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K-th Closest Distance

时间:2019-08-02 16:19:25      阅读:110      评论:0      收藏:0      [点我收藏+]

标签:rip   mod   contest   others   col   char   for   input   key   

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=6621

K-th Closest Distance

Time Limit: 20000/15000 MS (Java/Others)    Memory Limit: 524288/524288 K (Java/Others)
Total Submission(s): 2426    Accepted Submission(s): 871


Problem Description
You have an array: a1, a2, , an and you must answer for some queries.
For each query, you are given an interval [L, R] and two numbers p and K. Your goal is to find the Kth closest distance between p and aL, aL+1, ..., aR.
The distance between p and ai is equal to |p - ai|.
For example:
A = {31, 2, 5, 45, 4 } and L = 2, R = 5, p = 3, K = 2.
|p - a2| = 1, |p - a3| = 2, |p - a4| = 42, |p - a5| = 1.
Sorted distance is {1, 1, 2, 42}. Thus, the 2nd closest distance is 1.
 

 

Input
The first line of the input contains an integer T (1 <= T <= 3) denoting the number of test cases.
For each test case:
冘The first line contains two integers n and m (1 <= n, m <= 10^5) denoting the size of array and number of queries.
The second line contains n space-separated integers a1, a2, ..., an (1 <= ai <= 10^6). Each value of array is unique.
Each of the next m lines contains four integers L‘, R‘, p‘ and K‘.
From these 4 numbers, you must get a real query L, R, p, K like this: 
L = L‘ xor X, R = R‘ xor X, p = p‘ xor X, K = K‘ xor X, where X is just previous answer and at the beginning, X = 0.
(1 <= L < R <= n, 1 <= p <= 10^6, 1 <= K <= 169, R - L + 1 >= K).
 

 

Output
For each query print a single line containing the Kth closest distance between p and aL, aL+1, ..., aR.
 

 

Sample Input
1 5 2 31 2 5 45 4 1 5 5 1 2 5 3 2
 

 

Sample Output
0 1
 

 

Source
题目大意:T组样例,N个数 M次询问,L,R,P,K  问你L,R区间内 距离P第K近的距离是多少
思路:比赛的时候没啥思路,没写,看题解发现,主席树可以求区间内<=K的数有多少个  但是我们要求的是与某个值相减绝对值第K小啊,这有什么关系吗?
假设我们知道答案是几,那么此时求出来L,R区间内的数与P相减第K小是不是就是我们这个答案呢? 显然是的,但是问题是我们不知道答案啊
这就是二分的思想了,二分答案,查询范围在P-ans,P+ans之间的数有多少个,如果个数大于等于K的话,证明我们的ans还可以减小,一直这样下去
就会得到正确的答案了
看代码:
#include<iostream>
#include<vector>
#include<cstdio>
#include<algorithm>
#include<math.h>
using namespace std;
typedef long long LL;
const int maxn=1e5+5;
int N,M;
int sz,cnt=0,sum=0;
int root[maxn],a[maxn],v[maxn];
int L,R,P,K,X=0;
struct Node
{
    int l,r,sum;
    Node()
    {
        l=r=sum=0;
    }
}T[maxn<<6];
void Init()
{
    cnt=0;root[0]=0;T[cnt].l=T[cnt].r=T[cnt].sum=0;X=0;
}
void Read(int &n)//只能读入整数
{
    n=0;
    int f=1;//用于记录正负
    char ch=getchar();

    while(ch<0||ch>9)//
    {
        if(ch==-) f=-1;
        ch=getchar();
    }
    while(ch>=0&&ch<=9)//下面两种用法都可以
    {
        //n=(n<<1)+(n<<3)+(ch-‘0‘);//
        n=(n<<1)+(n<<3)+(ch^48);//相当于  x*10+ch-‘0‘;
        ch=getchar();
    }
    n=n*f;//切记乘以f  (记录的是+ -)
    return ;
}
void Update(int l,int r,int &x,int y,int pos)
{
    T[++cnt]=T[y];T[cnt].sum++;x=cnt;
    if(l==r) return ;
    int mid=(l+r)>>1;
    if(pos<=mid) Update(l,mid,T[x].l,T[y].l,pos);
    else Update(mid+1,r,T[x].r,T[y].r,pos);
}
int getid(int x)
{
    return lower_bound(v+1,v+1+sz,x)-(v);
}
void Query(int l,int r,int x,int y,int h)
{
//    cout<<"l:"<<l<<" r:"<<r<<" sum:"<<sum<<endl;
    if(l==r)
    {
        if(h>=v[l]) sum+=T[x].sum-T[y].sum;
        return ;
    }
    int mid=(l+r)>>1;
    if(h<=v[mid]) Query(l,mid,T[x].l,T[y].l,h);
    else
    {
        sum+=T[T[x].l].sum-T[T[y].l].sum;
        Query(mid+1,r,T[x].r,T[y].r,h);
    }
}
bool judge(int x)
{
    sum=0;Query(1,sz,root[R],root[L-1],P+x);
    int sum1=sum;
    sum=0;Query(1,sz,root[R],root[L-1],P-x-1);
    int sum2=sum;
    return sum1-sum2>=K;
}
int main()
{
    int T;
//    scanf("%d",&T);
Read(T);
    int ca=1;
    while(T--)
    {
        Init();
//        scanf("%d%d",&N,&M);
Read(N);Read(M);
        for(int i=1;i<=N;i++)
        {
            scanf("%d",&a[i]);v[i]=a[i];
        }
        sort(v+1,v+1+N);sz=unique(v+1,v+1+N)-(v+1);
//        for(int i=1;i<=sz;i++) cout<<v[i]<<" ";cout<<endl;
//        for(int i=1;i<=N;i++) cout<<getid(a[i])<<" ";cout<<endl;
        for(int i=1;i<=N;i++) Update(1,sz,root[i],root[i-1],getid(a[i]));
        while(M--)
        {
            sum=0;
//            scanf("%d%d%d%d",&L,&R,&P,&K);
Read(L);Read(R);Read(P);Read(K);
            L^=X;R^=X;P^=X;K^=X;
            int l=0,r=1e6,ans;
            while(l<=r)//二分答案
            {
                int mid=(l+r)>>1;
                if(judge(mid))
                {
                    ans=mid;r=mid-1;
                }
                else l=mid+1;
            }
            printf("%d\n",ans);
            X=ans;
        }
    }
    return 0;
}

 

K-th Closest Distance

标签:rip   mod   contest   others   col   char   for   input   key   

原文地址:https://www.cnblogs.com/caijiaming/p/11289099.html

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