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  • Median(二分+二分)

    Median

     http://poj.org/problem?id=3579

    Time Limit: 1000MS   Memory Limit: 65536K
    Total Submissions: 11225   Accepted: 4016

    Description

    Given N numbers, X1X2, ... , XN, let us calculate the difference of every pair of numbers: ∣Xi - Xj∣ (1 ≤ i  j  N). We can get C(N,2) differences through this work, and now your task is to find the median of the differences as quickly as you can!

    Note in this problem, the median is defined as the (m/2)-th  smallest number if m,the amount of the differences, is even. For example, you have to find the third smallest one in the case of = 6.

    Input

    The input consists of several test cases.
    In each test case, N will be given in the first line. Then N numbers are given, representing X1X2, ... , XN, ( X≤ 1,000,000,000  3 ≤ N ≤ 1,00,000 )

    Output

    For each test case, output the median in a separate line.

    Sample Input

    4
    1 3 2 4
    3
    1 10 2
    

    Sample Output

    1
    8

    Source

     1 #include<iostream>
     2 #include<algorithm>
     3 #include<string>
     4 #include<map>
     5 #include<vector>
     6 #include<cmath>
     7 #include<string.h>
     8 #include<stdlib.h>
     9 #include<stack>
    10 #include<queue>
    11 #include<cstdio>
    12 #define ll long long
    13 const long long MOD=1000000007;
    14 #define maxn 100005
    15 using namespace std;
    16 
    17 int n;
    18 int m;
    19 int a[maxn];
    20 
    21 bool Check(int mid){
    22     int sum=0;
    23     int p;
    24     for(int i=1;i<=n;i++){
    25         p=upper_bound(a+1,a+n+1,a[i]+mid)-a;
    26         sum+=p-i-1;//排除a[i]之前的那些元素,共有i+1;
    27     }
    28     if(sum>=m){
    29         return true;
    30     }
    31     return false;
    32 }
    33 
    34 int main(){
    35     while(~scanf("%d",&n)){
    36         m=n*(n-1)/2;
    37         m=(m+1)/2;
    38         for(int i=1;i<=n;i++){
    39             scanf("%d",&a[i]);
    40         }
    41         sort(a+1,a+n+1);
    42         ll L=0,R=1000000000,mid;
    43         while(L<=R){
    44             mid=L+R>>1;
    45             if(Check(mid)){
    46                 R=mid-1;
    47             }
    48             else{
    49                 L=mid+1;
    50             }
    51         }
    52         printf("%d
    ",L);
    53     }
    54 
    55 }
    View Code
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  • 原文地址:https://www.cnblogs.com/Fighting-sh/p/10054652.html
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