hdu 4995(离散化下标+模拟)

Revenge of kNN

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 584    Accepted Submission(s): 136

Problem Description

In pattern recognition, the k-Nearest Neighbors algorithm (or k-NN for short) is a non-parametric method used for classification and regression. In both cases, the input consists of the k closest training examples in the feature space.
In k-NN regression, the output is the property value for the object. This value is the average of the values of its k nearest neighbors.
---Wikipedia

Today, kNN takes revenge on you. You have to handle a kNN case in one-dimensional coordinate system. There are N points with a position Xi and value Vi. Then there are M kNN queries for point with index i, recalculate its value by averaging the values its k-Nearest Neighbors. Note you have to replace the value of i-th point with the new calculated value. And if there is a tie while choosing k-Nearest Neighbor, choose the one with the minimal index first.

 

Input

The first line contains a single integer T, indicating the number of test cases.

Each test case begins with three integers N, M and K, in which K indicating the number of k-Nearest Neighbors. Then N lines follows, each line contains two integers Xi and Vi. Then M lines with the queried index Qi follows.

[Technical Specification]
1. 1 <= T <= 5
2. 2<=N<= 100 000, 1<=M<=100 000
3. 1 <= K <= min(N – 1, 10)
4. 1 <= Vi <= 1 000
5. 1 <= Xi <= 1 000 000 000, and no two Xi are identical.
6. 1 <= Qi <= N

 

Output

For each test case, output sum of all queries rounded to six fractional digits.

 

Sample Input

1 5 3 2 1 2 2 3 3 6 4 8 5 8 2 3 4

 

Sample Output

17.000000

做这题让我知道了如何解决一个很常见但是也很难想的问题:一个数组如果排序后被打乱了，知道它原来的位置，如何对应出现在的位置？

题意:X轴上有 n 个点，每个点都有个初始位置和权值(这些位置是杂乱无章的)，现在给m次询问：每次询问第 i 个给出的点，找出离他最近的 k 个点，然后将 k 个点的权值相加取平均值赋值给当前询问的点，输出的最终答案就是这m 次询问每次询问的平均值之和。还有就是关于 k 个点的选取，当距离相同时，选择给出顺序小的。

题解:由于要找到邻居，排序是无疑的，但是询问却是询问的以前的位置。排完序之后如何找到原来的位置？？循环？不行，10^5次询问每次找点也要10^5，肯定会超时？这时我们可以利用一个数组来记录排完序后元素原来的位置。但是，元素的下标是从 1 <= Xi <= 1 000 000 000,数组肯定存不下，怎么办？离散化呗，这样寻找的时间就变成 O(1)了。

可能有人不懂离散化后数组存的意思，这里举个例子：

原来的X轴分布假设为：

3 1 2 100 99

我们记录一下每个Xi 出现的位置 3(1) 1(2) 2(3) 100(4) 99(5)

排个序: 1(2) 2(3) 3(1) 99(5) 100(4)

弄个数组将括号里面的数表示成下标分别赋值给 1-5  a[2]=1 a[3]=2 a[1]=3 a[5]=4 a[4]=5

然后对应查询,假设我们查询初始位置是第 4 位的那个 Xi=100,对应排完序后的数组的位置是 a[4] = 5 而新的数组第5个数字等于100！！是不是很神奇，这就是离散化的好处了.不懂我说的同学可以看下acdreamer大神的博客：http://blog.csdn.net/acdreamers/article/details/8520096

 

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
typedef long long LL;
const int N = 111111;
struct Node{
    LL x;
    int id1;
    double v;
}node[N];
int idx[N];
int cmp(Node a,Node b){
    return a.x<b.x;
}
int main()
{
    int tcase,n,m,k,x;
    scanf("%d",&tcase);
    while(tcase--)
    {
        scanf("%d%d%d",&n,&m,&k);
        for(int i=1;i<=n;i++){
            scanf("%lld%lf",&node[i].x,&node[i].v);
            node[i].id1 = i;
        }
        sort(node+1,node+1+n,cmp);
        for(int i=1;i<=n;i++){
            idx[node[i].id1] = i;
        }
        double sum = 0;
        while(m--){
            int id;
            scanf("%d",&id);
            int now = idx[id];
            double avg = 0;
            int l = now-1,r = now+1;
            for(int i=1;i<=k;i++){
                if(l>=1&&r<=n){
                    LL dis1 = node[now].x - node[l].x;
                    LL dis2 = node[r].x - node[now].x;
                    if(dis1<dis2){
                        avg+=node[l--].v;
                    }else if(dis1>dis2){
                        avg+=node[r++].v;
                    }else { ///相等的话按照邻居原来的下标进行选择
                        int ori_l = node[l].id1;
                        int ori_r = node[r].id1;
                        if(ori_l<ori_r) {
                            avg+=node[l--].v;
                        }else{
                            avg+=node[r++].v;
                        }
                    }
                }else if(l>=1){
                    avg+=node[l--].v;
                }else if(r<=n){
                    avg+=node[r++].v;
                }
            }
            /*  ///不知道WA的原因
            int l=1,r=1;
            for(int i=1;i<=k;i++){
                if(now-l>=1&&now+r<=n){
                    LL dis1 = node[now].x - node[now-l].x;
                    LL dis2 = node[now+r].x - node[now].x;
                    if(dis1<dis2){
                        avg+=node[now-l].v;
                        l++;
                    }else if(dis1>dis2){
                        avg+=node[now+r].v;
                        r++;
                    }else { ///相等的话按照邻居原来的下标进行选择
                        int ori_l = node[now+l].id1;
                        int ori_r = node[now+r].id1;
                        if(ori_l<ori_r) {
                            avg+=node[now-l].v;
                            l++;
                        }else{
                            avg+=node[now+r].v;
                            r++;
                        }
                    }
                }else if(now-l>=1){
                    avg+=node[now-l].v;
                    l++;
                }else if(now+r<=n){
                    avg+=node[now+r].v;
                    r++;
                }
            }*/
            node[now].v = avg/k;
            sum+=avg/k;
        }
        printf("%.6lf
",sum);
    }
    return 0;
}