monkey and the oiled bamboo

#include<bits/stdc++.h>
using namespace std;

const int maxN = 1e5;
int a[maxN];

bool f (int k,int n) {
	for (int i = 1; i <= n; ++i) {
		if (a[i] - a[i - 1] > k) return false;
		if (a[i] - a[i - 1] == k) --k;
	}
	return true;
}

int main () {
	 ios::sync_with_stdio(false);
	 cin.tie(nullptr);
	 cout.tie(nullptr);
	 int T;
	 cin >> T;
	 for (int test_case = 1; test_case <= T; ++test_case) {
		 int n;
		 cin >> n;
		 for (int i = 1; i <= n; ++i) cin >> a[i];
		 a[0] = 0;
		 int l = a[1],r = 1e8;
		 int res = 0;
		 while (l <= r) {
			 int mid = (l + r) / 2;
			 if (f(mid,n)) {
				 res = mid;
				 r = mid - 1;
			 } else {
				 l = mid + 1;
			 }
		 }
		 cout << "Case " << test_case << ": " << res << '\n';
	 }
}