LeetCode in Kotlin

3605. Minimum Stability Factor of Array

Hard

You are given an integer array nums and an integer maxC.

A subarray is called stable if the highest common factor (HCF) of all its elements is greater than or equal to 2.

The stability factor of an array is defined as the length of its longest stable subarray.

You may modify at most maxC elements of the array to any integer.

Return the minimum possible stability factor of the array after at most maxC modifications. If no stable subarray remains, return 0.

Note:

• The highest common factor (HCF) of an array is the largest integer that evenly divides all the array elements.
• A subarray of length 1 is stable if its only element is greater than or equal to 2, since HCF([x]) = x.

Example 1:

Input: nums = [3,5,10], maxC = 1

Output: 1

Explanation:

• The stable subarray [5, 10] has HCF = 5, which has a stability factor of 2.
• Since maxC = 1, one optimal strategy is to change nums[1] to 7, resulting in nums = [3, 7, 10].
• Now, no subarray of length greater than 1 has HCF >= 2. Thus, the minimum possible stability factor is 1.

Example 2:

Input: nums = [2,6,8], maxC = 2

Output: 1

Explanation:

• The subarray [2, 6, 8] has HCF = 2, which has a stability factor of 3.
• Since maxC = 2, one optimal strategy is to change nums[1] to 3 and nums[2] to 5, resulting in nums = [2, 3, 5].
• Now, no subarray of length greater than 1 has HCF >= 2. Thus, the minimum possible stability factor is 1.

Example 3:

Input: nums = [2,4,9,6], maxC = 1

Output: 2

Explanation:

• The stable subarrays are:
  • [2, 4] with HCF = 2 and stability factor of 2.
  • [9, 6] with HCF = 3 and stability factor of 2.
• Since maxC = 1, the stability factor of 2 cannot be reduced due to two separate stable subarrays. Thus, the minimum possible stability factor is 2.

Constraints:

• 1 <= n == nums.length <= 105
• 1 <= nums[i] <= 109
• 0 <= maxC <= n

Solution

class Solution {
    fun minStable(nums: IntArray, maxC: Int): Int {
        val n = nums.size
        var cnt = 0
        var idx = 0
        while (idx < n) {
            cnt += if (nums[idx] >= 2) 1 else 0
            idx++
        }
        if (cnt <= maxC) {
            return 0
        }
        val logs = IntArray(n + 1)
        var maxLog = 0
        var temp = n
        while (temp > 0) {
            maxLog++
            temp = temp shr 1
        }
        val table = Array<IntArray>(maxLog + 1) { IntArray(n) }
        buildLogs(logs, n)
        buildTable(table, nums, n, maxLog)
        return binarySearch(nums, maxC, n, logs, table)
    }

    private fun buildLogs(logs: IntArray, n: Int) {
        var i = 2
        while (i <= n) {
            logs[i] = logs[i shr 1] + 1
            i++
        }
    }

    private fun buildTable(table: Array<IntArray>, nums: IntArray, n: Int, maxLog: Int) {
        System.arraycopy(nums, 0, table[0], 0, n)
        var level = 1
        while (level <= maxLog) {
            var start = 0
            while (start + (1 shl level) <= n) {
                table[level][start] =
                    gcd(table[level - 1][start], table[level - 1][start + (1 shl (level - 1))])
                start++
            }
            level++
        }
    }

    private fun binarySearch(nums: IntArray, maxC: Int, n: Int, logs: IntArray, table: Array<IntArray>): Int {
        var left = 1
        var right = n
        var result = n
        while (left <= right) {
            val mid = left + ((right - left) shr 1)
            val valid = isValid(nums, maxC, mid, logs, table)
            result = if (valid) mid else result
            val newLeft = if (valid) left else mid + 1
            val newRight = if (valid) mid - 1 else right
            left = newLeft
            right = newRight
        }
        return result
    }

    private fun isValid(arr: IntArray, limit: Int, segLen: Int, logs: IntArray, table: Array<IntArray>): Boolean {
        val n = arr.size
        val window = segLen + 1
        var cuts = 0
        var prevCut = -1
        var pos = 0
        while (pos + window - 1 < n && cuts <= limit) {
            val rangeGcd = getRangeGcd(pos, pos + window - 1, logs, table)
            if (rangeGcd >= 2) {
                val shouldCut = prevCut < pos
                cuts += if (shouldCut) 1 else 0
                prevCut = if (shouldCut) pos + window - 1 else prevCut
            }
            pos++
        }
        return cuts <= limit
    }

    private fun getRangeGcd(left: Int, right: Int, logs: IntArray, table: Array<IntArray>): Int {
        val k = logs[right - left + 1]
        return gcd(table[k][left], table[k][right - (1 shl k) + 1])
    }

    private fun gcd(a: Int, b: Int): Int {
        return if (b == 0) a else gcd(b, a % b)
    }
}

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