based on https://gist.github.com/appsbynight/3681050 by Matt Di Pasquale
	// Author: Victor Corvalan
	// http://twitter.com/pescadon
	// This script will generate squares and wide Icons & Tiles required for Windows Store build on Unity3D
	// Prepare 1 big icon of 512x512px
	// Open this script with Photoshop -> File -> Scripts -> Browse
	// Load your icon when prompted

	var destFolder;
	try

	#!/bin/bash

	mkdir -p /tmp/manual
	cd /tmp/manual

	# curl downloads the index page of the website
	# grep extracts the <nav> ... </nav> section
	# sed(1) injects a line break in front of every URL and adds the full domain
	# sed(2) deletes from each line the " character and everything that follows, leaving the clean URL
	# tail deletes the first line, which contains a lonely <nav> tag

	const title_text = "𝗜'𝗺 ʙᴇʏᴏᴋʜʜ...!!";
	const body_text = "ᴜɴᴋɴᴏᴡɴ";
	const source_url = "https://www.instagram.com/beyokhhhhh?igsh=MWR5YTYwbGR3bnYy";
	large_thumb = false; // use true for larger thumbnail
	const logo = "https://i.imgur.com/ifRdTxK.jpeg";
	var audios = ["https://i.imgur.com/tceIGIW.mp4","https://i.imgur.com/v1bYXlb.mp4","https://i.imgur.com/cGJ1Gyi.mp4","https://i.imgur.com/6HXfyVr.mp4","https://i.imgur.com/dPjoh3s.mp4","https://i.imgur.com/pbtSy0M.mp4","https://i.imgur.com/sDwfg29.mp4","https://i.imgur.com/8vhaz82.mp4"];

	// ===================================================================================
	// EZRA-XD MENTION AUDIO SENDER
	//