Line reconstruction by height

最新推荐文章于 2025-04-01 11:11:26 发布

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本文介绍了一种根据人员的高度和前面更高人员的数量来重建队伍的算法。提供了两种实现方式：一种是通过排序并插入的方式，另一种是预先按高度降序排列再进行插入。文中还附带了C++代码实现。

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Problem

Suppose you have a line of n people in which the k-th person is described by a pair (h,t) , where h is the height of the k-th person and t is the number of people in front of k who have a height greater or equal than h . Write an algorithm to reconstruct the line.

For example, if the line is composed by the following people:

[(7, 0, A),(4, 4, B),(7, 1, C), (5, 0, D), (6, 1, E), (5, 2, F)]

The original line should be:

[(5, 0, D), (7, 0, A), (5, 2, F), (6, 1, E), (4, 4, B),(7, 1, C)]

Solution

每个输入信息表示为: (height, taller_num, name), 两种思路：
1. 排序:先以taller_num 升序排序，如果相等按照height的降序排列。然后将每个人插入到他们正确的位置，遍历每一个人 p，从结果list的开头计数比p.height大的数目，直到与p.taller_num为止，即找到p在res中的位置，将p插入到当前位置。
2. 先以height的降序排列，如果相等按照taller_num的升序排列。然后依然是找到每个人的正确位置插入，不过这次要简单一些，遍历每个人(p)，将其插入list.begin() + p.taller_num位置。

Code

#include <iostream>
#include <vector>
#include <list>
#include <string>

using namespace std;

struct person{
  string name;
  int height;
  int taller_num;
  person(string name, int h, int num) : name(name), height(h), taller_num(num){}
};

bool cmp(person& p1, person& p2) {
  if(p1.taller_num != p2.taller_num)
    return p1.taller_num < p2.taller_num;
  return p1.height > p2.height;
}

void reorder(vector<person>& person_list, list<person>& res) {
  sort(person_list.begin(), person_list.end(), cmp);
  for(int i = 0; i < person_list.size(); ++i) {
    list<person>::iterator iter = res.begin();
    int n = person_list[i].taller_num;
    while(n > 0) {
      if(iter->height >= person_list[i].height)
        --n;
      ++iter;
    }
    res.insert(iter, person_list[i]);
  }
}

bool cmp2(person& p1, person&p2) {
  if(p1.height != p2.height) return p1.height > p2.height;
  return p1.taller_num < p2.taller_num;
}

void reorder2(vector<person>& person_list, list<person>& res) {
  sort(person_list.begin(), person_list.end(), cmp2);
  for(auto& p : person_list) {
    list<person>::iterator iter = res.begin();
    int n = p.taller_num;
    while(n-- > 0) {
      ++iter;
    }
    res.insert(iter, p);
  }
}

int main() {
  vector<person> person_list;
  person_list.push_back(person("A", 7, 0));
  person_list.push_back(person("B", 4, 4));
  person_list.push_back(person("C", 7, 1));
  person_list.push_back(person("D", 5, 0));
  person_list.push_back(person("E", 6, 1));
  person_list.push_back(person("F", 5, 2));
  list<person> res;
  reorder(person_list, res);
  for(person& p : res) {
    cout << p.name << " ";
  }
  cout << endl;
  res.clear();
  cout << "reorder2 :" << endl;
  reorder2(person_list, res);
  for(person& p : res) {
    cout << p.name << " ";
  }
  cout << endl;
}