03 mono

zeby ograniczyć ilość obliczeń

01-rozwiazanie.js

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+const rl = require('readline').createInterface({
+  input: process.stdin,
+  output: process.stdout
+});
+
+//zapytanie o wartosc n
+rl.question('n? ', n => {
+  n = parseInt(n);
+  //sprawdzenie czy n na pewno jest liczba
+  if (isNaN(n)) throw Error('Must be Number');
+  // deklarowanie slownikow dla poszczegolnych elementow(aby się nie powtorzyly)
+  let elOdw = new Dictionary();
+  let dzielZero = new Dictionary();
+  let elNil = new Dictionary();
+  let elIden = new Dictionary();
+  //#region dodanie trywalnych
+  dzielZero.add(0, 0);
+  elNil.add(0, 0);
+  elIden.add(0, 0);
+  //#endregion
+  for (let y = 0; y < n; y++) {
+    //#region Obliczanie elementow Idenpotetnych
+    if (Math.pow(y, 2) % n == y) {
+      elIden.add(y, y);
+    }
+    //#endregion
+    for (let x = 0; x < n; x++) {
+      //#region obliczanie elementow Nilpotetnych
+      if (Math.pow(y, x) % n == 0) {
+        elNil.add(y, y);
+      }
+      //#endregion
+      //#region Obliczanie elementow odwracalnych'
+      if (x >= y && (x * y) % n == 1) {
+        elOdw.add(x, x);
+        elOdw.add(y, y);
+      }
+      //#endregion
+      //#region obliczanie dzielnikow zera
+      if (x >= y && x != 0 && y != 0 && (x * y) % n == 0) {
+        dzielZero.add(x, x);
+        dzielZero.add(y, y);
+      }
+      //#endregion
+    }
+  }
+  //wypisanie obliczonych wartosci wartosci
+  console.log([
+    elOdw.getValues(),
+    dzielZero.getValues(),
+    elNil.getValues(),
+    elIden.getValues()
+  ]);
+  //zamkniecie połaczenia z input/output
+  rl.close();
+});
+
+function NWD(a, b) {
+  return b ? NWD(b, a % b) : a;
+}
+// klasa słownika
+class Dictionary {
+  constructor() {
+    this.elements = {};
+  }
+  add(key, value) {
+    this.elements[key] = value;
+  }
+  remove(key, value) {
+    delete this.elements[key];
+  }
+
+  getKeys() {
+    let keys = [];
+    for (let key in this.elements) {
+      keys.push(key);
+    }
+    return keys;
+  }
+  getValues() {
+    let values = [];
+    for (let key in this.elements) {
+      values.push(this.elements[key]);
+    }
+    return values;
+  }
+}

02-rozwiazanie.js

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+let Polynomial = require('./polynomial.js');
+let mul, div, gcd;
+
+
+let n = parseInt(process.argv[2]);
+let p1 = JSON.parse(process.argv[3].replace(/'/g, '"'));
+let p2 = JSON.parse(process.argv[4].replace(/'/g, '"'));
+
+let f = new Polynomial.Class(n, p1);
+let g = new Polynomial.Class(n, p2);
+mul = Polynomial.multiply(f, g).coefficients;
+try {
+    div = Polynomial.divide(f, g).coefficients
+} catch (e) {
+    console.log(e)
+}
+try {
+    gcd = Polynomial.gcd(f, g).coefficients;
+} catch (e) {
+    console.log(e);
+}
+console.log([mul, div, gcd])

03-rozwiazanie.js

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+const crc = require("./crc.js");
+const message = process.argv[3];
+const flag = process.argv[2];
+
+switch (flag) {
+    case '-e':
+        console.log(crc.encode(message).encoded);
+        break;
+    case '-d':
+        let fcs = JSON.parse(process.argv[4].replace(/'/g, '"'));
+        console.log(crc.decode(message, fcs));
+        break;
+    case '-t':
+        let res = crc.encode(message);
+        console.log(res.encoded);
+        console.log(crc.decode(message, res.FCS))
+        break;
+    default:
+        throw "incorect flag"
+}

crc.js

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+const Polynomial = require('./polynomial.js');
+
+const L = new Polynomial.Class(2, new Array(16).fill(1));
+const X16 = new Polynomial.Class(2, [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]); //jako ze można to od razu wymnożyć
+const G = new Polynomial.Class(2, [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]); //jako ze można to od razu wymnożyć
+
+const to_bin = a => {
+    var result = "";
+    for (var i = 0; i < a.length; i++) {
+        var bin = a[i].charCodeAt().toString(2);
+        result += Array(8 - bin.length + 1).join("0") + bin;
+    }
+    return result;
+}
+const to_ascii = a => {
+    a = a.join('');
+    a = parseInt(a, 2);
+    //nie znalazłem innego sposobu w js na osiągniecie tego efektu..
+    // if (a < 126) //ponieważ wieksze liczby nie należą do typowego Ascii//porzucone ze wzgledu na decode
+    return String.fromCharCode(a);
+    // else {
+    //     return "0x" + a.toString(16);
+    //     //  return "\\x" + a.toString(16); //escape \ nie wiem czemu dobrze nie działą i i tak wypisuje \\
+    // }
+
+
+}
+const mod8format = array => {
+    while (array.length % 8 != 0) {
+        array.push(0);
+    }
+    return array;
+}
+
+const fcs = m => {
+    let bits = m.map(to_bin); //message in binary
+    bits = bits.join('').split('').reverse(); //reverse binary decoded message
+    let M = new Polynomial.Class(2, bits);
+    let fcs = Polynomial.multiply(X16, M);
+
+    fcs = Polynomial.add(fcs,
+        Polynomial.multiply(
+            Polynomial.Mono(m.length * 8, 1, 2),
+            L
+        )
+    )
+    fcs = Polynomial.divide(fcs, G);
+    for (let i = 0; i < 16 - fcs.coefficients.length; i++) fcs.coefficients.push(0);
+    fcs.coefficients.reverse();
+    return fcs.coefficients;
+}
+
+
+
+const check = m => {
+
+    let bits = m.map(to_bin); //message in binary
+    bits = bits.join('').split('').reverse(); //reverse binary decoded message
+
+    let fcs = Polynomial.Mono(bits.length, 1, 2);
+
+
+    let C = new Polynomial.Class(2, bits);
+    C = Polynomial.multiply(X16, C);
+    C.coefficients = mod8format(C.coefficients);
+    let S = Polynomial.add(
+        C,
+        Polynomial.multiply(
+            fcs,
+            L
+        )
+    )
+
+    S = Polynomial.divide(S, G)
+    if (S.coefficients.length === 0) {
+        return true;
+    } else
+        return false;
+}
+
+function encode(m) {
+    m = m.split('');
+    let res = fcs(m);
+
+    let f1 = [];
+    let f2 = [];
+    for (let i = 0; i < res.length; i++) {
+        if (i < 8) {
+            f1.push(res[i]);
+        } else {
+            f2.push(res[i]);
+        }
+    }
+    f1 = to_ascii(f1);
+    f2 = to_ascii(f2);
+    m.push(f1);
+    m.push(f2);
+    return {
+        encoded: m,
+        FCS: [f1, f2]
+
+    };
+
+}
+
+exports.encode = encode;
+
+function decode(m, fcs) {
+    m = m.split('');
+    to_check = fcs;
+    for (let char in fcs) {
+        m.push(fcs[char]);
+    }
+    return check(m)
+
+}
+exports.decode = decode;

polynomial.js

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+class Polynomial {
+    constructor(mod, coefArray) {
+        this.mod = mod;
+        this.degree = (coefArray.length - 1);
+
+        this.coefficients = Array.from(coefArray); //zeby nie przekazywać referencji
+        this.normalize();
+    }
+    normalize() {
+        while (this.coefficients && this.coefficients[this.coefficients.length - 1] == 0) {
+            this.coefficients.pop();
+        }
+    }
+}
+
+exports.Class = Polynomial;
+
+function get_mod(p1, p2) {
+    let n;
+    if (p1.mod !== p2.mod) {
+        throw "different modulo"
+    } else {
+        return p1.mod;
+    }
+}
+
+function prepare(p1, p2) {
+    let n = get_mod(p1, p2);
+    let len_p1 = p1.coefficients.length;
+    let len_p2 = p2.coefficients.length;
+    result = new Array(Math.max(len_p1, len_p2)).fill(0);
+    if (len_p1 > len_p2) {
+        for (let x = 0; x < len_p1 - len_p2; x++) p2.coefficients.push(0);
+    } else {
+        for (let x = 0; x < len_p2 - len_p1; x++) p1.coefficients.push(0);
+    }
+    return {
+        result,
+        n
+    };
+
+}
+
+function add(p1, p2) {
+
+    let {
+        result,
+        n
+    } = prepare(p1, p2);
+    for (let i = 0; i < result.length; i++) {
+        result[i] = (p1.coefficients[i] + p2.coefficients[i]) % n;
+    }
+    return new Polynomial(n, result);
+}
+exports.add = add;
+
+function sub(p1, p2) {
+    let {
+        result,
+        n
+    } = prepare(p1, p2);
+    for (let i = 0; i < result.length; i++) {
+        result[i] = (p1.coefficients[i] - p2.coefficients[i]) % n;
+    }
+    return new Polynomial(n, result);
+}
+exports.sub = sub;
+
+function sub(p1, p2) {
+    let n = get_mod(p1, p2);
+    let len_p1 = p1.coefficients.length;
+    let len_p2 = p2.coefficients.length;
+    result = new Array(Math.max(len_p1, len_p2)).fill(0);
+    if (len_p1 > len_p2) {
+        for (let x = 0; x < len_p1 - len_p2; x++) p2.coefficients.push(0);
+    } else {
+        for (let x = 0; x < len_p2 - len_p1; x++) p1.coefficients.push(0);
+    }
+    for (let i = 0; i < result.length; i++) {
+        result[i] = (p1.coefficients[i] - p2.coefficients[i]) % n;
+    }
+    return new Polynomial(n, result);
+}
+exports.add = add;
+
+function multiply(p1, p2) {
+    let n = get_mod(p1, p2);
+    let f = p1.coefficients;
+    let g = p2.coefficients;
+    result = new Array(f.length + g.length - 1).fill(0);
+
+    let tmp = [];
+    for (let i = 0; i < f.length; i++) {
+        for (let j = 0; j < g.length; j++) {
+            result[i + j] += f[i] * g[j];
+        }
+    }
+    return new Polynomial(n, result.map(x => (x % n) + (x < 0 ? n : 0)));
+}
+exports.multiply = multiply;
+
+function power(p1, pow) {
+    let result = p1;
+    for (let i = 1; i < pow; i++) {
+        result = multiply(result, p1);
+    }
+    return result;
+}
+exports.power = power;
+
+function divide(p1, p2) {
+    let n;
+    if (p1.mod !== p2.mod) {
+        throw "different modulo"
+    } else {
+        n = p1.mod;
+    }
+    let inverse = (x) => {
+        for (let i = 1; i < 2; i++) {
+            let r = (i * x) % 2;
+            if (r == 1)
+                return i
+            else
+                throw "divisionError"
+
+        }
+    }
+    if (p1.degree < p2.degree)
+        return p1;
+    let f = p1.coefficients;
+    let g = p2.coefficients;
+    let g_lead_coef = g[g.length - 1];
+    let g_deg = p2.degree;
+
+    while (f.length >= g.length) {
+
+        let f_lead_coef = f[f.length - 1];
+        let tmp_coef = f_lead_coef * inverse(g_lead_coef);
+        let tmp_exp = f.length - 1 - g_deg;
+        let tmp = [];
+        for (let i = 0; i < tmp_exp; i++) {
+            tmp.push(0);
+        }
+        tmp.push(tmp_coef);
+        tmp_poly = new Polynomial(n, tmp);
+        let sub = multiply(p2, tmp_poly, n);
+        let tmp_f = [];
+        for (let i = 0; i < f.length; i++) {
+            for (let j = 0; j < sub.coefficients.length; j++) {
+                if (i == j)
+                    tmp_f.push(f[i] - sub.coefficients[j]);
+            }
+        }
+
+        f = tmp_f.map(x => (x % n) + (x < 0 ? n : 0));
+        while (f && f[f.length - 1] === 0)
+            f.pop();
+
+    }
+    return new Polynomial(n, f);
+}
+
+exports.divide = divide;
+
+function gcd(p1, p2) {
+    if (p2.coefficients.length === 0) {
+        return p1;
+    }
+    return gcd(p2, divide(p1, p2));
+}
+
+
+exports.gcd = gcd;
+
+function Mono(n, c, mod) {
+    let coef = new Array(n).fill(0);
+    coef.push(c);
+    return new Polynomial(mod, coef);
+}
+exports.Mono = Mono;