优先队列+二分
题目需要找到中位数最大,那么我们直接按照价值升序排序,再把体重升序排序。
从头把m对半分开,求前m最小和后m最小,如果是奇数最终加上当前这位的体积比v小于等于,直接这一位的价值就是答案。
如果是偶数,这个会复杂一点,因为你无法保证某一次价值大的体重小,但是可以发现,我们是求中间两个取平均,我们已经对这个物品先按价值升序排序,那么我们就在这个合理的区间中可以发现,如果存在符合V的区间,显然我们希望这个区间越靠后面越高兴,所以我们要接一个二分去寻找合理的最大值。
代码写的比较玄乎,码了注释。
#pragma GCC target("avx,sse2,sse3,sse4,popcnt")
#pragma GCC optimize("O2,O3,Ofast,inline,unroll-all-loops,-ffast-math")
#include <bits/stdc++.h>
using namespace std;
#define js ios::sync_with_stdio(false);cin.tie(0); cout.tie(0)
#define all(vv) (vv).begin(), (vv).end()
#define endl "\n"
typedef long long ll; typedef unsigned long long ull; typedef long double ld;
const ll MOD = 1e9 + 7;
inline ll read() { ll s = 0, w = 1; char ch = getchar(); for (; !isdigit(ch); ch = getchar()) if (ch == '-') w = -1; for (; isdigit(ch); ch = getchar()) s = (s << 1) + (s << 3) + (ch ^ 48); return s * w; }
inline void write(ll x) { if (!x) { putchar('0'); return; } char F[40]; ll tmp = x > 0 ? x : -x; if (x < 0)putchar('-'); int cnt = 0; while (tmp > 0) { F[cnt++] = tmp % 10 + '0'; tmp /= 10; } while (cnt > 0)putchar(F[--cnt]); }
inline ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }
ll qpow(ll a, ll b) { ll ans = 1; while (b) { if (b & 1) ans *= a; b >>= 1; a *= a; } return ans; } ll qpow(ll a, ll b, ll mod) { ll ans = 1; while (b) { if (b & 1)(ans *= a) %= mod; b >>= 1; (a *= a) %= mod; }return ans % mod; }
inline int lowbit(int x) { return x & (-x); }
const int N = 1e5 + 7;
pair<ll, ll> a[N];
ll sum1[N], sum2[N]; //前面一半的和,后面一半的和
priority_queue<ll> pq;
int main() {
ll v = read(), n = read(), m = read();
for (int i = 1; i <= n; ++i) a[i].first = read(), a[i].second = read();
sort(a + 1, a + 1 + n);
int x = m & 1; m >>= 1;
for (int i = 1; i <= n; ++i) {
pq.push(a[i].second), sum1[i] = sum1[i - 1] + a[i].second; //求前i个数中m前半段最小值
if (pq.size() > m - 1 + x) sum1[i] -= pq.top(), pq.pop(); //去掉最大的
}
while (pq.size()) pq.pop();
for (int i = n; i; --i) {
pq.push(a[i].second), sum2[i] = sum2[i + 1] + a[i].second; //后缀和求m后半段最小值
if (pq.size() > m) sum2[i] -= pq.top(), pq.pop();
}
if (x) { //如果是奇数
ll ans = 0;
for (int i = m + 1; i <= n - m; ++i)
if (sum1[i - 1] + sum2[i + 1] + a[i].second <= v) ans = a[i].first; //已经按照first升序排过序
cout << ans << endl;
}
else {
ll ans = 0;
for (int i = m; i <= n - m; ++i) {
int l = i + 1, r = n - m + 1;
while (l <= r) {
int mid = l + r >> 1;
if (sum1[i - 1] + sum2[mid] + a[i].second <= v) l = mid + 1;
else r = mid - 1;
}
if (r > i) ans = max(ans, 1ll * a[i].first + a[r].first);
}
cout << ans / 2 << endl;
}
return 0;
} 
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