UVA 10935 - Throwing cards away I

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本文介绍了一个有趣的算法问题——卡片丢弃问题，该问题要求从有序的卡片堆中按照特定规则丢弃卡片，并最终确定剩余的卡片。文章提供了两种解决方案，一种使用静态数组模拟队列操作，另一种利用标准库中的队列实现。

Problem B: Throwing cards away I

Given is an ordered deck of n cards numbered 1 to n with card 1 at the top and card n at the bottom. The following operation is performed as long as there are at least two cards in the deck:

Throw away the top card and move the card that is now on the top of the deck to the bottom of the deck.

Your task is to find the sequence of discarded cards and the last, remaining card.

Each line of input (except the last) contains a number n ≤ 50. The last line contains 0 and this line should not be processed. For each number from the input produce two lines of output. The first line presents the sequence of discarded cards, the second line reports the last remaining card. No line will have leading or trailing spaces. See the sample for the expected format.

Sample input

Output for sample input

Discarded cards: 1, 3, 5, 7, 4, 2
Remaining card: 6
Discarded cards: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 4, 8, 12, 16, 2, 10, 18, 14
Remaining card: 6
Discarded cards: 1, 3, 5, 7, 9, 2, 6, 10, 8
Remaining card: 4
Discarded cards: 1, 3, 5, 2, 6
Remaining card: 4

特殊情况：n=1时，

Discarded cards:<- No space here!!!
Remaining card: 1

Solution1:

//#define RUN
#ifdef RUN


#include<stdio.h>

const int MAXN = 50;
int queue[MAXN];


int main() {

#ifndef ONLINE_JUDGE
	freopen("10935.in", "r", stdin);
	freopen("10935.out", "w", stdout); 
#endif

  int n, front, rear;
  while(scanf("%d", &n)==1 && n!=0){
	  // 初始化队列
	  for(int i = 0; i < n; i++) 
		  queue[i] = i+1;
	  front = 0;	// 队首元素的位置
	  rear = n;		// 队尾元素的后一个位置

	  printf("Discarded cards:");
	  // 队列非空
	  while(front < rear-1) {
		  if(front == rear-2){
			  printf(" %d", queue[front]);
		  }
		  else{
			  printf(" %d,", queue[front]);	
		  }
		  // 输出并抛弃原队首元素，front指向新队首元素
		  front++;
		  queue[rear] = queue[front];	// 队首元素转移至队尾，同时更新队首和队尾元素
		  front++;
		  rear++;
	  }
	  printf("\n");
	  printf("Remaining card: %d\n", queue[front]);

	  //printf("\nFinal front: %d\n", front);
	  //printf("Final rear: %d\n", rear);
  }
  
  
  return 0;
}

#endif

Solution2:

#define RUN
#ifdef RUN

#include<cstdio>
#include<queue>

using namespace std;

queue<int> q;

int main() {

#ifndef ONLINE_JUDGE
	freopen("10935.in", "r", stdin);
	freopen("10935.out", "w", stdout); 
#endif


  int n, front, rear;

  while(scanf("%d", &n)==1 && n!=0){

	  // 初始化队列
	  for(int i = 0; i < n; i++) 
		  q.push(i+1);

	  printf("Discarded cards:");
	  while(q.size() > 1) {

		  if(q.size() == 2){
			  printf(" %d", q.front());	// 打印队首元素
		  }
		  else{
			  printf(" %d,", q.front());	// 打印队首元素
		  }
		  

		  q.pop();			// 抛弃队首元素
		  q.push(q.front());	// 把队首元素加入到队尾
		  q.pop();			// 抛弃队首元素
	  }
	  printf("\n");
	  printf("Remaining card: %d\n", q.front());
	  q.pop();
  }
  
  return 0;
}

#endif