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[Practice exercise] Baffling Birthdays (#496)
* [Practice exercise] Baffling Birthdays * changed library imports
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‎config.json‎

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"prerequisites": [],
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"difficulty": 6
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},
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{
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"slug": "baffling-birthdays",
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"name": "Baffling Birthdays",
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"uuid": "fd94d735-3d0e-4c6d-8b65-5fe170e00f1e",
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"practices": [],
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"prerequisites": [],
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"difficulty": 6
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},
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{
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"slug": "zebra-puzzle",
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"name": "Zebra Puzzle",

‎exercises/practice/baffling-birthdays/.docs/instructions.md‎

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# Instructions
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Your task is to estimate the birthday paradox's probabilities.
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To do this, you need to:
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- Generate random birthdates.
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- Check if a collection of randomly generated birthdates contains at least two with the same birthday.
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- Estimate the probability that at least two people in a group share the same birthday for different group sizes.
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~~~~exercism/note
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A birthdate includes the full date of birth (year, month, and day), whereas a birthday refers only to the month and day, which repeat each year.
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Two birthdates with the same month and day correspond to the same birthday.
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~~~~
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~~~~exercism/caution
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The birthday paradox assumes that:
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- There are 365 possible birthdays (no leap years).
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- Each birthday is equally likely (uniform distribution).
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Your implementation must follow these assumptions.
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~~~~

‎exercises/practice/baffling-birthdays/.docs/introduction.md‎

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# Introduction
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Fresh out of college, you're throwing a huge party to celebrate with friends and family.
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Over 70 people have shown up, including your mildly eccentric Uncle Ted.
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In one of his usual antics, he bets you £100 that at least two people in the room share the same birthday.
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That sounds ridiculous — there are many more possible birthdays than there are guests, so you confidently accept.
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To your astonishment, after collecting the birthdays of just 32 guests, you've already found two guests that share the same birthday.
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Accepting your loss, you hand Uncle Ted his £100, but something feels off.
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The next day, curiosity gets the better of you.
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A quick web search leads you to the [birthday paradox][birthday-problem], which reveals that with just 23 people, the probability of a shared birthday exceeds 50%.
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Ah. So _that's_ why Uncle Ted was so confident.
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Determined to turn the tables, you start looking up other paradoxes; next time, _you'll_ be the one making the bets.
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~~~~exercism/note
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The birthday paradox is a [veridical paradox][veridical-paradox]: even though it feels wrong, it is actually true.
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[veridical-paradox]: https://en.wikipedia.org/wiki/Paradox#Quine's_classification
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~~~~
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[birthday-problem]: https://en.wikipedia.org/wiki/Birthday_problem

‎exercises/practice/baffling-birthdays/.meta/config.json‎

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{
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"authors": [
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"colinleach"
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],
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"files": {
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"solution": [
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"baffling-birthdays.R"
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],
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"test": [
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"test_baffling-birthdays.R"
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],
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"example": [
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".meta/example.R"
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]
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},
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"blurb": "Estimate the birthday paradox's probabilities.",
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"source": "Erik Schierboom",
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"source_url": "https://github.com/exercism/problem-specifications/pull/2539"
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}

‎exercises/practice/baffling-birthdays/.meta/example.R‎

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library(lubridate)
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library(dplyr)
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shared_birthday <- function(birthdates) {
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birthdays <- birthdates |> str_sub(6)
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length(birthdays) > length(unique(birthdays))
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}
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random_birthdates <- function(groupsize) {
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randyear <- sample(1900:year(today()), groupsize, replace = TRUE)
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no_leaps <- if_else(leap_year(randyear), randyear - 1, randyear)
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make_date(year = no_leaps) + days(sample(0:364, groupsize, replace = TRUE))
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}
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estimate_probability_of_shared_birthday <- function(groupsize) {
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reps <- 500
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runs <- replicate(reps, shared_birthday(random_birthdates(groupsize)))
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sum(runs) / reps
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}

‎exercises/practice/baffling-birthdays/.meta/template.j2‎

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{%- import "generator_macros.j2" as macros with context -%}
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{{ macros.canonical_ref() }}
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{{ macros.header() }}
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library(lubridate)
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{% for case in cases -%}
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# {{ case["description"] }}
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{% if case["description"].startswith("shared") -%}
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{%- for subcase in case["cases"] -%}
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test_that("{{ subcase["description"] }}", {
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input <- c{{ subcase["input"]["birthdates"] | list_to_tuple }}
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expect_{{ subcase["expected"] | lower }}( shared_birthday(input) )
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})
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{% endfor %}
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{% elif case["description"].startswith("random") %}
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{# non-deterministic results unsuitable for templating #}
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test_that("random birthdates generate requested number of birthdates", {
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expect_all_true( sapply(1:20, \(groupsize) length(random_birthdates(groupsize)) == groupsize) )
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})
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test_that("random birthdates are not in leap years", {
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expect_all_false( leap_year(random_birthdates(100)) )
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})
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test_that("random birthdates appear random", {
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birthdates <- random_birthdates(500)
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months <- month(birthdates) |> unique()
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days <- day(birthdates) |> unique()
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expect_gte( length(months), 10 )
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expect_gte( length(days), 28 )
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})
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{% elif case["description"].startswith("estimated") %}
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{% for subcase in case["cases"] %}
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test_that("{{ subcase["description"] }}", {
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expected <- {{ subcase["expected"] / 100 }}
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rtol <- ifelse(expected > 0.1 && expected < 0.9, 0.1, 0.01)
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expect_equal(
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estimate_probability_of_shared_birthday({{ subcase["input"]["groupSize"] }}),
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expected,
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tolerance = rtol)
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})
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{% endfor %}
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{% endif %}
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{% endfor %}

‎exercises/practice/baffling-birthdays/.meta/tests.toml‎

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# This is an auto-generated file.
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#
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# Regenerating this file via `configlet sync` will:
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# - Recreate every `description` key/value pair
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# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
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# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
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# - Preserve any other key/value pair
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#
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# As user-added comments (using the # character) will be removed when this file
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# is regenerated, comments can be added via a `comment` key.
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[716dcc2b-8fe4-4fc9-8c48-cbe70d8e6b67]
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description = "shared birthday -> one birthdate"
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[f7b3eb26-bcfc-4c1e-a2de-af07afc33f45]
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description = "shared birthday -> two birthdates with same year, month, and day"
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[7193409a-6e16-4bcb-b4cc-9ffe55f79b25]
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description = "shared birthday -> two birthdates with same year and month, but different day"
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[d04db648-121b-4b72-93e8-d7d2dced4495]
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description = "shared birthday -> two birthdates with same month and day, but different year"
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[3c8bd0f0-14c6-4d4c-975a-4c636bfdc233]
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description = "shared birthday -> two birthdates with same year, but different month and day"
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[df5daba6-0879-4480-883c-e855c99cdaa3]
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description = "shared birthday -> two birthdates with different year, month, and day"
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[0c17b220-cbb9-4bd7-872f-373044c7b406]
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description = "shared birthday -> multiple birthdates without shared birthday"
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[966d6b0b-5c0a-4b8c-bc2d-64939ada49f8]
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description = "shared birthday -> multiple birthdates with one shared birthday"
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[b7937d28-403b-4500-acce-4d9fe3a9620d]
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description = "shared birthday -> multiple birthdates with more than one shared birthday"
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[70b38cea-d234-4697-b146-7d130cd4ee12]
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description = "random birthdates -> generate requested number of birthdates"
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[d9d5b7d3-5fea-4752-b9c1-3fcd176d1b03]
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description = "random birthdates -> years are not leap years"
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[d1074327-f68c-4c8a-b0ff-e3730d0f0521]
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description = "random birthdates -> months are random"
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[7df706b3-c3f5-471d-9563-23a4d0577940]
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description = "random birthdates -> days are random"
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[89a462a4-4265-4912-9506-fb027913f221]
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description = "estimated probability of at least one shared birthday -> for one person"
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[ec31c787-0ebb-4548-970c-5dcb4eadfb5f]
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description = "estimated probability of at least one shared birthday -> among ten people"
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[b548afac-a451-46a3-9bb0-cb1f60c48e2f]
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description = "estimated probability of at least one shared birthday -> among twenty-three people"
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[e43e6b9d-d77b-4f6c-a960-0fc0129a0bc5]
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description = "estimated probability of at least one shared birthday -> among seventy people"

‎exercises/practice/baffling-birthdays/baffling-birthdays.R‎

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shared_birthday <- function(birthdates) {
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}
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random_birthdates <- function(groupsize) {
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}
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estimate_probability_of_shared_birthday <- function(groupsize) {
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}

‎exercises/practice/baffling-birthdays/test_baffling-birthdays.R‎

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# These tests are auto-generated with test data from:
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# https://github.com/exercism/problem-specifications/tree/main/exercises/baffling-birthdays/canonical-data.json
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# File last updated on 2026-03-26
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source("./baffling-birthdays.R")
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library(testthat)
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library(lubridate)
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# shared birthday
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test_that("one birthdate", {
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input <- c('2000-01-01')
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expect_false(shared_birthday(input))
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})
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test_that("two birthdates with same year, month, and day", {
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input <- c('2000-01-01', '2000-01-01')
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expect_true(shared_birthday(input))
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})
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test_that("two birthdates with same year and month, but different day", {
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input <- c('2012-05-09', '2012-05-17')
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expect_false(shared_birthday(input))
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})
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test_that("two birthdates with same month and day, but different year", {
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input <- c('1999-10-23', '1988-10-23')
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expect_true(shared_birthday(input))
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})
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test_that("two birthdates with same year, but different month and day", {
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input <- c('2007-12-19', '2007-04-27')
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expect_false(shared_birthday(input))
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})
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test_that("two birthdates with different year, month, and day", {
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input <- c('1997-08-04', '1963-11-23')
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expect_false(shared_birthday(input))
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})
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test_that("multiple birthdates without shared birthday", {
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input <- c('1966-07-29', '1977-02-12', '2001-12-25', '1980-11-10')
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expect_false(shared_birthday(input))
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})
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test_that("multiple birthdates with one shared birthday", {
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input <- c('1966-07-29', '1977-02-12', '2001-07-29', '1980-11-10')
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expect_true(shared_birthday(input))
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})
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test_that("multiple birthdates with more than one shared birthday", {
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input <- c(
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'1966-07-29',
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'1977-02-12',
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'2001-12-25',
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'1980-07-29',
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'2019-02-12'
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)
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expect_true(shared_birthday(input))
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})
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# random birthdates
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test_that("random birthdates generate requested number of birthdates", {
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expect_all_true(sapply(1:20, \(groupsize) {
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length(random_birthdates(groupsize)) == groupsize
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}))
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})
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test_that("random birthdates are not in leap years", {
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expect_all_false(leap_year(random_birthdates(100)))
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})
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test_that("random birthdates appear random", {
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birthdates <- random_birthdates(500)
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months <- month(birthdates) |> unique()
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days <- day(birthdates) |> unique()
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expect_gte(length(months), 10)
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expect_gte(length(days), 28)
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})
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# estimated probability of at least one shared birthday
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test_that("for one person", {
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expected <- 0.0
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rtol <- ifelse(expected > 0.1 && expected < 0.9, 0.1, 0.01)
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expect_equal(
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estimate_probability_of_shared_birthday(1),
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expected,
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tolerance = rtol
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)
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})
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test_that("among ten people", {
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expected <- 0.11694818
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rtol <- ifelse(expected > 0.1 && expected < 0.9, 0.1, 0.01)
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expect_equal(
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estimate_probability_of_shared_birthday(10),
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expected,
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tolerance = rtol
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)
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})
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test_that("among twenty-three people", {
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expected <- 0.50729723
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rtol <- ifelse(expected > 0.1 && expected < 0.9, 0.1, 0.01)
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expect_equal(
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estimate_probability_of_shared_birthday(23),
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expected,
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tolerance = rtol
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)
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})
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test_that("among seventy people", {
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expected <- 0.99915958
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rtol <- ifelse(expected > 0.1 && expected < 0.9, 0.1, 0.01)
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expect_equal(
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estimate_probability_of_shared_birthday(70),
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expected,
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tolerance = rtol
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)
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})

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