[Luogu]中位数

Description

Luogu1168

Solution

一种神奇的做法：开一个大根堆和小根堆，保证大根堆比小根堆多1个元素，且大根堆堆顶元素比小根堆堆顶元素小，那么大根堆堆顶就是中位数。插入的时候用交换堆顶元素的方法维护一下这个性质就行。

Code

#include <cstdio>
#include <queue>

const int N = 100010;

int n, a[N];
std::priority_queue<int> big;
std::priority_queue<int, std::vector<int>, std::greater<int> > small;

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
    int p = 1;
    big.push(a[p++]);
    printf("%d\n", big.top());
    if (!n%2) n--;
    while (p < n) {
        int x = a[p++], y = a[p++];
        if (x > y) std::swap(x, y);
        big.push(x);
        small.push(y);
        if (big.top() > small.top()) {
            int x = big.top(), y = small.top();
            big.pop(); big.push(y);
            small.pop(); small.push(x);
        }
        printf("%d\n", big.top());
    }
    return 0;
}