[51NOD1105]第k大的数(二分答案)

题目链接：http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1105

先排序，二分上下界分别是最小的两个数和最大的两个数的乘积。注意到一个性质，就是a[i]*b[j]，i从左到右，j从右到左。假如遇到一组a[i]*b[j]<=x，j就不必再减小了。这时候比x小的数一定是j个。下一次继续找i，这个b[j]一定不可能大于b[j+1]。问题就由找第k大的数，转换成找第n*n-k+1小的数。每次二分这个乘积x，看看是否符合条件即可。

  1 /*
  2 ━━━━━┒ギリギリ♂ eye！
  3 ┓┏┓┏┓┃キリキリ♂ mind！
  4 ┛┗┛┗┛┃＼○／
  5 ┓┏┓┏┓┃ /
  6 ┛┗┛┗┛┃ノ)
  7 ┓┏┓┏┓┃
  8 ┛┗┛┗┛┃
  9 ┓┏┓┏┓┃
 10 ┛┗┛┗┛┃
 11 ┓┏┓┏┓┃
 12 ┛┗┛┗┛┃
 13 ┓┏┓┏┓┃
 14 ┃┃┃┃┃┃
 15 ┻┻┻┻┻┻
 16 */
 17 #include <algorithm>
 18 #include <iostream>
 19 #include <iomanip>
 20 #include <cstring>
 21 #include <climits>
 22 #include <complex>
 23 #include <fstream>
 24 #include <cassert>
 25 #include <cstdio>
 26 #include <bitset>
 27 #include <vector>
 28 #include <deque>
 29 #include <queue>
 30 #include <stack>
 31 #include <ctime>
 32 #include <set>
 33 #include <map>
 34 #include <cmath>
 35 using namespace std;
 36 #define fr first
 37 #define sc second
 38 #define cl clear
 39 #define BUG puts("here!!!")
 40 #define W(a) while(a--)
 41 #define pb(a) push_back(a)
 42 #define Rint(a) scanf("%d", &a)
 43 #define Rll(a) scanf("%lld", &a)
 44 #define Rs(a) scanf("%s", a)
 45 #define Cin(a) cin >> a
 46 #define FRead() freopen("in", "r", stdin)
 47 #define FWrite() freopen("out", "w", stdout)
 48 #define Rep(i, len) for(int i = 0; i < (len); i++)
 49 #define For(i, a, len) for(int i = (a); i < (len); i++)
 50 #define Cls(a) memset((a), 0, sizeof(a))
 51 #define Clr(a, x) memset((a), (x), sizeof(a))
 52 #define Full(a) memset((a), 0x7f7f, sizeof(a))
 53 #define lp p << 1
 54 #define rp p << 1 | 1
 55 #define pi 3.14159265359
 56 #define RT return
 57 #define lowbit(x) x & (-x)
 58 #define onenum(x) __builtin_popcount(x)
 59 typedef long long LL;
 60 typedef long double LD;
 61 typedef unsigned long long ULL;
 62 typedef pair<int, int> pii;
 63 typedef pair<string, int> psi;
 64 typedef map<string, int> msi;
 65 typedef vector<int> vi;
 66 typedef vector<LL> vl;
 67 typedef vector<vl> vvl;
 68 typedef vector<bool> vb;
 69 
 70 const int maxn = 50050;
 71 LL n, k, ans;
 72 LL a[maxn], b[maxn];
 73 
 74 bool ok(LL x) {
 75     LL ret = 0;
 76     LL j = n;
 77     For(i, 1, n+1) {
 78         while(j) {
 79             if(a[i] * b[j] > x) j--;
 80             else break;
 81         }
 82         ret += j;
 83     }
 84     return ret >= k;
 85 }
 86 
 87 int main() {
 88     // FRead();
 89     while(cin >> n >> k) {
 90         k = n * n - k + 1;
 91         For(i, 1, n+1) {
 92             cin >> a[i] >> b[i];
 93         }
 94         sort(a+1, a+n+1); sort(b+1, b+n+1);
 95         LL l = a[1] * b[1], r = a[n] * b[n];
 96         while(l <= r) {
 97             LL m = (l + r) >> 1;
 98             if(ok(m)) {
 99                 r = m - 1;
100                 ans = m;
101             }
102             else l = m + 1;
103         }
104         cout << ans << endl;
105     }
106     RT 0;
107 }

 

posted @ 2016-05-25 16:32  Kirai  阅读(393)  评论(0)  编辑  收藏  举报