Initial commit

README.md

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+REFERENCES
+
+- H. Fredricksen and I. J. Kessler, "An algorithm for generating necklaces of beads in two colors," Discrete Mathematics 61 (1986) 181-188
+- H. Fredricksen and J. Maiorana, "Necklaces of beads in k colors and k-ary de Bruijn sequences," Discrete Mathematics 23, No. 3 (1978) 207-210
+- F. Ruskey, C. Savage, and T. Wang, "Generating Necklaces," Journal of Algorithms 13, No.3 (1992) 414-430
+- J.Sawada, "Generating bracelets in constant amortized time,", Society for Industrial and Applied Mathematics 31, No.1 (2001) 259-268
+- J.Davies, “Combinatorial Necklaces and Bracelets”, www.jasondavies.com/necklaces, Accessed 15 Nov. 2023

generate.js

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+/**
+ *  REFERENCES
+ * [1] H. Fredricksen and I. J. Kessler, "An algorithm for generating necklaces of beads in two colors," Discrete Mathematics 61 (1986) 181-188
+ * [2] H. Fredricksen and J. Maiorana, "Necklaces of beads in k colors and k-ary de Bruijn sequences," Discrete Mathematics 23, No. 3 (1978) 207-210
+ * [3] F. Ruskey, C. Savage, and T. Wang, "Generating Necklaces," Journal of Algorithms 13, No.3 (1992) 414-430
+ * [4] J.Sawada, "Generating bracelets in constant amortized time,", Society for Industrial and Applied Mathematics 31, No.1 (2001) 259-268
+ * [5] J.Davies, “Combinatorial Necklaces and Bracelets”, www.jasondavies.com/necklaces, Accessed 15 Nov. 2023
+ */
+
+const BEADS_RADIUS = 5;
+const BEADS_COLOR = ["red", "orange", "green", "blue", "purple"];
+
+document.addEventListener("DOMContentLoaded", function (event) {
+  const length = document.querySelector(".length");
+  const kind = document.querySelector(".kind");
+  const type = document.querySelector(".type");
+  const generateButton = document.querySelector(".generate");
+  const result = document.querySelector(".result");
+  const resultNum = document.querySelector(".result-number");
+
+  generateButton.addEventListener("click", (event) => {
+    [result.innerHTML, resultNum.innerHTML] = generate(
+      length.value,
+      kind.value,
+      type.value
+    );
+  });
+});
+
+function getCoordinates(length) {
+  let angle = (Math.PI * 2) / length;
+  const angles = [];
+  const coordinates = [];
+  for (let i = 0; i < length; i++) {
+    angles.push(angle * i);
+  }
+  for (beadsAngle of angles) {
+    coordinates.push([Math.sin(beadsAngle), -Math.cos(beadsAngle)]);
+  }
+  return coordinates;
+}
+
+const generate = (length, kind, type) => {
+  const resultArr =
+    type === "0" ? getNecklaces(length, kind) : getBracelets(length, kind);
+
+  const beadsCoordinates = getCoordinates(length);
+  let drawing = "";
+  resultArr.forEach((uniqueOutcome, i) => {
+    drawing += `<svg width="100" height="100" fill="none" xmlns="http://www.w3.org/2000/svg"  viewBox="-7.5 -7.5 15 15"
+    <defs>
+      
+    </defs>
+    >
+      <circle cx="0" cy="0" r="5" stroke-width="0.2" stroke="silver"></circle>`;
+    uniqueOutcome.forEach((bead, j) => {
+      drawing += `<circle cx="${beadsCoordinates[j][0] * BEADS_RADIUS}" cy="${
+        beadsCoordinates[j][1] * BEADS_RADIUS
+      }" r="1" fill="url(#beadGradient${i}_${j}_${bead})"></circle>
+      <defs>
+        <radialGradient id="beadGradient${i}_${j}_${bead}" cx="40%" cy="40%" >
+          <stop offset="0%" style="stop-color: #ffffc6; stop-opacity: 1" />
+          <stop offset="100%" style="stop-color: ${
+            BEADS_COLOR[bead]
+          }; stop-opacity: 1" />
+        </radialGradient>
+      </defs>`;
+    });
+    drawing += `</svg>`;
+  });
+  return [drawing, "Number of unique arrangements: " + resultArr.length];
+};

getBracelets.js

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+/*
+  Joe Sawada,
+  Generating bracelets in constant amortized time,
+  Society for Industrial and Applied Mathematics,
+  Volume 31, Issue 1,
+  2001,
+  Pages 259-268,
+  https://epubs.siam.org/doi/10.1137/S0097539700377037
+ */
+function getBracelets(n, k) {
+  const a = [];
+  for (let i = 0; i < n; i++) a[i] = 0;
+
+  return generateBracelets(1, 1, 1, -1, 0, false);
+
+  function checkRev(t, i) {
+    for (let j = i + 1; j <= (t + 1) / 2; j++) {
+      if (a[j] < a[t - j + 1]) return 0;
+      if (a[j] > a[t - j + 1]) return -1;
+    }
+    return 1;
+  }
+
+  function generateBracelets(t, p, r, u, v, rs) {
+    let outcomes = [];
+    if (t - 1 > (n - r) / 2 + r) {
+      if (a[t - 1] > a[n - t + 2 + r]) rs = false;
+      else if (a[t - 1] < a[n - t + 2 + r]) rs = true;
+    }
+    if (t > n) {
+      if (!rs && n % p === 0) outcomes.push(a.slice(1));
+    } else {
+      a[t] = a[t - p];
+
+      if (a[t] === a[1]) v++;
+      else v = 0;
+
+      if (u === -1 && a[t - 1] !== a[1]) u = r = t - 2;
+      if (u === -1 || t !== n || a[n] !== a[1]) {
+        if (u === v) {
+          let rev = checkRev(t, u);
+          if (rev !== -1)
+            outcomes = outcomes.concat(
+              generateBracelets(t + 1, p, rev ? t : r, u, v, rev ? false : rs)
+            );
+        } else {
+          outcomes = outcomes.concat(generateBracelets(t + 1, p, r, u, v, rs));
+        }
+      }
+      for (let j = a[t - p] + 1; j < k; j++) {
+        a[t] = j;
+        outcomes = outcomes.concat(generateBracelets(t + 1, t, r, u, 0, rs));
+      }
+    }
+    return outcomes;
+  }
+}

getNecklaces.js

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+/*
+  Frank Ruskey, Carla Savage, Terry Min Yih Wang,
+  Generating necklaces,
+  Journal of Algorithms,
+  Volume 13, Issue 3,
+  1992,
+  Pages 414-430,
+  ISSN 0196-6774,
+  https://doi.org/10.1016/0196-6774(92)90047-G.
+ */
+function getNecklaces(length, kind) {
+  const outcomes = [];
+  const a = [];
+  for (let i = 0; i <= length; i++) a[i] = 0;
+  outcomes.push(a.slice(1, length + 1));
+  let i = length;
+  do {
+    a[i] = a[i] + 1;
+    for (let j = 1; j <= length - i; j++) {
+      a[j + i] = a[j];
+    }
+
+    if (length % i === 0) {
+      outcomes.push(a.slice(1, length + 1));
+    }
+
+    i = length;
+    while (a[i] === kind - 1) {
+      i = i - 1;
+    }
+  } while (i !== 0);
+
+  return outcomes;
+}

index.html

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+<!DOCTYPE html>
+<html lang="en">
+  <head>
+    <meta charset="UTF-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <meta http-equiv="X-UA-Compatible" content="ie=edge" />
+    <title>Combinatorics - Necklaces</title>
+    <link rel="stylesheet" href="style.css" />
+  </head>
+  <body>
+    <h1>Combinatorics - Necklaces</h1>
+    <div class="body-wrapper">
+      <div class="inputs-container">
+        <label for="length">Length<input type="number" class="length" name="length" max="6" min="1" value="2"></input></label>
+        <label for="kind">Kind<input type="number" class="kind" name="kind" max="6" min="1" value="3"></input></label>
+        <label for="type">Type
+          <select class="type" name="type">
+            <option value="0" selected>Necklace</option>
+            <option value="1">Bracelet</option>
+          </select>
+        </label>
+        <button class="generate" name="generate">Generate</button>
+      </div>
+      <div class="result-number"></div>
+      <div class="result"></div>
+    </div>
+    <footer>
+      <ul>
+        <li>H. Fredricksen and I. J. Kessler, "An algorithm for generating necklaces of beads in two colors," Discrete Mathematics 61 (1986) 181-188</li>
+        <li>H. Fredricksen and J. Maiorana, "Necklaces of beads in k colors and k-ary de Bruijn sequences," Discrete Mathematics 23, No. 3 (1978) 207-210</li>
+        <li>F. Ruskey, C. Savage, and T. Wang, "Generating Necklaces," Journal of Algorithms 13, No.3 (1992) 414-430</li>
+        <li>J.Sawada, "Generating bracelets in constant amortized time,", Society for Industrial and Applied Mathematics 31, No.1 (2001) 259-268</li>
+        <li>J.Davies, “Combinatorial Necklaces and Bracelets”, www.jasondavies.com/necklaces, Accessed 15 Nov. 2023
+      </ul>
+    </footer>
+  </body>
+  <script src="getBracelets.js"></script>
+  <script src="getNecklaces.js"></script>
+  <script src="generate.js"></script>
+</html>

linearFinite.js

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+function linearFinite(n, k) {
+  result = [];
+  const beadsKinds = [];
+  for (let i = 0; i < n; i++) beadsKinds[i] = i;
+
+  function generate(availableBeads, prevBeads) {
+    if (availableBeads.length === 0) {
+      result.push(prevBeads);
+      return;
+    }
+
+    for (let i = 0; i < availableBeads.length; i++) {
+      const nextPermute = [...prevBeads, availableBeads[i]];
+      const beadsLeft = availableBeads.filter((_, index) => i !== index);
+      generate(beadsLeft, nextPermute);
+    }
+
+    return [];
+  }
+  generate(beadsKinds, "");
+  return result;
+}

linearInfinite.js

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+function linearInfinite(n, k) {
+  result = [];
+  const beadsKinds = [];
+  for (let i = 0; i < n; i++) beadsKinds[i] = i;
+
+  function generate(prevBeads) {
+    if (prevBeads.length === n) {
+      result.push(prevBeads);
+      return;
+    }
+    for (let i = 0; i < n; i++) {
+      const nextPermute = [...prevBeads, beadsKinds[i]];
+      generate(nextPermute);
+    }
+  }
+  generate("");
+  return result;
+}

style.css

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+@import url("https://fonts.googleapis.com/css2?family=Dhurjati&family=Dosis:wght@300&family=Josefin+Slab:wght@300&display=swap");
+
+input[type="number"],
+select {
+  width: 50px;
+  padding: 6px 10px;
+  margin: 8px 0;
+  display: inline-block;
+  border: 1px solid #ccc;
+  border-radius: 4px;
+  box-sizing: border-box;
+}
+select {
+  width: 150px;
+}
+button {
+  background-color: #4caf50;
+  color: white;
+  padding: 6px 10px;
+  margin: 8px 0;
+  border: none;
+  border-radius: 4px;
+  cursor: pointer;
+  height: 32px;
+}
+
+button:hover {
+  background-color: #45a049;
+}
+
+.inputs-container {
+  display: flex;
+  gap: 10px;
+  align-items: flex-end;
+  justify-content: center;
+}
+
+.inputs-container > label {
+  display: flex;
+  flex-direction: column;
+}
+
+.result-number {
+  margin: 30px auto;
+  text-align: center;
+  font-size: 20px;
+}
+
+.body-wrapper {
+  max-width: 500px;
+  margin: auto;
+}
+
+footer {
+  margin-top: auto;
+  background-color: rgb(216, 216, 216);
+  color: gray;
+}
+
+body {
+  height: 100vh;
+  font-family: "Dosis", sans-serif;
+  display: flex;
+  flex-direction: column;
+  overflow: auto;
+}
+
+h1 {
+  margin-top: 50px;
+  text-align: center;
+  font-family: "Josefin Slab", serif;
+}