Careercup - Google面试题 - 4699414551592960

2014-05-06 13:34

题目链接

原题：

we have a random list of people. each person knows his own height and the number of tall people in front of him. write a code to make the equivalent queue.
for example :
input: <"Height","NumberOfTall","Name">,
<,,"A">,<,,"B">,<,,"C">,<,,"D">,<,,"E">,<,,"F">
output: "F","E","D","C","B","A" --> end of queue

题目：有一队人正在排队，告诉你每个人的姓名、身高(目前默认都不相同)，以及他/她所看到的前面比他高的人。请你计算出这个队伍里各个人的顺序。

解法：从最矮的人入手。对于最矮的人，他所看到的所有人都比他高，所以如果他看到有K个人比他高，那么他一定排在K + 1名。我的代码是当时琢磨了很久，采用树状数组写出来的。此处的树状数组提供快速修改区间、查询单个元素的能力，能做到对数时间。现在居然已经忘了当时的具体思路。总体思想是先按身高升序排序，然后逐个确定每个人在队列里的位置。关键的一点：每次都只能确定当前最矮的人排在哪儿。树状数组中维护的值c[i]的意义，是记录当前位置的前面有多少个比它高。其中还有个方法用到二分搜索，所以整体复杂度是比较奇怪的O(n * log(n) +  n * log^2(n)) = O(n * log^2(n))。

代码：

 // http://www.careercup.com/question?id=4699414551592960
 #include <algorithm>
 #include <iostream>
 #include <string>
 #include <vector>
 using namespace std;

 struct Person {
     int height;
     int taller;
     string name;
     Person(int _height = , int _taller = , string _name = ""):
         height(_height), taller(_taller), name(_name) {};
     bool operator < (const Person &other) {
         return this->height < other.height;
     };

     friend ostream& operator << (ostream &cout, const Person &p) {
         cout << '<'<< p.name << p.height << '>';
         return cout;
     };
 };

 template <class T>
 class BinaryIndexedTree {
 public:
     BinaryIndexedTree(int _n = ): n(_n), v(_n + ) {};

     int size() {
         return n;
     };

     void addAll(int x, const T &val) {
         while (x >=  && x <= n) {
             v[x] += val;
             x -= lowBit(x);
         }
     };

     void addInterval(int x, int y, const T &val) {
         addAll(x - , -val);
         addAll(y, val);
     };

     void clear() {
         v.resize();
         n = ;
     };

     void resize(int new_n) {
         v.resize(new_n + );
         n = new_n;
     }

     T sum(int x) {
         T res = ;
         while (x >=  && x <= n) {
             res += v[x];
             x += lowBit(x);
         }

         return res;
     };

     int lowerBound(const T &val) {
         int ll, mm, rr;

         if (n == ) {
             return ;
         }

         T res;
         if (val <= (res = sum())) {
             return ;
         }
         if (val > (res = sum(n))) {
             return n + ;
         }

         ll = ;
         rr = n;
         while (rr - ll > ) {
             mm = (ll + rr) / ;
             res = sum(mm);
             if (val > res) {
                 ll = mm;
             } else {
                 rr = mm;
             }
         }

         return rr;
     }
 private:
     vector<T> v;
     int n;

     int lowBit(int x) {
         return x & -x;
     };
 };

 int main()
 {
     vector<Person> people;
     vector<int> queue;
     BinaryIndexedTree<int> bit;
     int i, j;
     int n;

     while (cin >> n && n > ) {
         people.resize(n);
         for (i = ; i < n; ++i) {
             cin >> people[i].height >> people[i].taller >> people[i].name;
         }
         sort(people.begin(), people.end());
         bit.resize(n);
         queue.resize(n);
         for (i = ; i <= n; ++i) {
             bit.addInterval(i, n, );
         }
         for (i = ; i <= n; ++i) {
             j = bit.lowerBound(people[i - ].taller + );
             queue[j - ] = i;
             bit.addInterval(j, n, -);
         }
         for (i = ; i < n; ++i) {
             cout << people[queue[i] - ];
         }
         cout << endl;

         people.clear();
         queue.clear();
         bit.clear();
     }

     return ;
 }