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| 1 | +/** |
| 2 | + * 2111. Minimum Operations to Make the Array K-Increasing |
| 3 | + * https://leetcode.com/problems/minimum-operations-to-make-the-array-k-increasing/ |
| 4 | + * Difficulty: Hard |
| 5 | + * |
| 6 | + * You are given a 0-indexed array arr consisting of n positive integers, and a positive integer k. |
| 7 | + * |
| 8 | + * The array arr is called K-increasing if arr[i-k] <= arr[i] holds for every index i, where |
| 9 | + * k <= i <= n-1. |
| 10 | + * |
| 11 | + * - For example, arr = [4, 1, 5, 2, 6, 2] is K-increasing for k = 2 because: |
| 12 | + * - arr[0] <= arr[2] (4 <= 5) |
| 13 | + * - arr[1] <= arr[3] (1 <= 2) |
| 14 | + * - arr[2] <= arr[4] (5 <= 6) |
| 15 | + * - arr[3] <= arr[5] (2 <= 2) |
| 16 | + * - However, the same arr is not K-increasing for k = 1 (because arr[0] > arr[1]) or k = 3 (because |
| 17 | + * arr[0] > arr[3]). |
| 18 | + * |
| 19 | + * In one operation, you can choose an index i and change arr[i] into any positive integer. |
| 20 | + * |
| 21 | + * Return the minimum number of operations required to make the array K-increasing for the given k. |
| 22 | + */ |
| 23 | + |
| 24 | +/** |
| 25 | + * @param {number[]} arr |
| 26 | + * @param {number} k |
| 27 | + * @return {number} |
| 28 | + */ |
| 29 | +var kIncreasing = function(arr, k) { |
| 30 | + let result = 0; |
| 31 | + for (let i = 0; i < k; i++) { |
| 32 | + const subsequence = []; |
| 33 | + for (let j = i; j < arr.length; j += k) { |
| 34 | + subsequence.push(arr[j]); |
| 35 | + } |
| 36 | + result += longestNonDecreasingSubsequence(subsequence); |
| 37 | + } |
| 38 | + |
| 39 | + return result; |
| 40 | + |
| 41 | + function longestNonDecreasingSubsequence(nums) { |
| 42 | + const tails = []; |
| 43 | + for (const num of nums) { |
| 44 | + let left = 0; |
| 45 | + let right = tails.length; |
| 46 | + while (left < right) { |
| 47 | + const mid = Math.floor((left + right) / 2); |
| 48 | + if (tails[mid] <= num) { |
| 49 | + left = mid + 1; |
| 50 | + } else { |
| 51 | + right = mid; |
| 52 | + } |
| 53 | + } |
| 54 | + tails[left] = num; |
| 55 | + } |
| 56 | + return nums.length - tails.length; |
| 57 | + } |
| 58 | +}; |
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