二分贪心 X - 24

Description

The whole family was excited by the news. Everyone knew grandpa had been an extremely good bridge player for decades, but when it was announced he would be in the Guinness Book of World Records as the most successful bridge player ever, whow, that was astonishing! 
The International Bridge Association (IBA) has maintained, for several years, a weekly ranking of the best players in the world. Considering that each appearance in a weekly ranking constitutes a point for the player, grandpa was nominated the best player ever because he got the highest number of points. 
Having many friends who were also competing against him, grandpa is extremely curious to know which player(s) took the second place. Since the IBA rankings are now available in the internet he turned to you for help. He needs a program which, when given a list of weekly rankings, finds out which player(s) got the second place according to the number of points.

Input

The input contains several test cases. Players are identified by integers from 1 to 10000. The first line of a test case contains two integers N and M indicating respectively the number of rankings available (2 <= N <= 500) and the number of players in each ranking (2 <= M <= 500). Each of the next N lines contains the description of one weekly ranking. Each description is composed by a sequence of M integers, separated by a blank space, identifying the players who figured in that weekly ranking. You can assume that: 
  • in each test case there is exactly one best player and at least one second best player, 
  • each weekly ranking consists of M distinct player identifiers.

The end of input is indicated by N = M = 0.

Output

For each test case in the input your program must produce one line of output, containing the identification number of the player who is second best in number of appearances in the rankings. If there is a tie for second best, print the identification numbers of all second best players in increasing order. Each identification number produced must be followed by a blank space.

Sample Input

4 5
20 33 25 32 99
32 86 99 25 10
20 99 10 33 86
19 33 74 99 32
3 6
2 34 67 36 79 93
100 38 21 76 91 85
32 23 85 31 88 1
0 0

Sample Output

32 33
1 2 21 23 31 32 34 36 38 67 76 79 88 91 93 100


         这道题的基本题意为要求求出现次数第二多的数,如果有多个的话按数从小到大的顺序输出。

         基本思路为设一个结构体,一个数表示标号,另一个数表示出现的个数,然后结构体数组进行排列,输出出现个数第二多的数即可。


源代码如下:

#include<iostream>
#include <stdio.h>
#include<algorithm>
#include<string.h>
using namespace std;
class A
{ public:
  int x,y;
};
bool cmp(A p,A q)
{
if(p.y!=q.y)return p.y>q.y;
  else return p.x<q.x;
}
int main()
{ int i,j,n,m,b,h,max;
  while(scanf("%d%d",&n,&m)&&n!=0&&m!=0)
  { A a[10001];
    memset(a,0,sizeof(a));
   for(i=0;i<n;++i)
    for(j=0;j<m;++j)
    {
 scanf("%d",&b);
 a[b].x=b;
 a[b].y++;
    }
    sort(a,a+10001,cmp);
    
    for(i=1,h=-1;i<m*n;++i)
     { if(h>a[i].y)break;
 if(a[i].y!=a[0].y)
      { h=a[i].y;
       printf("%d ",a[i].x);
 }
    }
    printf("\n");
  }


         需要注意的是输入输出要用scanf跟printf,否则会超时。



### 关于贪心算法解决找零钱问题 对于给定金额的找零问题,可以采用贪心算法来尝试解决问题。然而,在某些情况下,贪心算法可能无法提供最优解。具体来说,当硬币面额设置合理时(如常见的1分、5分、10分、25分),贪心算法能够有效地找到最少数量的硬币组合;但对于任意设定的硬币面额,则不一定适用。 针对特定条件下的换硬币问题,即每种硬币至少要有一个的情况,直接应用标准的贪心策略并不合适。因为这道题不仅限于最小化使用的硬币总数,还涉及到满足额外约束——确保三种类型的硬币都存在。因此,更合适的解决方案可能是通过遍历所有可能性并筛选符合条件的结果[^1]。 下面是一个Python程序实现的例子,该例子展示了如何处理这个问题: ```python def coin_change(x): solutions = [] for i in range((x - 3) // 5, 0, -1): # 至少一枚五分硬币 for j in range((x - 5 * i - 1) // 2, 0, -1): # 至少一枚二分硬币 k = x - 5 * i - 2 * j # 剩余部分由一分组成 if k >= 1: # 确保至少有一枚一分硬币 total_coins = i + j + k solution_str = f'fen5:{i}, fen2:{j}, fen1:{k}, total:{total_coins}' solutions.append(solution_str) print('\n'.join(solutions)) print(f'count = {len(solutions)}') coin_change(13) ``` 此代码片段实现了上述逻辑,并按照指定格式打印出了所有的可行方案及其对应的硬币总数。注意这里并没有严格遵循贪心原则,而是穷举了所有合法的选择路径。
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