There is a problem of finding the index of a specific permutation among the permutations that can be made from the given numbers.<\/p>\n
For example, when the numbers 1, 2, and 3 are given, all the possible permutations are as follows:<\/p>\n
The question is to find out the index of a specific number’s permutation. In the above example, 231 corresponds to the 4th position.<\/p>\n
The first line contains the number of digits The second line contains The third line contains the desired permutation index Print the desired permutation.<\/p>\n To solve this problem, we define the following steps:<\/p>\n Here, we will describe the process of generating permutations and finding a specific order using JavaScript. We will use the DFS (Depth-First Search)<\/strong> method to generate permutations.<\/p>\n The above code consists of two functions:<\/p>\n This function generates permutations recursively:<\/p>\n This function goes through the following steps:<\/p>\nn<\/code> (1 \u2264 n \u2264 10).<\/p>\nn<\/code> natural numbers. (Each number is a different natural number from 1 to n<\/code>.)<\/p>\nk<\/code> (1 \u2264 k \u2264 n!).<\/p>\nOutput Format<\/h2>\n
Problem Solving<\/h2>\n
Approach<\/h3>\n
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Permutation Generation Algorithm<\/h3>\n
JavaScript Code<\/h3>\n
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\nfunction getPermutations(arr) {\n const result = [];\n \n const backtrack = (current, remaining) => {\n if (remaining.length === 0) {\n result.push(current);\n return;\n }\n \n for (let i = 0; i < remaining.length; i++) {\n const newCurrent = [...current, remaining[i]];\n const newRemaining = [...remaining.slice(0, i), ...remaining.slice(i + 1)];\n backtrack(newCurrent, newRemaining);\n }\n };\n \n backtrack([], arr);\n return result;\n}\n\nfunction findPermutation(n, nums, k) {\n const permutations = getPermutations(nums);\n return permutations[k - 1].join('');\n}\n\n\/\/ Example input\nconst n = 3;\nconst nums = [1, 2, 3];\nconst k = 4;\n\n\/\/ Output\nconsole.log(findPermutation(n, nums, k)); \/\/ 231\n <\/code>\n <\/pre>\nCode Explanation<\/h3>\n
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Detailed Explanation of getPermutations Function<\/h3>\n
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Detailed Explanation of findPermutation Function<\/h3>\n