POJ - 3685 (二分、枚举)

Given a $N$ × $N$ matrix $A$, whose element in the i-th row and j-th column $A_{ij}$ is an number that equals $i^2$ + $100000$ × $i$ + $j^2$ - $100000$ × $j$ + $i$ × $j$, you are to find the M-th smallest element in the matrix.

题意：有一个N × N的矩阵，其中 $A_{ij}$ ＝ $i^2$ + $i$ × $100000$ - $100000$ × $j$ + $j^2$ + $i$ × $j$,问这个矩阵中，第M小的数是多少？

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>

#define IOS ios::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define ll long long

using namespace std;
ll n, m;

ll cal(int i, int j) { return ll(i + 100000 + j) * i + ll(j - 100000) * j; }

bool check(ll x)
{
    ll sum = 0;
    for (int i = 1; i <= n; ++i)
    {
        int l = 1, r = n;
        while (l <= r)
        {
            int mid = l + r >> 1;
            if (cal(mid, i) <= x)
                l = mid + 1;
            else
                r = mid - 1;
        }
        sum += l - 1;
    }
    return sum < m;
}

int main()
{
    IOS;
    int t;
    cin >> t;
    while (t--)
    {
        cin >> n >> m;
        ll l = -((ll)n * n * 3 + 100000 * n), r = (ll)n * n * 3 + 100000 * n;

        while (l <= r)
        {
            ll mid = l + r >> 1;
            if (check(mid))
                l = mid + 1;
            else
                r = mid - 1;
        }
        printf("%lld\n", l);
    }

    return 0;
}