題目：
對於一個區域中N個地理格子，給定很多人走過的軌跡，求找出N個格子中前m個最多人走過的格子？？

實現：

package grid.geo;

import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.
 
TreeMap;
import java.util.TreeSet;
import java.util.Map.Entry;

import cetc.ocean.common.geohash.GeoHash;


/** 
* 描述:對於一個區域中N個地理格子，給定很多人走過的軌跡orignGrid ，求找出N個格子中前m個最多人走過的格子？？
* @author: fangchangtan
* @version 建立時間：2018年12月19日 下午1:56:24 
*/
public class GridCountTop {

	//orignGrid 表示原始N個格子，此處使用geohash代替
 

	String orignGrid ="geohash1,geohash2,....";
	//初始化讀取orignGrid 格子到快取中
	static HashSet<String> setInitGridNum = new HashSet<>();
	//歷史軌跡點，存入有序集合中
	ArrayList<TrackPointBean> trackHistory = new ArrayList<>();
	//mapTrackPoints  表示輔助快取：HashSet自動過濾掉重複的人
	Map<String, HashSet<Integer>
 
> mapTrackPoints  = new HashMap<>();
	public static void main(String[] args) {
		GridCountTop gridCountTop = new GridCountTop();
		gridCountTop.initGrid();
		List<String> gridTopN = gridCountTop.getGridTopN(5);
		for (String geohash : gridTopN) {
			System.out.println("N個格子中前m個最多人走過的格子geohash為："+geohash);
		}
		
	}
	/*讀取初始N個格子
	*/
	public void initGrid() {
		String[] split = orignGrid.split(",");
		for (String grid : split) {
			setInitGridNum.add(grid);
		}
		System.out.println("orign grid num:"+setInitGridNum.size());
		//初始化軌跡快取trackHistory 
		//........
	}
	
	/*topN 表示：前m個格子
	*/
	public List<String> getGridTopN(int topN ) {
		
		for (TrackPointBean trackPointBean : trackHistory) {
			int userId = trackPointBean.getUserId();
			String curr_geohash5 = GeoHash.geoHashStringWithCharacterPrecision(trackPointBean.getLat(), trackPointBean.getLon(), 5);
			if (setInitGridNum.contains(curr_geohash5)) {
				if (mapTrackPoints.containsKey(curr_geohash5)) {
					mapTrackPoints.get(curr_geohash5).add(userId);
				}else {
					mapTrackPoints.put(curr_geohash5,new HashSet<Integer>(){{add(userId);}});
				}
			}
		}
		TreeSet<KeyBean> treeSet = new TreeSet<>();
		for (Entry<String, HashSet<Integer>> entry : mapTrackPoints.entrySet()) {
			int size = entry.getValue().size();
			String geohash5 = entry.getKey();
			KeyBean keyBean = new KeyBean(size, geohash5);
			treeSet.add(keyBean);
		}
		
		ArrayList<String> arrayList = new ArrayList<>();
		if (treeSet.size() > topN) {
			Iterator<KeyBean> iterator = treeSet.iterator();
			for (int i = 0; i < topN; i++) {
				arrayList.add(iterator.next().getGeohash());
			}
		}else {
			Iterator<KeyBean> iterator = treeSet.iterator();
			while (iterator.hasNext()) {
				arrayList.add(iterator.next().getGeohash());
			}
		}
		return arrayList;
	}
	
	/*自定義從大到小的類比較器
	*/
	class KeyBean implements Comparator<KeyBean> {
		int num;
		String geohash;
		
		public KeyBean(int num, String geohash) {
			super();
			this.num = num;
			this.geohash = geohash;
		}
		public int getNum() {
			return num;
		}
		public void setNum(int num) {
			this.num = num;
		}
		public String getGeohash() {
			return geohash;
		}
		public void setGeohash(String geohash) {
			this.geohash = geohash;
		}
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + getOuterType().hashCode();
			result = prime * result + ((geohash == null) ? 0 : geohash.hashCode());
			result = prime * result + num;
			return result;
		}


		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			KeyBean other = (KeyBean) obj;
			if (!getOuterType().equals(other.getOuterType()))
				return false;
			if (geohash == null) {
				if (other.geohash != null)
					return false;
			} else if (!geohash.equals(other.geohash))
				return false;
			if (num != other.num)
				return false;
			return true;
		}
		
		//逆序輸出
		@Override
		public int compare(KeyBean o1, KeyBean o2) {
			// TODO Auto-generated method stub
			if (o1.getNum() != o2.getNum()) {
				return o2.getNum()-o1.getNum();
			}else {
				return o2.getGeohash().compareTo(o1.getGeohash());
			}
		}
	
	}
	/*自定義軌跡點
	*/
	class TrackPointBean {
		private int userId;
		private double lon;
		private double lat;
		private double utc;
		
		
		
		public TrackPointBean(int userId, double lon, double lat, double utc) {
			super();
			this.userId = userId;
			this.lon = lon;
			this.lat = lat;
			this.utc = utc;
		}
		public int getUserId() {
			return userId;
		}
		public void setUserId(int userId) {
			this.userId = userId;
		}
		public double getLon() {
			return lon;
		}
		public void setLon(double lon) {
			this.lon = lon;
		}
		public double getLat() {
			return lat;
		}
		public void setLat(double lat) {
			this.lat = lat;
		}
		public double getUtc() {
			return utc;
		}
		public void setUtc(double utc) {
			this.utc = utc;
		}
		@Override
		public String toString() {
			return "TrackPointBean [userId=" + userId + ", lon=" + lon + ", lat=" + lat + ", utc=" + utc + "]";
		}
		

	}


}

寫完程式碼我們看一下程式碼的演算法複雜度：
第一步：遍歷所有的軌跡點（數量為P），存入mapTrackPoints中；
第二步：遍歷mapTrackPoints的結果中value和key反向解析組合成KeyBean後存入TreeSet（大小為Q）中（倒敘輸出）；這時候直接取出前N個至就行了；
演算法複雜度為P+Q+N;

存在的問題：
1.沒有考慮相鄰軌跡點同是跨過N個格子的問題；比如從第1格直接跳到第3個格子的問題；
2.這種依靠java中集合來實現的功能並不是最有的，前N問題，是否可以轉換為樹的大頂錐問題；