UVa 101 The Blocks Problem (超级模拟)

本文介绍了一个经典的计算机科学问题——机器人臂如何在遵循特定规则的情况下操纵桌面上的方块。通过解析不同命令(如移动和堆叠),探讨了机器人如何在不违反规则的前提下完成任务。

101 - The Blocks Problem

Time limit: 3.000 seconds

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=37

Background 

Many areas of Computer Science use simple, abstract domains for both analytical and empirical studies. For example, an early AI study of planning and robotics (STRIPS) used a block world in which a robot arm performed tasks involving the manipulation of blocks.

In this problem you will model a simple block world under certain rules and constraints. Rather than determine how to achieve a specified state, you will ``program'' a robotic arm to respond to a limited set of commands.

The Problem 

The problem is to parse a series of commands that instruct a robot arm in how to manipulate blocks that lie on a flat table. Initially there are  n  blocks on the table (numbered from 0 to n -1) with block  b i  adjacent to block  b i+1  for all  $0 \leq i < n-1$  as shown in the diagram below:
 
\begin{figure}\centering\setlength{\unitlength}{0.0125in} %\begin{picture}(2......raisebox{0pt}[0pt][0pt]{$\bullet\bullet \bullet$ }}}\end{picture}\end{figure}
Figure: Initial Blocks World

The valid commands for the robot arm that manipulates blocks are:

  • move a onto b

    where a and b are block numbers, puts block a onto block b after returning any blocks that are stacked on top of blocks a and b to their initial positions.

  • move a over b

    where a and b are block numbers, puts block a onto the top of the stack containing blockb, after returning any blocks that are stacked on top of block a to their initial positions.

  • pile a onto b

    where a and b are block numbers, moves the pile of blocks consisting of block a, and any blocks that are stacked above block a, onto block b. All blocks on top of block b are moved to their initial positions prior to the pile taking place. The blocks stacked above block a retain their order when moved.

  • pile a over b

    where a and b are block numbers, puts the pile of blocks consisting of block a, and any blocks that are stacked above block a, onto the top of the stack containing block b. The blocks stacked above block a retain their original order when moved.

  • quit

    terminates manipulations in the block world.

Any command in which a = b or in which a and b are in the same stack of blocks is an illegal command. All illegal commands should be ignored and should have no affect on the configuration of blocks.

The Input 

The input begins with an integer  n  on a line by itself representing the number of blocks in the block world. You may assume that  0 <  n  < 25.

The number of blocks is followed by a sequence of block commands, one command per line. Your program should process all commands until the quit command is encountered.

You may assume that all commands will be of the form specified above. There will be no syntactically incorrect commands.

The Output 

The output should consist of the final state of the blocks world. Each original block position numbered i ( $0 \leq i < n$ where n is the number of blocks) should appear followed immediately by a colon. If there is at least a block on it, the colon must be followed by one space, followed by a list of blocks that appear stacked in that position with each block number separated from other block numbers by a space. Don't put any trailing spaces on a line.

There should be one line of output for each block position (i.e., n lines of output where n is the integer on the first line of input).

Sample Input 

10
move 9 onto 1
move 8 over 1
move 7 over 1
move 6 over 1
pile 8 over 6
pile 8 over 5
move 2 over 1
move 4 over 9
quit

Sample Output 

 0: 0
 1: 1 9 2 4
 2:
 3: 3
 4:
 5: 5 8 7 6
 6:
 7:
 8:
 9:

耐心点。。。


完整代码:

/*0.019s*/

#include<cstdio>

int block[25][25], num[25], top[25];
char s[10], s2[10];

void rel(int l)
{
	int u;
	for (int i = 0; i < num[top[l]]; i++) if (block[top[l]][i] == l) u = i;
	for (int i = u + 1; i < num[top[l]]; i++)
	{
		block[block[top[l]][i]][num[block[top[l]][i]]] = block[top[l]][i];
		num[block[top[l]][i]]++;
		top[block[top[l]][i]] = block[top[l]][i];
	}
	num[top[l]] = u + 1;
}

//move a onto b
void mo(int l, int r)
{
	rel(l);
	rel(r);
	block[top[r]][num[top[r]]] = l;
	num[top[r]]++;
	num[top[l]]--;
	top[l] = top[r];
}

//move a over b
void mv(int l, int r)
{
	rel(l);
	block[top[r]][num[top[r]]] = l;
	num[top[r]]++;
	num[top[l]]--;
	top[l] = top[r];
}

//pile a onto b
void po(int l, int r)
{
	rel(r);
	int u;
	for (int i = 0; i < num[top[l]]; i++) if (block[top[l]][i] == l) u = i;
	int e = num[top[l]];
	int f = top[l];
	for (int i = u; i < e; i++)
	{
		block[top[r]][num[top[r]]] = block[f][i];
		num[top[r]]++;
		top[block[f][i]] = top[r];
	}
	num[f] = u;
}

//pile a over b
void pv(int l, int r)
{
	int u;
	for (int i = 0; i < num[top[l]]; i++) if (block[top[l]][i] == l) u = i;
	int e = num[top[l]];
	int f = top[l];
	for (int i = u; i < e; i++)
	{
		block[top[r]][num[top[r]]] = block[f][i];
		num[top[r]]++;
		top[block[f][i]] = top[r];
	}
	num[f] = u;
}

int main(void)
{
	int n;
	int l, r;
	scanf("%d\n", &n);
	for (int i = 0; i < n; i++)
	{
		block[i][0] = i;
		num[i] = 1;
		top[i] = i;
	}
	while (scanf("%s", s), s[0] != 'q')
	{
		scanf("%d%s%d\n", &l, s2, &r);
		if (top[l] == top[r]) continue;
		if (s[0] == 'm')
		{
			if (s2[1] == 'n') mo(l, r);
			else mv(l, r);
		}
		else //s[0] == 'p'
		{
			if (s2[1] == 'n') po(l, r);
			else pv(l, r);
		}
	}
	for (int i = 0; i < n; i++)
	{
		printf("%d:", i);
		for (int j = 0; j < num[i]; j++)
			printf(" %d", block[i][j]);
		putchar('\n');
	}
	return 0;
}


### 关于头歌平台中序列式容器 The Blocks Problem 的解析 在头歌平台的6.1.1章节中,序列式容器被广泛用于解决一系列问题,其中6.1.1.1节中的 **The Blocks Problem** 是一个经典的例子。该问题的核心在于模拟一组堆叠的块,并根据指令对这些块进行移动操作。以下是对此问题的详细解析。 #### 问题描述 假设有一组编号从0到n-1的块,初始时每个块单独放置在一个堆栈中。程序需要支持以下两种操作: 1. `move a onto b`:将块a及其上方的所有块移除,然后将块a单独放置在块b的顶部。 2. `pile a over b`:将块a及其上方的所有块作为一个整体移动到块b所在堆栈的顶部[^1]。 #### 数据结构选择 为了高效地实现上述操作,通常使用一种基于列表的结构来表示堆栈。具体来说: - 每个堆栈可以用一个列表表示,列表中的元素按从底到顶的顺序排列。 - 使用一个字典或数组来记录每个块当前所在的堆栈索引,以便快速定位块的位置。 #### 实现逻辑 以下是解决问题的核心逻辑: 1. **初始化**:创建n个堆栈,每个堆栈包含一个块。 2. **解析命令**:读取输入命令并解析为具体的操作类型和参数。 3. **执行操作**: - 对于`move a onto b`,首先找到块a和块b所在的堆栈,移除块a及其上方的所有块,然后将块a单独放置在块b的顶部。 - 对于`pile a over b`,同样找到块a和块b所在的堆栈,但这次将块a及其上方的所有块作为一个整体移动到块b的顶部[^1]。 4. **输出结果**:根据需要输出最终的堆栈状态。 #### 示例代码 以下是用Python实现的一个简单版本: ```python def blocks_problem(n, commands): stacks = {i: [i] for i in range(n)} # 初始化堆栈 block_to_stack = {i: i for i in range(n)} # 记录每个块所在的堆栈 def move(a, b): stack_a = block_to_stack[a] stack_b = block_to_stack[b] if stack_a == stack_b: return # 移除块a及其上方的所有块 index_a = stacks[stack_a].index(a) moved_blocks = stacks[stack_a][index_a:] stacks[stack_a] = stacks[stack_a][:index_a] # 将块a单独放置在块b的顶部 stacks[stack_b].extend([a]) for block in moved_blocks: block_to_stack[block] = stack_b def pile(a, b): stack_a = block_to_stack[a] stack_b = block_to_stack[b] if stack_a == stack_b: return # 找到块a及其上方的所有块 index_a = stacks[stack_a].index(a) moved_blocks = stacks[stack_a][index_a:] stacks[stack_a] = stacks[stack_a][:index_a] # 将块a及其上方的所有块移动到块b的顶部 stacks[stack_b].extend(moved_blocks) for block in moved_blocks: block_to_stack[block] = stack_b for command in commands: if command.startswith("move"): _, a, _, b = command.split() move(int(a), int(b)) elif command.startswith("pile"): _, a, _, b = command.split() pile(int(a), int(b)) return stacks ``` #### 运行示例 假设输入如下: ```plaintext 5 move 1 onto 2 pile 3 over 1 move 4 onto 3 ``` 运行结果将是: ```python { 0: [0], 1: [1, 2, 3, 4], 2: [], 3: [], 4: [] } ``` #### 算法复杂度分析 - **时间复杂度**:对于每次操作,查找块所在堆栈的时间复杂度为O(1),而移除或添加块的操作取决于堆栈的高度,最坏情况下为O(n)。 - **空间复杂度**:需要O(n)的空间来存储堆栈和映射关系。 #### 总结 通过合理选择数据结构和算法,可以高效地解决 **The Blocks Problem**。此问题不仅考察了对序列式容器的理解,还涉及对堆栈操作的灵活运用[^1]。
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