- Commit
- fa97703c1cdc4ffe9f8128e814b09fd8f57fd27a
- Parent
- ea51224d227b1056ee562dba10f035f2a2729fa4
- Author
- Gark Garcia <37553739+GarkGarcia@users.noreply.github.com>
- Date
Optimized the rust and haskell implementations.
a-conjecture-of-mine
An exercise on polyglossy: the same problem solved on multiple languages
Diffstat
18 files changed, 116 insertions, 881 deletions
| Status | File Name | N° Changes | Insertions | Deletions |
| Modified | .gitignore | 4 | 4 | 0 |
| Modified | Haskell/app/Main.hs | 39 | 16 | 23 |
| Modified | Haskell/conjecture.cabal | 4 | 2 | 2 |
| Modified | Haskell/package.yaml | 1 | 1 | 0 |
| Deleted | Latex/digital_sum.aux | 1 | 0 | 1 |
| Deleted | Latex/digital_sum.log | 384 | 0 | 384 |
| Deleted | Latex/digital_sum.pdf | 0 | 0 | 0 |
| Deleted | Latex/digital_sum.synctex.gz | 0 | 0 | 0 |
| Deleted | Latex/digital_sum.tex | 43 | 0 | 43 |
| Modified | README.md | 9 | 4 | 5 |
| Modified | Rust/src/main.rs | 96 | 48 | 48 |
| Deleted | TypeScript/script.js | 109 | 0 | 109 |
| Deleted | TypeScript/script.min.js | 2 | 0 | 2 |
| Deleted | TypeScript/script.ts | 141 | 0 | 141 |
| Modified | script.js | 15 | 3 | 12 |
| Modified | script.py | 39 | 13 | 26 |
| Modified | script.ts | 103 | 20 | 83 |
| Modified | script.ts.js | 7 | 5 | 2 |
diff --git a/.gitignore b/.gitignore @@ -0,0 +1,3 @@ +*.exe +Statistics +Latex+ \ No newline at end of file
diff --git a/Haskell/app/Main.hs b/Haskell/app/Main.hs @@ -3,44 +3,37 @@ module Main where import Numeric import Numeric.Natural import System.Clock +import GHC.Conc main :: IO () main = do + -- Configure the number of threads used by the program + setNumCapabilities 1 + putStrLn "\nThis program is a simple test for the following conjecture:\n" putStrLn "Let S: N -> N be the sum of the digits of a positive integer." putStrLn "For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n" putStrLn "What value would you like to test the conjecture for?" - maxStr <- getLine - let max = readDec maxStr - if (not $ null max) && ((snd $ head max ) == "") - then let counter = exceptions' 0 (fst $ head max) in do + case readDec maxStr :: [(Natural, String)] of + [(max, "")] -> do start <- getTime Monotonic putStrLn "\nLOADING. . ." - if null counter - then do + case exceptions' 0 max of + [] -> do end <- getTime Monotonic - putStrLn $ "LOADED in " ++ formatTime (end - start) ++ "s [1 Thread]" - putStrLn $ "\nThe conjecture is proved for all natural numbers smaller or equals to " ++ show (fst $ head max) ++ "!" - exit - else do - putStrLn $ "\nThe conjecture is disproved! Here are the counter examples:\n" ++ (init $ tail $ show counter) - exit - else do - putStrLn $ "\n'" ++ maxStr ++ "' is not a natural number!" - exit - -exit :: IO () -exit = do - putStrLn "Press any key to continue. . ." - getChar - return () + putStrLn $ "LOADED. . . in " ++ formatTime (end - start) ++ "s [1 Thread]" + putStrLn $ "\nThe conjecture is proved for all natural numbers smaller or equals to " ++ show max ++ "!" + counter -> putStrLn $ "\nThe conjecture is disproved! Here are the counter examples:\n" ++ (init $ tail $ show counter) + + _ -> putStrLn $ "\n'" ++ maxStr ++ "' is not a natural number!" digs :: Natural -> [Natural] -digs 0 = [0] -digs x = digs (x `div` 10) ++ [x `mod` 10] +digs x = case x of + 0 -> [0] + x -> digs (x `div` 10) ++ [x `mod` 10] sum' :: Natural -> Natural sum' x = sum $ digs x
diff --git a/Haskell/conjecture.cabal b/Haskell/conjecture.cabal @@ -4,7 +4,7 @@ cabal-version: 1.12 -- -- see: https://github.com/sol/hpack -- --- hash: 3cf9a6d881ec7aedbc39501d43197ec9a1e4562b5d73a7f1f14420405cc67697 +-- hash: 8aa8667b3d4cd7fa12aca4ea4b2ddbfe34b6f53704ead53843307c5cd05e1045 name: conjecture version: 1.0.0.0 @@ -34,7 +34,7 @@ executable conjecture-exe Paths_conjecture hs-source-dirs: app - ghc-options: -threaded -rtsopts -with-rtsopts=-N + ghc-options: -threaded -rtsopts -with-rtsopts=-N -O build-depends: base >=4.7 && <5 , clock ==0.7.2
diff --git a/Haskell/package.yaml b/Haskell/package.yaml @@ -31,6 +31,7 @@ executables: - -threaded - -rtsopts - -with-rtsopts=-N + - -O dependencies: - conjecture - clock == 0.7.2
diff --git a/Latex/digital_sum.aux b/Latex/digital_sum.aux @@ -1 +0,0 @@ -\relax
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diff --git a/Latex/digital_sum.tex b/Latex/digital_sum.tex @@ -1,42 +0,0 @@ -\documentclass{article} -\usepackage{blindtext} -\usepackage{amsfonts} -\usepackage{mathtools} -\pagenumbering{gobble} -\usepackage[a4paper, total={6in, 9in}]{geometry} -\usepackage[utf8]{inputenc} -\title{Conjectura Mia} -\author{Eli \& Thiago} -\date{29 de dezembro de 2018} -\begin{document} - \maketitle - \section*{\textit{Conjecture:}} - Let $S:\mathbb{N} \rightarrow \mathbb{N}$ be the sum of digits of a number $n \in \mathbb{N}$ --- represented in a \textit{base $\delta$ posicional system} --- and let $\nu \coloneqq \delta - 1$. We have: - - $$ - \forall a, b \in \mathbb{N} : S_{a+b}=S_a + S_b + \nu k, k \in \mathbb{Z} - $$ - - \section*{\textit{Proof:}} - For all $a \in \mathbb{N}$: - $$ - a = a_0 \cdot 10_\delta^0 + a_1 \cdot 10_\delta^1 + \dots + a_n \cdot 10_\delta^n \Rightarrow S_a = a_0 + a_1 + \dots + a_n - $$ - \noindent Therefore: - $$ - \begin{matrix} - a = a_0 \cdot (1 + \nu)^0 + \dots + a_n (1 + \nu)^n = a_0 \cdot (1 + \nu k_0) + \dots + a_n \cdot (1 + \nu k_n) \\ = a_0 + \dots + a_n + \nu k = S_a + \nu k, k \in \mathbb{Z} - \end{matrix} - $$ - - \noindent Thus, for $c \coloneqq a + b$: - $$ - \begin{cases} - & c = S_c + \nu k, k \in \mathbb{Z} \\ - & a + b = (S_a + \nu k) + (S_b + \nu k') = S_a + S_b + \nu k''\;|\; k, k', k''\in \mathbb{Z} - \end{cases} - $$ - - Therefore $c = a + b \Rightarrow S_c + \nu k = S_a + S_b + \nu k'\;|\; k, k'\in \mathbb{Z} \Rightarrow S_c = S_{a + b} = S_a + S_b + \nu k, k \in \mathbb{Z}$ - \noindent \textbf{Q.E.D} -\end{document}- \ No newline at end of file
diff --git a/README.md b/README.md @@ -11,8 +11,8 @@ The conjecture was [proved by exhaustion](https://en.wikipedia.org/wiki/Proof_by |Language |Time |Number of Threads Used| |--------------|-------|----------------------| |**Rust** |22 _s_ |2 | -|**Haskell** |60 _s_ |1 | -|**TypeScript**|198 _s_|1 | -|**JavaScript**|202 _s_|1 | +|**Haskell** |48 _s_ |1 | +|**JavaScript**|197 _s_|1 | +|**TypeScript**|219 _s_|1 | |**Ruby** |273 _s_|1 | -|**Python** |400 _s_|1 |- \ No newline at end of file +|**Python** |522 _s_|1 |
diff --git a/Rust/src/main.rs b/Rust/src/main.rs @@ -8,7 +8,7 @@ extern crate num_cpus; extern crate rand; use std::{env, thread, time::Instant, sync::mpsc, sync::mpsc::{Sender, Receiver}}; -use crossterm::{terminal, input, ClearType}; +use crossterm::{terminal, input}; use rand::prelude::*; fn main() { @@ -18,14 +18,14 @@ fn main() { // Assign the correct number of threads to run the application with // The default is the number of cores in the machine let n_cores = num_cpus::get_physical(); - let n_threads = if args.len() == 0 { n_cores } else { - match args[0].trim().parse::<usize>() { + let n_threads = if args.len() <= 1 { n_cores } else { + match args[1].trim().parse::<usize>() { Ok(n_arg) => std::cmp::min(n_arg, n_cores), Err(_) => n_cores } }; - println!("This program is a simple test for the following conjecture:\n"); + println!("\nThis program is a simple test for the following conjecture:\n"); println!("Let S: N -> N be the sum of the digits of a positive integer."); println!("For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer."); @@ -41,61 +41,67 @@ fn main() { let duration = start_time.elapsed(); // Print the results - if let Err(err) = prompt.clear(ClearType::All) { panic!(err); } - println!("LOADED. . . 100% in {}s [{} threads]\n", duration.as_secs(), n_threads); + println!("LOADED. . . in {}s [{} Threads]\n", duration.as_secs(), n_threads); if counterexpls.len() == 0 { println!("The conjecture is proved for all natural numbers smaller or equals to {}!", max); } else { println!("The conjecture is disproved! Here are the counter examples:"); - let mut counterexpls_str = String::new(); - - for pair in counterexpls { - let ordered_pair = format!("({}, {})", pair[0], pair[1]); - counterexpls_str = format!("{}, {}", counterexpls_str, ordered_pair); - } - - println!("{}\n", counterexpls_str); + let counterexpls_str: Vec<String> = counterexpls.iter().map(|(a, b)| format!("({}, {})", a, b)).collect(); + println!("{}\n", counterexpls_str.join(",")); } - - if let Err(err) = prompt.write("Press any key to continue. . . ") { panic!(err); } - let _ = input().read_char(); }, Err(_) => println!("'{}' is not a natural number!", user_input.trim()) } } -fn get_all_countrexpls(max: usize, n_threads: usize) -> Vec<[usize; 2]> { +fn get_all_countrexpls(max: usize, n_threads: usize) -> Vec<(usize, usize)> { if max / n_threads > 0 && n_threads > 1 { // Thread related variables - let (coutexpl_sender, coutexpl_reciever): (Sender<Vec<[usize; 2]>>, Receiver<Vec<[usize; 2]>>) = mpsc::channel(); + let (coutexpl_sender, coutexpl_reciever): (Sender<Vec<(usize, usize)>>, Receiver<Vec<(usize, usize)>>) = mpsc::channel(); let mut child_threads = Vec::new(); let range_lenght = max / n_threads; let mut range: Vec<usize> = (0..max).collect(); // Conjecture related variables - let mut counterexpls: Vec<[usize; 2]> = Vec::new(); + let mut counterexpls: Vec<(usize, usize)> = Vec::new(); - // Shuffle the values in the range to get an even distribution of calculations across all threads + // Shuffle the values in the range to get an even distribution of + // calculations across all threads range.shuffle(&mut thread_rng()); - for i in 1..n_threads { - let thread_countr_sd = coutexpl_sender.clone(); + // Separate a specific slice of the range and assign it to the thread + let mut sub_ranges = Vec::new(); + for i in 0..n_threads { + let start = i * range_lenght; + let end = start + range_lenght; + sub_ranges.push(range[(start as usize)..(end as usize)].to_vec()); + } - // Separate a specific slice of the range and assign it to the thread - let start = (i - 1) * range_lenght; - let end = start + range_lenght - 1; - let thread_range = range[(start as usize)..(end as usize)].to_vec(); + // Account for the fact that the maximum number tested may not be + // a multiple of the numbers of threads used for computations, hence + // the number of test performed by each thread may not be constant + if max % n_threads != 0 { + let mut rng = thread_rng(); + let end = sub_ranges.len() - 1; + let mut remainders = range[(max - max % n_threads)..max].to_vec(); + + while let Some(val) = remainders.pop() { + sub_ranges[rng.gen_range(0, end)].push(val); + } + } + + for i in 0..n_threads { + let thread_countr_sd = coutexpl_sender.clone(); + let thread_range = sub_ranges.pop().unwrap(); let child = thread::spawn(move || { thread_countr_sd.send(get_range_countrexpls(thread_range, max)) .expect(&format!("Thread n°{} was unable to sent a message trought the channel", i)); }); + child_threads.push(child); - } - - for _ in 1..n_threads { counterexpls.append(&mut coutexpl_reciever.recv().unwrap()); } @@ -109,15 +115,15 @@ fn get_all_countrexpls(max: usize, n_threads: usize) -> Vec<[usize; 2]> { } } -fn get_range_countrexpls(range: Vec<usize>, max: usize) -> Vec<[usize; 2]> { +fn get_range_countrexpls(range: Vec<usize>, max: usize) -> Vec<(usize, usize)> { let mut counterexpls = Vec::new(); for a in range { for b in a..max { let difference = sum_digits(a + b) - sum_digits(a) - sum_digits(b); - if !is_multiple_of_nine(difference) { - counterexpls.push([a, b]); + if difference % 9 != 0 { + counterexpls.push((a, b)); } } } @@ -125,23 +131,17 @@ fn get_range_countrexpls(range: Vec<usize>, max: usize) -> Vec<[usize; 2]> { counterexpls } -fn is_multiple_of_nine(n: isize) -> bool { - let floor = n / 9; - let neerest_mult = floor * 9; - - n == neerest_mult -} +fn get_digits(n: usize) -> Vec<usize> { + if n == 0 { + vec![0] + } else { + let mut digs = vec![n % 10]; + digs.append(&mut get_digits(n / 10)); -fn get_digits(n: usize) -> Vec<u32> { - n.to_string().chars().map(|d| d.to_digit(10).unwrap()).collect() + digs + } } fn sum_digits(n: usize) -> isize { - let mut sum = 0; - - for d in get_digits(n) { - sum += d as isize; - } - - sum + get_digits(n).iter().sum::<usize>() as isize } \ No newline at end of file
diff --git a/TypeScript/script.js b/TypeScript/script.js @@ -1,109 +0,0 @@ -// The following script is a simple test for the following conjecture: -// Let S: N -> N be the sum of the digits of a positive integer. -// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger. -const readline = require('readline'); -class Int { - constructor(n) { - this.val = n; - } - add(n) { - return new Int(this.val + n.val); - } - subtrack(n) { - return new Int(this.val - n.val); - } - multiply(n) { - return new Int(this.val * n.val); - } - divide(n) { - return new Int(Math.floor(this.val / n.val)); - } - incrementBy(n) { - this.val += n.val; - } - divides(n) { - return (n.val / this.val) % 1 == 0; - } - getDigits() { - return Array.from(this.val.toString()).map(char => Int.from(char)); - } - sumDigits() { - let sum = Int.zero(); - const digits = this.getDigits(); - for (const n of digits) - sum.incrementBy(n); - return sum; - } - toString() { - return `${this.val}`; - } - static from(a) { - return new Int(Math.round(Number(a))); - } - static getRange(a, b) { - const start = a.val, end = b.val, range = []; - for (let i = start; i < end; i++) { - range.push(Int.from(i)); - } - return range; - } - static zero() { - return new Int(0); - } - static one() { - return new Int(1); - } -} -function askQuestion(query) { - const rl = readline.createInterface({ - input: process.stdin, - output: process.stdout, - }); - return new Promise((resolve) => rl.question(query, (ans) => { - rl.close(); - resolve(ans); - })); -} -function getCounterExp(max) { - const starTime = new Date(), counterexmpls = [], nine = Int.from(9); - let loadBar = Int.zero(); - for (const a of Int.getRange(Int.one(), max)) { - const newLoadBar = a.multiply(Int.from(100)).divide(max); - if (loadBar != newLoadBar) { - console.clear(); - loadBar = newLoadBar; - console.log(`LOADING. . . ${loadBar}%`); - } - for (const b of Int.getRange(a, max)) { - // Check if the difference between S(a + b) and (S(a) + S(b)) is a multiple of 9 - const conjectureHolds = nine.divides(a.add(b).sumDigits().subtrack(a.sumDigits().add(b.sumDigits()))); - if (!conjectureHolds) - counterexmpls.push([a, b]); - } - } - const elepsedTime = (new Date().getTime() - starTime.getTime()) / 1000; - console.clear(); - console.log(`LOADED. . . ${loadBar}% in ${elepsedTime}s\n`); - return counterexmpls; -} -console.log(`This script is a simple test for the following conjecture: - -Let S: N -> N be the sum of the digits of a positive integer. -For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger. -`); -askQuestion("What value would you like to test the conjecture for? ").then(ans => { - if (!isNaN(Number(ans))) { - const max = Int.from(ans), counterexmpls = getCounterExp(max); - if (counterexmpls.length == 0) - console.log(`The conjecture is proved for all natural numbers smaller or equals to ${max}!`); - else { - console.log("The conjecture is disproved! Here are the counter examples:"); - let counterexmplsStr = ""; - for (const pair of counterexmpls) - counterexmplsStr = `${counterexmplsStr}, (${pair[0]}, ${pair[1]})`; - console.log(counterexmplsStr); - } - } - else - console.log(`'${ans}' is not an interger!`); -}).catch(console.error);
diff --git a/TypeScript/script.min.js b/TypeScript/script.min.js @@ -1 +0,0 @@ -const e=require("readline");class t{constructor(e){this.val=e}add(e){return new t(this.val+e.val)}subtrack(e){return new t(this.val-e.val)}multiply(e){return new t(this.val*e.val)}divide(e){return new t(Math.floor(this.val/e.val))}incrementBy(e){this.val+=e.val}divides(e){return e.val/this.val%1==0}getDigits(){return Array.from(this.val.toString()).map(e=>t.from(e))}sumDigits(){let e=t.zero();const o=this.getDigits();for(const t of o)e.incrementBy(t);return e}toString(){return`${this.val}`}static from(e){return new t(Math.round(Number(e)))}static getRange(e,o){const r=e.val,n=o.val,s=[];for(let e=r;e<n;e++)s.push(t.from(e));return s}static zero(){return new t(0)}static one(){return new t(1)}}console.log("This script is a simple test for the following conjecture:\n \nLet S: N -> N be the sum of the digits of a positive integer.\nFor all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n"),function(t){const o=e.createInterface({input:process.stdin,output:process.stdout});return new Promise(e=>o.question(t,t=>{o.close(),e(t)}))}("What value would you like to test the conjecture for? ").then(e=>{if(isNaN(Number(e)))console.log(`'${e}' is not an interger!`);else{const o=t.from(e),r=function(e){const o=new Date,r=[],n=t.from(9);let s=t.zero();for(const o of t.getRange(t.one(),e)){const i=o.multiply(t.from(100)).divide(e);s!=i&&(console.clear(),s=i,console.log(`LOADING. . . ${s}%`));for(const s of t.getRange(o,e))n.divides(o.add(s).sumDigits().subtrack(o.sumDigits().add(s.sumDigits())))||r.push([o,s])}const i=((new Date).getTime()-o.getTime())/1e3;return console.clear(),console.log(`LOADED. . . ${s}% in ${i}s\n`),r}(o);if(0==r.length)console.log(`The conjecture is proved for all natural numbers smaller or equals to ${o}!`);else{console.log("The conjecture is disproved! Here are the counter examples:");let e="";for(const t of r)e=`${e}, (${t[0]}, ${t[1]})`;console.log(e)}}}).catch(console.error);- \ No newline at end of file
diff --git a/TypeScript/script.ts b/TypeScript/script.ts @@ -1,140 +0,0 @@ -// The following script is a simple test for the following conjecture: - -// Let S: N -> N be the sum of the digits of a positive integer. -// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger. - -const readline = require('readline'); - -class Int { - private val: number; - - private constructor(n: number) { - this.val = n; - } - - public add(n: Int): Int { - return new Int(this.val + n.val); - } - - public subtrack(n: Int): Int { - return new Int(this.val - n.val); - } - - public multiply(n: Int): Int { - return new Int(this.val * n.val); - } - - public divide(n: Int): Int { - return new Int(Math.floor(this.val / n.val)); - } - - public incrementBy(n: Int) { - this.val += n.val; - } - - public divides(n: Int): boolean { - return (n.val / this.val) % 1 == 0; - } - - public getDigits(): Int[] { - return Array.from(this.val.toString()).map(char => Int.from(char)); - } - - public sumDigits(): Int { - let sum = Int.zero(); - const digits = this.getDigits(); - - for (const n of digits) - sum.incrementBy(n); - - return sum; - } - - public toString(): string { - return `${this.val}`; - } - - static from(a: number | string): Int { - return new Int(Math.round(Number(a))); - } - - static getRange(a: Int, b: Int): Int[] { - const start = a.val, end = b.val, range: Int[] = []; - - for (let i = start; i < end; i++) { - range.push(Int.from(i)); - } - - return range; - } - - static zero(): Int { - return new Int(0); - } - - static one(): Int { - return new Int(1); - } -} - -function askQuestion(query: string): Promise<string> { - const rl = readline.createInterface({ - input: process.stdin, - output: process.stdout, - }); - - return new Promise(resolve => rl.question(query, (ans: string) => { - rl.close(); - resolve(ans); - })); -} - -function getCounterExp(max: Int) { - const starTime = new Date(), counterexmpls: [Int, Int][] = [], nine = Int.from(9); - let loadBar = Int.zero(); - - for (const a of Int.getRange(Int.one(), max)) { - - const newLoadBar = a.multiply(Int.from(100)).divide(max); - if (loadBar != newLoadBar) { - console.clear(); - loadBar = newLoadBar; - console.log(`LOADING. . . ${loadBar}%`); - } - - for (const b of Int.getRange(a, max)) { - // Check if the difference between S(a + b) and (S(a) + S(b)) is a multiple of 9 - const conjectureHolds = nine.divides(a.add(b).sumDigits().subtrack(a.sumDigits().add(b.sumDigits()))); - if (!conjectureHolds) counterexmpls.push([a, b]); - } - } - - const elepsedTime = (new Date().getTime() - starTime.getTime()) / 1000; - console.clear(); - console.log(`LOADED. . . ${loadBar}% in ${elepsedTime}s\n`); - return counterexmpls; -} - -console.log(`This script is a simple test for the following conjecture: - -Let S: N -> N be the sum of the digits of a positive integer. -For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger. -`); - -askQuestion("What value would you like to test the conjecture for? ").then(ans => { - if (!isNaN(Number(ans))) { - const max = Int.from(ans), counterexmpls = getCounterExp(max); - - if (counterexmpls.length == 0) - console.log(`The conjecture is proved for all natural numbers smaller or equals to ${max}!`); - else { - console.log("The conjecture is disproved! Here are the counter examples:"); - - let counterexmplsStr = ""; - for (const pair of counterexmpls) - counterexmplsStr = `${counterexmplsStr}, (${pair[0]}, ${pair[1]})`; - - console.log(counterexmplsStr); - } - } else console.log(`'${ans}' is not an interger!`); -}).catch(console.error);- \ No newline at end of file
diff --git a/script.js b/script.js @@ -9,7 +9,7 @@ Array.prototype.none = function() { return this.length == 0; } -Number.prototype.getDigits = function() { +Number.prototype.digits = function() { return Array.from(String(this)).map(char => Number(char)); } @@ -18,13 +18,7 @@ Number.prototype.divides = function(n) { } Number.prototype.sumDigits = function() { - let sum = 0; - const digits = this.getDigits(); - - for (n of digits) - sum += n; - - return sum; + return this.digits().reduce((a, b) => a + b); } function askQuestion(query) { @@ -56,11 +50,8 @@ function getCounterExp(max) { } for (b = a; b <= max; b++) { - // Check if the difference between S(a + b) and (S(a) + S(b)) is a multiple of 9 - const conjectureHolds = (9).divides( - (a + b).sumDigits() - (a.sumDigits() + b.sumDigits()) - ); + const conjectureHolds = (9).divides((a + b).sumDigits() - (a.sumDigits() + b.sumDigits())); if (!conjectureHolds) counterexmpls.push([a, b]); } }
diff --git a/script.py b/script.py @@ -6,32 +6,19 @@ import sys import os import time +from functools import reduce # A function for clearing the prompt clear = (lambda : os.system("cls")) if sys.platform.startswith("win") else (lambda : os.system("clear")) -def is_multiple_of_nine(n): - return (n / 9) % 1 == 0 - -def get_digits(n): - output = [] - - for ch in str(n): - output.append(int(ch)) - - return output +def digits(n): + return map(lambda c: int(c), list(str(n))) def sum_digits(n): - digits = get_digits(n) - output = 0 - - for d in digits: - output += d - - return output + return reduce((lambda a, b: a + b), digits(n)) def get_counterexmpls(n): - start_time = time.time() + start = time.time() load_bar = 0 counterexmpls = [] @@ -42,18 +29,18 @@ def get_counterexmpls(n): if not round(a * 100 / n) == load_bar: load_bar = round(a * 100 / n) clear() - print("LOADING. . . %s%%" % load_bar) + print("LOADING. . . {}%".format(load_bar)) for b in range(a, n + 1): - difference = sum_digits(a + b) - (sum_digits(a) + sum_digits(b)) + diff = sum_digits(a + b) - (sum_digits(a) + sum_digits(b)) - if not is_multiple_of_nine(difference): + if not diff % 9 == 0: counterexmpls.append([a, b]) # Mesure the elepsed time - elepsed_time = time.time() - start_time + elepsed = time.time() - start clear() - print("LOADED. . . %s%% in %ds\n" % (load_bar, elepsed_time)) + print("LOADED. . . {}% in {}s\n".format(load_bar, elepsed)) return counterexmpls @@ -71,14 +58,14 @@ try: counterexmpls = get_counterexmpls(maximum) if len(counterexmpls) == 0: - print("The conjecture is proved for all natural numbers smaller or equals to %s!" % maximum) + print("The conjecture is proved for all natural numbers smaller or equals to {}!".format(maximum)) else: print("The conjecture is disproved! Here are the counter examples:") counterexmpls_str = "" for pair in counterexmpls: - counterexmpls_str = "%s, (%d, %f)" % (counterexmpls_str, pair[0], pair[1]) + counterexmpls_str = "{}, ({}, {})".format(counterexmpls_str, pair[0], pair[1]) print(counterexmpls_str) except: - print("'%s' isn't a valid number!" % user_input) + print("'{}' isn't a valid number!".format(user_input))
diff --git a/script.ts b/script.ts @@ -5,108 +5,45 @@ const readline = require('readline'); -class Int { - private val: number; - - private constructor(n: number) { - this.val = n; - } - - public add(n: Int): Int { - return new Int(this.val + n.val); - } - - public subtrack(n: Int): Int { - return new Int(this.val - n.val); - } - - public multiply(n: Int): Int { - return new Int(this.val * n.val); - } - - public divide(n: Int): Int { - return new Int(Math.floor(this.val / n.val)); - } - - public incrementBy(n: Int) { - this.val += n.val; - } - - public divides(n: Int): boolean { - return (n.val / this.val) % 1 == 0; - } - - public getDigits(): Int[] { - return Array.from(this.val.toString()).map(char => Int.from(char)); - } - - public sumDigits(): Int { - let sum = Int.zero(); - const digits = this.getDigits(); - - for (const n of digits) - sum.incrementBy(n); - - return sum; - } - - public toString(): string { - return `${this.val}`; - } - - static from(a: number | string): Int { - return new Int(Math.round(Number(a))); - } - - static getRange(a: Int, b: Int): Int[] { - const start = a.val, end = b.val, range: Int[] = []; - - for (let i = start; i < end; i++) { - range.push(Int.from(i)); - } - - return range; - } +function digits(n: number) { + return Array.from(Math.round(Math.abs(n)).toString()).map(c => parseInt(c)); +} - static zero(): Int { - return new Int(0); - } +function sum(n: number) { + return digits(n).reduce((a, b) => a + b); +} - static one(): Int { - return new Int(1); - } +function test(a: number, b: number) { + return (sum(a + b) - (sum(a) + sum(b))) % 9 == 0; } -function askQuestion(query: string) { +function ask(question: string): Promise<string> { const rl = readline.createInterface({ input: process.stdin, output: process.stdout, }); - return new Promise((resolve: (value?: string | PromiseLike<string>) => void) => rl.question(query, (ans: string) => { + return new Promise(resolve => rl.question(question, (ans: string) => { rl.close(); resolve(ans); })); } -function getCounterExp(max: Int) { - const starTime = new Date(), counterexmpls: [Int, Int][] = [], nine = Int.from(9); - let loadBar = Int.zero(); +function getCounterExp(max: number) { + const starTime = new Date(), counterexmpls: [number, number][] = []; + let loadBar = 0; - for (const a of Int.getRange(Int.one(), max)) { + for (let a = 0; a <= max; a++) { - const newLoadBar = a.multiply(Int.from(100)).divide(max); + const newLoadBar = a * 100 / max; if (loadBar != newLoadBar) { console.clear(); loadBar = newLoadBar; console.log(`LOADING. . . ${loadBar}%`); } - for (const b of Int.getRange(a, max)) { - // Check if the difference between S(a + b) and (S(a) + S(b)) is a multiple of 9 - const conjectureHolds = nine.divides(a.add(b).sumDigits().subtrack(a.sumDigits().add(b.sumDigits()))); - if (!conjectureHolds) counterexmpls.push([a, b]); - } + for (let b = a; b <= max; b++) + if (!test(a, b)) counterexmpls.push([a, b]); } const elepsedTime = (new Date().getTime() - starTime.getTime()) / 1000; @@ -121,9 +58,9 @@ Let S: N -> N be the sum of the digits of a positive integer. For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger. `); -askQuestion("What value would you like to test the conjecture for? ").then(ans => { - if (!isNaN(Number(ans))) { - const max = Int.from(ans), counterexmpls = getCounterExp(max); +ask("What value would you like to test the conjecture for? ").then(ans => { + if (!isNaN(parseInt(ans))) { + const max = parseInt(ans), counterexmpls = getCounterExp(max); if (counterexmpls.length == 0) console.log(`The conjecture is proved for all natural numbers smaller or equals to ${max}!`);
diff --git a/script.ts.js b/script.ts.js @@ -1 +1,4 @@ -const e=require("readline");class t{constructor(e){this.val=e}add(e){return new t(this.val+e.val)}subtrack(e){return new t(this.val-e.val)}multiply(e){return new t(this.val*e.val)}divide(e){return new t(Math.floor(this.val/e.val))}incrementBy(e){this.val+=e.val}divides(e){return e.val/this.val%1==0}getDigits(){return Array.from(this.val.toString()).map(e=>t.from(e))}sumDigits(){let e=t.zero();const o=this.getDigits();for(const t of o)e.incrementBy(t);return e}toString(){return`${this.val}`}static from(e){return new t(Math.round(Number(e)))}static getRange(e,o){const r=e.val,n=o.val,s=[];for(let e=r;e<n;e++)s.push(t.from(e));return s}static zero(){return new t(0)}static one(){return new t(1)}}console.log("This script is a simple test for the following conjecture:\n \nLet S: N -> N be the sum of the digits of a positive integer.\nFor all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n"),function(t){const o=e.createInterface({input:process.stdin,output:process.stdout});return new Promise(e=>o.question(t,t=>{o.close(),e(t)}))}("What value would you like to test the conjecture for? ").then(e=>{if(isNaN(Number(e)))console.log(`'${e}' is not an interger!`);else{const o=t.from(e),r=function(e){const o=new Date,r=[],n=t.from(9);let s=t.zero();for(const o of t.getRange(t.one(),e)){const i=o.multiply(t.from(100)).divide(e);s!=i&&(console.clear(),s=i,console.log(`LOADING. . . ${s}%`));for(const s of t.getRange(o,e))n.divides(o.add(s).sumDigits().subtrack(o.sumDigits().add(s.sumDigits())))||r.push([o,s])}const i=((new Date).getTime()-o.getTime())/1e3;return console.clear(),console.log(`LOADED. . . ${s}% in ${i}s\n`),r}(o);if(0==r.length)console.log(`The conjecture is proved for all natural numbers smaller or equals to ${o}!`);else{console.log("The conjecture is disproved! Here are the counter examples:");let e="";for(const t of r)e=`${e}, (${t[0]}, ${t[1]})`;console.log(e)}}}).catch(console.error);- \ No newline at end of file +// The following script is a simple test for the following conjecture: +// Let S: N -> N be the sum of the digits of a positive integer. +// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger. +const e=require("readline");function o(e){return function(e){return Array.from(Math.round(Math.abs(e)).toString()).map(e=>parseInt(e))}(e).reduce((e,o)=>e+o)}function t(e,t){return(o(e+t)-(o(e)+o(t)))%9==0}console.log("This script is a simple test for the following conjecture:\n \nLet S: N -> N be the sum of the digits of a positive integer.\nFor all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n"),function(o){const t=e.createInterface({input:process.stdin,output:process.stdout});return new Promise(e=>t.question(o,o=>{t.close(),e(o)}))}("What value would you like to test the conjecture for? ").then(e=>{if(isNaN(parseInt(e)))console.log(`'${e}' is not an interger!`);else{const o=parseInt(e),n=function(e){const o=new Date,n=[];let r=0;for(let o=0;o<=e;o++){const s=100*o/e;r!=s&&(console.clear(),r=s,console.log(`LOADING. . . ${r}%`));for(let r=o;r<=e;r++)t(o,r)||n.push([o,r])}const s=((new Date).getTime()-o.getTime())/1e3;return console.clear(),console.log(`LOADED. . . ${r}% in ${s}s\n`),n}(o);if(0==n.length)console.log(`The conjecture is proved for all natural numbers smaller or equals to ${o}!`);else{console.log("The conjecture is disproved! Here are the counter examples:");let e="";for(const o of n)e=`${e}, (${o[0]}, ${o[1]})`;console.log(e)}}}).catch(console.error);+ \ No newline at end of file