模拟前几个样例可以发现需要根据奇偶性讨论。反向考虑,当结果为 $0, 1, 2, 3, 4$ 的时候的节点分配是怎样的,可以得到当答案 $k$ 是奇数的时候,能够放下的最多的点数是 $2(k + 1)(\frac{k}{2} + 1)$;当答案 $k$ 是偶数的时候,能够放下的最多的点数是 $(k + 1)^2$。然后就可以二分答案了。
// Date: Thu Dec 7 21:25:48 2023
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;
const int INF = 0x3f3f3f3f, MOD = 1e9 + 7;
const double eps = 1e-8;
const int dir[8][2] = {
{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1},
};
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> VI;
typedef pair<int, int> PII;
const ull Pr = 131;
#define For(i, a, b) for (int i = int(a); i < int(b); ++i)
#define Rof(i, a, b) for (int i = int(b) - 1; i >= int(a); --i)
#define For1(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define Rof1(i, a, b) for (int i = int(b); i >= int(a); --i)
#define ForE(i, j) for (int i = h[j]; i != -1; i = ne[i])
#define f1 first
#define f2 second
#define pb push_back
#define has(a, x) (a.find(x) != a.end())
#define nonempty(a) (!a.empty())
#define all(a) (a).begin(), (a).end()
#define SZ(a) int((a).size())
#ifdef _DEBUG
#define debug1(x) cout << #x " = " << x << endl;
#define debug2(x, y) cout << #x " = " << x << " " #y " = " << y << endl;
#define debug3(x, y, z) \
cout << #x " = " << x << " " #y " = " << y << " " #z " = " << z << endl;
#else
#define debug1
#define debug2
#define debug3
#endif
int t;
ll n;
bool check(ll x) {
ll cnt;
if (x & 1) {
cnt = (x + 1) * (x / 2 + 1) * 2;
} else {
cnt = (1 + x) * (1 + x);
}
return cnt < n;
}
int main(void) {
#ifdef _DEBUG
freopen("1809b.in", "r", stdin);
#endif
std::ios::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin >> t;
while (t--) {
cin >> n;
if (n == 1) {
cout << "0\n";
continue;
}
ll l = 0, r = 1e10, mid;
while (l < r) {
mid = (l + r + 1) / 2;
if (check(mid))
l = mid;
else
r = mid - 1;
}
cout << l + 1 << '\n';
}
return 0;
}