31:T46b,{ console.clear(); const n = 8; const k = 4; const combinations = []; for (let d = k-1; d < n; d++) { console.log(" ".repeat(0)+'d='+d); for (let c = k-2; c < d; c++) { console.log(" ".repeat(1)+'c='+c); for (let b = k-3; b < c; b++) { console.log(" ".repeat(2)+'b='+b); for (let a = k-4; a < b; a++) { const combination = [a, b, c, d]; const binary = combination.reduce((p, v) => { p[v] = 'X'; return p; }, Array(n).fill('-')) .join(''); const abc = combination.reduce((p, v, i) => { p[v] = String.fromCharCode(65+i); // asc(65)="A" return p; }, Array(n).fill('-')) .join(''); const sum = combination.reduce((p, v) => p+v, 0); const max = Math.max(...combination); combinations.push({ combination, binary, abc, max, sum, }); console.log(" ".repeat(3)+'a='+a, binary); } } } } return combinations; }32:[] 2f:{"title":"Generating k-Combinations","cells":[{"id":0,"value":"# Generating *k*-Combinations\n*...ordered by lowest values first.*","pinned":false,"hidden":false,"mode":"md"},{"id":317,"value":"## Parameters","pinned":false,"hidden":false,"mode":"md"},{"id":14,"value":"viewof n = Inputs.number([1, 99], { label: html`n =
size of the set`, value: 8 });","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"viewof k = Inputs.number([1, S.length], { label: html`k =
size of the unique subsets`, value: 4 });","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"S = Array.from({ length: n }, (_ ,i) => i);","pinned":false,"hidden":false,"mode":"ojs"},{"id":363,"value":"---\n## Calculate count of possible *k*-combinations","pinned":false,"hidden":false,"mode":"md"},{"id":50,"value":"factorial = (n) => {\n if (n < 0) return NaN;\n let f = BigInt(1);\n for (let i = BigInt(1); i <= BigInt(n); i++) {\n f = f * i;\n }\n return f;\n};","pinned":false,"hidden":false,"mode":"ojs"},{"id":87,"value":"combinations = (n, k) => factorial(n) / ( factorial(k) * factorial(n - k));","pinned":false,"hidden":false,"mode":"ojs"},{"id":117,"value":"md`Possible *k*-combinations: **${combinations(n, k)}**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":673,"value":"---\n ## Generate *k*-combinations","pinned":false,"hidden":false,"mode":"md"},{"id":566,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":332,"value":"---\n## Increment to the *next k-combination*:","pinned":false,"hidden":false,"mode":"md"},{"id":753,"value":"viewof rerun = Inputs.button(\"Regenerate\");","pinned":false,"hidden":false,"mode":"ojs"},{"id":720,"value":"viewof numberOfIncrements = Inputs.number([1, 100], { label: \"Number of Increments\", value: 10, reduce: () => rerun });","pinned":false,"hidden":false,"mode":"ojs"},{"id":536,"value":"{\n // helpers\n const generateRandomCombination = (n, k) => {\n const set = new Set();\n while (set.size < k) {\n const rand = Math.floor(Math.random() * n);\n set.add(rand);\n }\n return Array.from(set).sort((a, b) => a - b);\n }\n\n // get next combinations\n const combinations = [];\n combinations.push(generateRandomCombination(n, k))\n for (let i = 0; i < numberOfIncrements-1; i++) {\n combinations.push(getNextCombination(combinations[i], n));\n }\n\n // compile HTML string\n let str = '';\n combinations.forEach((v, i) => {\n\n \n if (v === null) {\n \n // null (maxed-out)\n str += `

null

`;\n \n } else {\n \n // convert to binary string\n const binary = v.reduce((a, c) => {\n a[c] = 'X';\n return a;\n }, Array(n).fill('-')).join('');\n str += `

[${v}]; ${binary}

`;\n }\n\n \n });\n str = `

${str}`;\n\n // return HTML string\n return html`${str}`;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":324,"value":"function getNextCombination(combination, n) {\n if (!combination) return null;\n\n // get index of next element to increment\n const nextIndex = combination.reduceRight((a, v, i, arr) => arr[i+1] - v > 1 ? i : a, combination.length-1);\n\n // guard against exceeding `n`\n if (combination[nextIndex] > n) return null;\n\n // increment elements into a new combination\n return combination.map((v, i) => {\n if (i < nextIndex) return i;\n if (i === nextIndex) return v + 1;\n if (i > nextIndex) return v;\n });\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":610,"value":"---\n# Sort-and-shuffle","pinned":false,"hidden":false,"mode":"md"},{"id":744,"value":"function shuffleAndSort(arr, onKey) {\n if (!onKey) {\n return arr.sort((a, b) => a !== b ? a - b : Math.random() - 0.5);\n }\n \n return arr.sort((a, b) => a[onKey] !== b[onKey]\n ? a[onKey] - b[onKey]\n : Math.random() - 0.5);\n}","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W32","stdlib":"1","titling":"auto"}