2020 CCPC Wannafly Winter Camp Day1-F-乘法

题目传送门

sol:二分答案$K$，算大于$K$的乘积有多少个。关键在于怎么算这个个数，官方题解上给出的复杂度是$O(nlogn)$，那么计算个数的复杂度是$O(n)$的。感觉写着有点困难，自己写了一个复杂度是$O(nlog^{2}n)$，也够AC了。有正有负，控制边界有点难度。

• 二分答案

  #include <bits/stdc++.h>
  using namespace std;
  typedef long long LL;
  typedef pair<int, int> PII;
  const int MAXN = 1e5 + 10;
  int a[MAXN], b[MAXN];
  int n, m; LL k;
  LL check(LL mid) {
      LL sum = 0;
      for (int i = 1; i <= n; i++) {
          if (a[i] == 0) {
              if (mid < 0) sum += m;
              continue;
          }
          if (a[i] > 0) {
              if (mid >= 0) {
                  sum += b + 1 + m - upper_bound(b + 1, b + 1 + m, mid / a[i]);
              } else {
                  sum += b + 1 + m - lower_bound(b + 1, b + 1 + m, (mid + 1) / a[i]);
              }
          } else {
              if (mid >= 0) {
                  sum += lower_bound(b + 1, b + 1 + m, mid / a[i]) - 1 - (b + 1 - 1);
              } else {
                  sum += upper_bound(b + 1, b + 1 + m, (mid + 1) / a[i]) - 1 - (b + 1 - 1);
              }
          }
      }
      return sum;
  }
  int main() {
      scanf("%d%d%lld", &n, &m, &k);
      for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
      for (int i = 1; i <= m; i++) scanf("%d", &b[i]);
      sort(b + 1, b + 1 + m);
      LL l = -1e12 - 10, r = 1e12 + 10;
      while (l + 1 < r) {
          LL mid = l + r >> 1;
          if (check(mid) < k) r = mid;
          else l = mid;
      }
      printf("%lld\n", r);
      return 0;
  }