LintCode 613: High Five (MinHeap)

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本文介绍了一种算法，用于从学生记录中找出每位学生的前五高分，并计算其平均值。通过使用最小堆（min-heap），确保了高效地找到每个学生最高五个成绩，即使学生分数数量不一。示例代码演示了如何使用C++ STL容器实现这一功能。

High Five
There are two properties in the node student id and scores, to ensure that each student will have at least 5 points, find the average of 5 highest scores for each person.

Example
Example 1:

Input:
[[1,91],[1,92],[2,93],[2,99],[2,98],[2,97],[1,60],[1,58],[2,100],[1,61]]
Output:
1: 72.40
2: 97.40

Example 2:

Input:
[[1,90],[1,90],[1,90],[1,90],[1,90],[1,90]]
Output:
1: 90.00

解法1：
利用min-heap，每个学生都分配要给min-heap (size = 5)。
记得最后算平均值的时候，priority-queue是不能用iterator或auto进行遍历的，只能看top()，然后pop()。C++ STL的容器里面只有vector/queue/deque/set/map之类的才能用iterator遍历，priority-queue好像不行。
注意：
1）求前k个最大的值最好用最小堆（这样堆的size()就是k就可以了)。如果用最大堆，堆的size()要是n。
代码同步在
https://github.com/luqian2017/Algorithm

/**
 * Definition for a Record
 * class Record {
 * public:
 *   int id, score;
 *   Record(int id, int score) {
 *     this->id = id;
 *     this->score = score;
 *   }
 * };
 */
class Solution {
public:
    /**
     * @param results a list of <student_id, score>
     * @return find the average of 5 highest scores for each person
     * map<int, double> (student_id, average_score)
     */
    map<int, double> highFive(vector<Record>& results) {
        int len = results.size();
        
        map<int, priority_queue<int, vector<int>, greater<int>> > mp; //id, min-heap
        map<int, double> result;  //id, average-top-five
        for (int i = 0; i < len; ++i) {
            int studentId = results[i].id;
            int studentScore = results[i].score;
            mp[studentId].push(studentScore);
            //get the largest 5 elements
            if (mp[studentId].size() > 5)
                mp[studentId].pop();
        }
        
        for (auto m : mp) {
            double sum = 0;
            while(m.second.size() > 0) {
                sum += m.second.top();
                m.second.pop();
            }
            result[m.first] = sum / 5; //strictly speacking, it needs to check if the student has >= 5 courses
        }
        return result;
    }
};