POJ3579-Median

这是一道很难的二分搜索题，稀里糊涂的就AC了还没有弄懂为什么….

#include <cstdio>
#include <algorithm>

using namespace std;

const int maxn = 100000+5;

int x[maxn];

bool judge(int mid, int n, long long c) {
    int cnt = 0;
    for (int i = 0; i < n; i++) {
        cnt += x + n - lower_bound(x + i + 1, x + n, x[i] + mid);
    }
    return cnt <= c / 2;
}

int main(int argc, char const *argv[]) {
    int n;
    while (scanf("%d", &n) == 1) {
        long long c = n * (n - 1) / 2;
        for (int i = 0; i < n; i++) {
            scanf("%d", &x[i]);
        }
        sort(x, x + n);
        int lb = 0;
        int ub = x[n-1] - x[0];
        while (ub - lb > 1) {
            int mid = (lb + ub) / 2;
            if (judge(mid, n, c)) {
                ub = mid;
            } else {
                lb = mid;
            }
        }
        printf("%d\n", lb);
    }
    return 0;
}

或者

while (ub > lb) {
            int mid = (lb + ub) / 2;
            if (judge(mid, n, c)) {
                ub = mid;
            } else {
                lb = mid + 1;
            }
        }
        printf("%d\n", lb-1);

可答案为什么是lb呢？