Added CRT Calculator

Rakesh9100 · Jan 14, 2025 · 08e2ca6 · 08e2ca6
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diff --git a/Calculators/Chinese-Remainder-Theorem-Calculator/assests/background.jpg b/Calculators/Chinese-Remainder-Theorem-Calculator/assests/background.jpg
diff --git a/Calculators/Chinese-Remainder-Theorem-Calculator/index.html b/Calculators/Chinese-Remainder-Theorem-Calculator/index.html
@@ -0,0 +1,27 @@
+<!DOCTYPE html>
+<html lang="en">
+  <head>
+    <meta charset="UTF-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>Chinese Remainder Theorem Calculator</title>
+    <link rel="stylesheet" href="style.css" />
+  </head>
+  <body>
+    <div class="container">
+      <h1>Chinese Remainder Theorem Calculator</h1>
+      <p>Add equations you want to solve:</p>
+      <div id="inputs">
+        <div class="equation">
+          <input type="number" placeholder="Remainder" class="remainder" />
+          <span>mod</span>
+          <input type="number" placeholder="Modulo" class="modulo" />
+          <button class="remove-btn" onclick="removeEquation(this)">-</button>
+        </div>
+      </div>
+      <button class="add-btn" onclick="addEquation()">+</button>
+      <button class="solve-btn" onclick="solve()">SOLVE ></button>
+      <div id="output" class="output"></div>
+    </div>
+    <script src="script.js"></script>
+  </body>
+</html>
diff --git a/Calculators/Chinese-Remainder-Theorem-Calculator/script.js b/Calculators/Chinese-Remainder-Theorem-Calculator/script.js
@@ -0,0 +1,77 @@
+function addEquation() {
+    const inputsDiv = document.getElementById("inputs");
+    const newEquation = document.createElement("div");
+    newEquation.className = "equation";
+    newEquation.innerHTML = `
+      <input type="number" placeholder="Remainder" class="remainder">
+      <span>mod</span>
+      <input type="number" placeholder="Modulo" class="modulo">
+      <button class="remove-btn" onclick="removeEquation(this)">-</button>
+    `;
+    inputsDiv.appendChild(newEquation);
+  }
+
+  function removeEquation(button) {
+    button.parentElement.remove();
+  }
+
+  function solve() {
+    const remainders = Array.from(document.querySelectorAll(".remainder")).map(input => parseInt(input.value));
+    const modulos = Array.from(document.querySelectorAll(".modulo")).map(input => parseInt(input.value));
+
+    if (remainders.includes(NaN) || modulos.includes(NaN) || modulos.includes(0)) {
+      alert("Please fill all fields correctly. Modulo cannot be 0.");
+      return;
+    }
+
+    if (!areCoprime(modulos)) {
+      document.getElementById("output").innerHTML = "The modulos are not pairwise coprime. Please use coprime values.";
+      return;
+    }
+
+    const m = modulos.reduce((acc, curr) => acc * curr, 1); // Find m
+    const M = modulos.map(mod => m / mod); // Find Mi
+    const y = M.map((Mi, index) => modularInverse(Mi, modulos[index])); // Find yi
+    const x = remainders.reduce((sum, a, index) => sum + a * M[index] * y[index], 0) % m;
+
+    // Generate explanation
+    let explanation = `<p>Using Chinese Remainder Theorem, solve the system of equations:</p>`;
+    explanation += `<p>${remainders.map((a, i) => `x ≡ ${a} (mod ${modulos[i]})`).join("<br>")}</p>`;
+    explanation += `<p>1. Verify moduli are pairwise coprime: ${modulos.map((m1, i) =>
+      modulos.slice(i + 1).map(m2 => `gcd(${m1}, ${m2}) = ${gcd(m1, m2)}`).join(", ")
+    ).join(", ")}.</p>`;
+    explanation += `<p>2. Calculate M = ${modulos.join(" × ")} = ${m}</p>`;
+    explanation += `<p>3. Calculate Mi and modular inverses:</p>`;
+    M.forEach((Mi, index) => {
+      explanation += `<p>M${index + 1} = ${Mi}, inverse (mod ${modulos[index]}) = ${y[index]}</p>`;
+    });
+    explanation += `<p>4. Calculate x using: x = Σ(ai * Mi * yi) mod M = ${x}</p>`;
+    explanation += `<p><strong>Final Answer: x = ${x}</strong></p>`;
+
+    document.getElementById("output").innerHTML = explanation;
+  }
+
+  function areCoprime(numbers) {
+    for (let i = 0; i < numbers.length; i++) {
+      for (let j = i + 1; j < numbers.length; j++) {
+        if (gcd(numbers[i], numbers[j]) !== 1) return false;
+      }
+    }
+    return true;
+  }
+
+  function gcd(a, b) {
+    while (b !== 0) {
+      [a, b] = [b, a % b];
+    }
+    return a;
+  }
+
+  function modularInverse(a, m) {
+    a = a % m;
+    for (let x = 1; x < m; x++) {
+      if ((a * x) % m === 1) return x;
+    }
+    return null;
+  }
+
diff --git a/Calculators/Chinese-Remainder-Theorem-Calculator/style.css b/Calculators/Chinese-Remainder-Theorem-Calculator/style.css
@@ -0,0 +1,76 @@
+body {
+    font-family: Arial, sans-serif;
+    margin: 0;
+    padding: 0;
+    background: url(./assests/background.jpg);
+    background-size: cover;
+    color: white;
+
+  }
+
+  .container {
+    max-width: 800px;
+    margin: 50px auto;
+    background: rgba(0, 0, 0, 0.8);
+    padding: 20px;
+    border-radius: 10px;
+    box-shadow: 0 5px 15px rgba(0, 0, 0, 0.5);
+  }
+
+  h1 {
+    text-align: center;
+  }
+
+  p {
+    text-align: center;
+  }
+
+  #inputs .equation {
+    display: flex;
+    align-items: center;
+    justify-content: center;
+    margin-bottom: 10px;
+  }
+
+  #inputs .equation input {
+    margin: 0 5px;
+    padding: 5px;
+    width: 80px;
+    border-radius: 5px;
+    border: 1px solid #ccc;
+  }
+
+  #inputs .equation span {
+    font-size: 16px;
+    margin: 0 5px;
+  }
+
+  button {
+    cursor: pointer;
+    padding: 8px 15px;
+    font-size: 14px;
+    border-radius: 5px;
+    border: none;
+  }
+
+  .add-btn,
+  .solve-btn {
+    display: block;
+    margin: 20px auto;
+    background: #6200ea;
+    color: white;
+  }
+
+  .remove-btn {
+    background: red;
+    color: white;
+  }
+
+  .output {
+    margin-top: 20px;
+    padding: 10px;
+    background: lightblue;
+    color: black;
+    border-radius: 5px;
+  }
+