Minimum Stability Factor of Array
Time complexity: $O(n\log n)$
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#include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
#include <cmath>
class Solution {
public:
int minStable(std::vector<int>& nums, int maxC) {
int n = nums.size();
if (n == 0) {
return 0;
}
int logN = std::log2(n) + 1;
std::vector<std::vector<int>> st(n, std::vector<int>(logN));
for (int i = 0; i < n; ++i) {
st[i][0] = nums[i];
}
for (int j = 1; j < logN; ++j) {
for (int i = 0; i + (1 << j) <= n; ++i) {
st[i][j] = std::gcd(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
}
}
auto GCD = [&](int L, int R) {
int len = R - L + 1;
int k = std::log2(len);
return std::gcd(st[L][k], st[R - (1 << k) + 1][k]);
};
int left = 1, right = n;
for (int mid = (left + right) / 2; right >= left; ) {
bool valid = true;
int ops = 0, i = 0;
while (i <= n - mid) {
int cm = GCD(i, i + mid - 1);
if (cm > 1) {
++ops;
if (ops > maxC) {
valid = false;
break;
}
i += mid;
}
else {
++i;
}
}
if (valid) {
right = mid - 1;
}
else {
left = mid + 1;
}
mid = (left + right) / 2;
}
return right;
}
};
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