图解LeetCode:79递归实现单词搜索

网格 (board):

79. 单词搜索
    中等
    给定一个 m x n 二维字符网格 board 和一个字符串单词 word 。如果 word 存在于网格中，返回 true ；否则，返回 false 。
    单词必须按照字母顺序，通过相邻的单元格内的字母构成，其中“相邻”单元格是那些水平相邻或垂直相邻的单元格。同一个单元格内的字母不允许被重复使用。
    

[['A', 'B', 'C', 'E'],['S', 'F', 'C', 'S'],['A', 'D', 'E', 'E']
]- 单词 (word): "ABCCED"

代码拆解：exist 函数

bool exist(vector<vector<char>> &board, string word) {if (board.empty() || word.empty())return false;for (int i = 0; i < board.size(); i++) {for (int j = 0; j < board[0].size(); j++) {if (board[i][j] == word[0]) {  // 找到首字母匹配的单元格if (backtrack(board, word, i, j, 0)) {return true;}}}}return false;
}

执行步骤
遍历网格：外层循环 i 遍历行，内层循环 j 遍历列。
找到首字母匹配：当 board[i][j] == word[0] 时，调用 backtrack 函数开始回溯搜索。
示例中，找到两个匹配位置：(0,0) 和 (2,0)。
我们先从 (0,0) 开始分析。

bool backtrack(vector<vector<char>> &board, string &word, int i, int j, int index) {// 边界检查和字符匹配检查if (i < 0 || i >= board.size() || j < 0 || j >= board[0].size() ||board[i][j] != word[index]) {return false;}// 所有字符都已匹配成功if (index == word.length() - 1) {return true;}// 标记当前单元格为已访问char temp = board[i][j];board[i][j] = '#';// 递归检查四个方向bool found = backtrack(board, word, i + 1, j, index + 1) || // 下backtrack(board, word, i - 1, j, index + 1) || // 上backtrack(board, word, i, j + 1, index + 1) || // 右backtrack(board, word, i, j - 1, index + 1);   // 左// 恢复当前单元格board[i][j] = temp;return found;
}

详细执行过程陈述：从 (0,0) 开始

backtrack(0,0,0)  →  A↓ 右
backtrack(0,1,1)  →  B↓ 右
backtrack(0,2,2)  →  C↓ 下
backtrack(1,2,3)  →  C↓ 下
backtrack(2,2,4)  →  E↓ 左
backtrack(2,1,5)  →  D ✅

文本描述补充

> 边界检查：i=0, j=0 在网格内，且 board[0][0] == 'A' == word[0]，通过检查。
是否匹配最后一个字符：index=0，word.length()-1=5，不满足，继续。
标记当前单元格：board[0][0] 被标记为 '#'。
递归检查四个方向：
下：i+1=1, j=0，board[1][0]='S' != word[1]='B'，返回 false。
上：i-1=-1，越界，返回 false。
右：i=0, j+1=1，board[0][1]='B' == word[1]，递归调用 backtrack(0,1,1)。
左：j-1=-1，越界，返回 false。递归调用 backtrack (0,1,1)
边界检查：i=0, j=1 在网格内，且 board[0][1] == 'B' == word[1]，通过检查。
是否匹配最后一个字符：index=1，不满足，继续。
标记当前单元格：board[0][1] 被标记为 '#'。
递归检查四个方向：
下：i+1=1, j=1，board[1][1]='F' != word[2]='C'，返回 false。
上：i-1=-1，越界，返回 false。
右：i=0, j+1=2，board[0][2]='C' == word[2]，递归调用 backtrack(0,2,2)。
左：board[0][0]='#' != word[2]='C'，返回 false。
递归调用 backtrack (0,2,2)边界检查：i=0, j=2 在网格内，且 board[0][2] == 'C' == word[2]，通过检查。
是否匹配最后一个字符：index=2，不满足，继续。
标记当前单元格：board[0][2] 被标记为 '#'。
递归检查四个方向：
下：i+1=1, j=2，board[1][2]='C' == word[3]，递归调用 backtrack(1,2,3)。
上：i-1=-1，越界，返回 false。
右：i=0, j+1=3，board[0][3]='E' != word[3]='C'，返回 false。
左：board[0][1]='#' != word[3]='C'，返回 false。递归调用 backtrack (1,2,3)
边界检查：i=1, j=2 在网格内，且 board[1][2] == 'C' == word[3]，通过检查。
是否匹配最后一个字符：index=3，不满足，继续。
标记当前单元格：board[1][2] 被标记为 '#'。
递归检查四个方向：
下：i+1=2, j=2，board[2][2]='E' == word[4]，递归调用 backtrack(2,2,4)。
上：board[0][2]='#' != word[4]='E'，返回 false。
右：i=1, j+1=3，board[1][3]='S' != word[4]='E'，返回 false。
左：i=1, j-1=1，board[1][1]='F' != word[4]='E'，返回 false。递归调用 backtrack (2,2,4)
边界检查：i=2, j=2 在网格内，且 board[2][2] == 'E' == word[4]，通过检查。
是否匹配最后一个字符：index=4，不满足，继续。
标记当前单元格：board[2][2] 被标记为 '#'。
递归检查四个方向：
下：i+1=3，越界，返回 false。
上：board[1][2]='#' != word[5]='D'，返回 false。
右：i=2, j+1=3，board[2][3]='E' != word[5]='D'，返回 false。
左：i=2, j-1=1，board[2][1]='D' == word[5]，递归调用 backtrack(2,1,5)。递归调用 backtrack (2,1,5)
边界检查：i=2, j=1 在网格内，且 board[2][1] == 'D' == word[5]，通过检查。
是否匹配最后一个字符：index=5 == word.length()-1，满足！返回 true。
回溯恢复过程当 backtrack(2,1,5) 返回 true 后，递归调用逐层返回：backtrack(2,2,4) 恢复 board[2][2] 为 'E'，返回 true。
backtrack(1,2,3) 恢复 board[1][2] 为 'C'，返回 true。
backtrack(0,2,2) 恢复 board[0][2] 为 'C'，返回 true。
backtrack(0,1,1) 恢复 board[0][1] 为 'B'，返回 true。
backtrack(0,0,0) 恢复 board[0][0] 为 'A'，返回 true。
最终结果
从 (0,0) 出发，成功找到路径 A → B → C → C → E → D。
exist 函数返回 true。

网格状态变化

1. 初始状态:[['A', 'B', 'C', 'E'],['S', 'F', 'C', 'S'],['A', 'D', 'E', 'E']]2. 标记 (0,0):[['#', 'B', 'C', 'E'],['S', 'F', 'C', 'S'],['A', 'D', 'E', 'E']]3. 标记 (0,1):[['#', '#', 'C', 'E'],['S', 'F', 'C', 'S'],['A', 'D', 'E', 'E']]4. 标记 (0,2):[['#', '#', '#', 'E'],['S', 'F', 'C', 'S'],['A', 'D', 'E', 'E']]5. 标记 (1,2):[['#', '#', '#', 'E'],['S', 'F', '#', 'S'],['A', 'D', 'E', 'E']]6. 标记 (2,2):[['#', '#', '#', 'E'],['S', 'F', '#', 'S'],['A', 'D', '#', 'E']]7. 标记 (2,1):[['#', '#', '#', 'E'],['S', 'F', '#', 'S'],['A', '#', '#', 'E']] ✅

总结

递归回溯：通过递归尝试所有可能的路径，遇到不匹配的情况时回溯。
标记与恢复：临时标记已访问的单元格，防止重复使用，递归返回前恢复现场。
剪枝优化：一旦找到完整路径，立即终止搜索，避免不必要的计算。

这个过程展示了回溯算法如何高效地在二维网格中搜索目标单词

补充实现动画演示的HTML代码（AI生成)

<!DOCTYPE html>
<html lang="zh-CN">
<head><meta charset="UTF-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>单词搜索回溯过程可视化</title><script src="https://cdn.tailwindcss.com"></script><link href="https://cdn.jsdelivr.net/npm/font-awesome@4.7.0/css/font-awesome.min.css" rel="stylesheet"><link href="https://fonts.googleapis.com/css2?family=Inter:wght@300;400;500;600;700&display=swap" rel="stylesheet"><script>tailwind.config = {theme: {extend: {colors: {primary: '#6C5CE7',secondary: '#00CEFF',accent: '#FC5C65',danger: '#E55039',dark: '#2D3436',light: '#F7F1E3'},fontFamily: {inter: ['Inter', 'sans-serif'],},}}}</script><style type="text/tailwindcss">@layer utilities {.content-auto {content-visibility: auto;}.grid-cell {@apply w-14 h-14 flex items-center justify-center border-2 rounded-xl font-bold text-xl transition-all duration-300 shadow-md;}.grid-cell-start {@apply bg-primary/20 border-primary text-primary animate-pulse;}.grid-cell-current {@apply bg-accent/30 border-accent text-accent transform scale-110 z-10 animate-bounce;}.grid-cell-visited {@apply bg-secondary/20 border-secondary text-secondary;}.grid-cell-failed {@apply bg-danger/20 border-danger text-danger line-through;}.step-card {@apply p-4 rounded-xl shadow-lg bg-white transition-all duration-300 hover:shadow-xl;}.step-number {@apply inline-flex items-center justify-center w-10 h-10 rounded-full bg-primary text-white font-bold mr-3 text-lg;}.direction-arrow {@apply text-xl font-bold transition-all duration-300;}.direction-arrow-active {@apply text-accent scale-125;}.recursive-call {@apply pl-6 border-l-4 border-primary/30 ml-4 my-2;}.stack-item {@apply px-3 py-1 rounded-lg bg-primary/10 text-primary my-1 inline-block;}}</style>
</head>
<body class="bg-gradient-to-br from-purple-50 to-indigo-100 min-h-screen font-inter"><div class="container mx-auto px-4 py-8 max-w-7xl"><header class="text-center mb-10"><h1 class="text-[clamp(2rem,5vw,3rem)] font-bold text-transparent bg-clip-text bg-gradient-to-r from-primary to-indigo-600 mb-4">单词搜索回溯过程可视化</h1><p class="text-gray-600 max-w-2xl mx-auto text-lg">通过动画演示回溯算法如何在二维网格中搜索目标单词 "ABCCED"</p></header><div class="grid grid-cols-1 lg:grid-cols-3 gap-8 mb-10"><!-- 左侧：步骤说明 --><div class="lg:col-span-1 space-y-6"><div class="step-card bg-primary/10"><div class="step-number">1</div><p class="text-dark">初始调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,0,0)</code></p><p class="mt-2 text-gray-600">检查 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][0]='A'</code> 是否匹配 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">word[0]='A'</code></p></div><div class="step-card bg-gray-100" id="step-2"><div class="step-number">2</div><p class="text-dark">匹配成功！标记当前单元格为已访问</p><p class="mt-2 text-gray-600">临时将 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][0]</code> 替换为 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">'#'</code> 防止重复访问</p></div><div class="step-card bg-gray-100" id="step-3"><div class="step-number">3</div><p class="text-dark">递归检查四个方向：</p><ul class="ml-6 mt-2 space-y-2"><li class="flex items-start"><i class="fa fa-arrow-down text-gray-400 mr-2 mt-1" id="arrow-down"></i><span><span class="font-semibold">下：</span><code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[1][0]='S'</code>，不匹配 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">word[1]='B'</code>，返回 <code class="bg-danger/20 px-1 py-0.5 rounded text-danger">false</code></span></li><li class="flex items-start"><i class="fa fa-arrow-up text-gray-400 mr-2 mt-1" id="arrow-up"></i><span><span class="font-semibold">上：</span>坐标 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">(i-1,j) = (-1,0)</code> 越界，返回 <code class="bg-danger/20 px-1 py-0.5 rounded text-danger">false</code></span></li><li class="flex items-start"><i class="fa fa-arrow-right text-gray-400 mr-2 mt-1" id="arrow-right"></i><span><span class="font-semibold">右：</span><code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][1]='B'</code>，匹配 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">word[1]='B'</code>，递归调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,1,1)</code></span></li><li class="flex items-start"><i class="fa fa-arrow-left text-gray-400 mr-2 mt-1" id="arrow-left"></i><span><span class="font-semibold">左：</span>坐标 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">(i,j-1) = (0,-1)</code> 越界，返回 <code class="bg-danger/20 px-1 py-0.5 rounded text-danger">false</code></span></li></ul></div><div class="step-card bg-gray-100 hidden" id="step-4"><div class="step-number">4</div><p class="text-dark">递归调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,1,1)</code></p><div class="recursive-call"><p class="mb-2"><span class="font-semibold">边界检查：</span><code class="bg-primary/20 px-1 py-0.5 rounded text-primary">i=0, j=1</code> 在网格内，且 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][1] == 'B' == word[1]</code></p><p class="mb-2"><span class="font-semibold">字符匹配：</span><code class="bg-primary/20 px-1 py-0.5 rounded text-primary">index=1</code>，未达到最后一个字符，继续递归</p><p><span class="font-semibold">标记单元格：</span>将 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][1]</code> 标记为 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">'#'</code></p></div></div><div class="step-card bg-gray-100 hidden" id="step-5"><div class="step-number">5</div><p class="text-dark">在 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,1,1)</code> 中检查四个方向：</p><ul class="ml-6 mt-2 space-y-2"><li class="flex items-start"><i class="fa fa-arrow-down text-gray-400 mr-2 mt-1" id="arrow-down-2"></i><span><span class="font-semibold">下：</span><code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[1][1]='F'</code>，不匹配 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">word[2]='C'</code>，返回 <code class="bg-danger/20 px-1 py-0.5 rounded text-danger">false</code></span></li><li class="flex items-start"><i class="fa fa-arrow-up text-gray-400 mr-2 mt-1" id="arrow-up-2"></i><span><span class="font-semibold">上：</span>坐标越界，返回 <code class="bg-danger/20 px-1 py-0.5 rounded text-danger">false</code></span></li><li class="flex items-start"><i class="fa fa-arrow-right text-gray-400 mr-2 mt-1" id="arrow-right-2"></i><span><span class="font-semibold">右：</span><code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][2]='C'</code>，匹配 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">word[2]='C'</code>，递归调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,2,2)</code></span></li><li class="flex items-start"><i class="fa fa-arrow-left text-gray-400 mr-2 mt-1" id="arrow-left-2"></i><span><span class="font-semibold">左：</span><code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][0]='#'</code> 已访问，返回 <code class="bg-danger/20 px-1 py-0.5 rounded text-danger">false</code></span></li></ul></div><!-- 更多步骤可以继续添加 --></div><!-- 右侧：网格可视化 --><div class="lg:col-span-2 bg-white rounded-2xl shadow-xl p-6 transform transition-all duration-500 hover:shadow-2xl"><div class="flex justify-between items-center mb-6"><h2 class="text-2xl font-bold text-transparent bg-clip-text bg-gradient-to-r from-primary to-indigo-600">网格状态</h2><div class="flex space-x-4"><button id="restart-btn" class="px-5 py-2.5 bg-gray-200 hover:bg-gray-300 rounded-xl transition-colors flex items-center"><i class="fa fa-refresh mr-2"></i> 重新开始</button><button id="prev-btn" class="px-5 py-2.5 bg-gray-200 hover:bg-gray-300 rounded-xl transition-colors disabled:opacity-50 flex items-center"><i class="fa fa-step-backward mr-2"></i> 上一步</button><button id="next-btn" class="px-5 py-2.5 bg-gradient-to-r from-primary to-indigo-600 hover:opacity-90 text-white rounded-xl transition-all shadow-md hover:shadow-lg flex items-center">下一步 <i class="fa fa-step-forward ml-2"></i></button></div></div><div class="flex justify-center mb-8"><div class="text-xl font-semibold text-dark" id="current-step">步骤 1/10</div></div><!-- 网格 --><div class="grid grid-cols-4 gap-4 justify-center mb-10 relative"><div class="grid-cell grid-cell-start" id="cell-0-0">A</div><div class="grid-cell" id="cell-0-1">B</div><div class="grid-cell" id="cell-0-2">C</div><div class="grid-cell" id="cell-0-3">E</div><div class="grid-cell" id="cell-1-0">S</div><div class="grid-cell" id="cell-1-1">F</div><div class="grid-cell" id="cell-1-2">C</div><div class="grid-cell" id="cell-1-3">S</div><div class="grid-cell" id="cell-2-0">A</div><div class="grid-cell" id="cell-2-1">D</div><div class="grid-cell" id="cell-2-2">E</div><div class="grid-cell" id="cell-2-3">E</div><!-- 方向箭头 --><div class="absolute invisible" id="direction-arrow" style="width: 30px; height: 30px; background-color: #FC5C65; clip-path: polygon(50% 0%, 0% 100%, 100% 100%); transform: rotate(90deg); z-index: 20;"></div></div><!-- 调用栈可视化 --><div class="bg-gray-50 rounded-xl p-4 mb-6"><h3 class="font-bold mb-3 text-dark flex items-center"><i class="fa fa-code mr-2 text-primary"></i> 递归调用栈</h3><div id="call-stack" class="flex flex-wrap gap-2"><div class="stack-item">backtrack(0,0,0)</div></div></div><!-- 当前状态 --><div class="bg-gradient-to-r from-primary/5 to-indigo-50 rounded-xl p-5"><h3 class="font-bold mb-3 text-dark text-lg">当前状态</h3><p id="status-text" class="text-gray-700 text-lg">正在检查 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][0]</code> 是否匹配 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">word[0]</code>...</p></div></div></div><!-- 单词匹配路径 --><div class="mt-10 bg-white rounded-2xl shadow-xl p-6"><h2 class="text-2xl font-bold text-transparent bg-clip-text bg-gradient-to-r from-primary to-indigo-600 mb-6">单词匹配路径</h2><div class="flex flex-wrap justify-center items-center space-x-4 md:space-x-8"><div class="w-16 h-16 rounded-full bg-primary flex items-center justify-center text-white font-bold text-2xl shadow-lg" id="path-0">A</div><div class="direction-arrow text-gray-400 text-2xl" id="path-arrow-1">→</div><div class="w-16 h-16 rounded-full bg-gray-200 flex items-center justify-center text-gray-700 font-bold text-2xl shadow-md" id="path-1">B</div><div class="direction-arrow text-gray-400 text-2xl">→</div><div class="w-16 h-16 rounded-full bg-gray-200 flex items-center justify-center text-gray-700 font-bold text-2xl shadow-md" id="path-2">C</div><div class="direction-arrow text-gray-400 text-2xl">→</div><div class="w-16 h-16 rounded-full bg-gray-200 flex items-center justify-center text-gray-700 font-bold text-2xl shadow-md" id="path-3">C</div><div class="direction-arrow text-gray-400 text-2xl">→</div><div class="w-16 h-16 rounded-full bg-gray-200 flex items-center justify-center text-gray-700 font-bold text-2xl shadow-md" id="path-4">E</div><div class="direction-arrow text-gray-400 text-2xl">→</div><div class="w-16 h-16 rounded-full bg-gray-200 flex items-center justify-center text-gray-700 font-bold text-2xl shadow-md" id="path-5">D</div></div></div><!-- 回溯算法说明 --><div class="mt-10 bg-white rounded-2xl shadow-xl p-6"><h2 class="text-2xl font-bold text-transparent bg-clip-text bg-gradient-to-r from-primary to-indigo-600 mb-4">回溯算法原理</h2><div class="grid grid-cols-1 md:grid-cols-2 gap-6"><div><h3 class="font-bold text-lg mb-3 text-primary">什么是回溯算法？</h3><p class="text-gray-700 mb-4">回溯算法是一种通过尝试所有可能的路径来寻找问题解的算法。当它发现当前路径不可能得到解时，它会"回溯"到上一步，尝试其他路径。</p><h3 class="font-bold text-lg mb-3 text-primary">在此问题中的应用</h3><p class="text-gray-700">在单词搜索问题中，回溯算法从网格的每个单元格开始，递归地检查四个方向：上、下、左、右。如果当前单元格匹配单词的当前字符，则继续递归检查下一个字符，直到找到完整的单词或确定无法找到。</p></div><div><h3 class="font-bold text-lg mb-3 text-primary">关键步骤</h3><ol class="list-decimal list-inside text-gray-700 space-y-2"><li><span class="font-semibold">边界检查：</span>确保当前位置在网格内</li><li><span class="font-semibold">字符匹配：</span>检查当前单元格是否匹配单词的当前字符</li><li><span class="font-semibold">标记访问：</span>临时标记当前单元格为已访问，防止重复使用</li><li><span class="font-semibold">递归搜索：</span>尝试四个方向的相邻单元格</li><li><span class="font-semibold">恢复状态：</span>递归返回后恢复单元格的原始值</li></ol></div></div></div></div><footer class="mt-16 py-8 bg-gradient-to-r from-primary/10 to-indigo-100"><div class="container mx-auto px-4 text-center text-gray-600"><p>单词搜索回溯过程可视化 &copy; 2023</p><p class="mt-2 text-sm">使用 Tailwind CSS 和 Font Awesome 构建</p></div></footer><script>// 当前步骤let currentStep = 1;// 总步骤数const totalSteps = 10;// 单元格状态const cells = {};for (let i = 0; i < 3; i++) {for (let j = 0; j < 4; j++) {cells[`${i}-${j}`] = document.getElementById(`cell-${i}-${j}`);}}// 路径节点const pathNodes = {};for (let i = 0; i < 6; i++) {pathNodes[i] = document.getElementById(`path-${i}`);}// 方向箭头const directionArrow = document.getElementById('direction-arrow');// 更新步骤显示function updateStepDisplay() {document.getElementById('current-step').textContent = `步骤 ${currentStep}/${totalSteps}`;// 重置所有步骤卡片样式document.querySelectorAll('.step-card').forEach(card => {card.classList.remove('bg-primary/10');card.classList.add('bg-gray-100');card.classList.add('hidden');});// 显示当前步骤及之前的步骤for (let i = 1; i <= Math.min(currentStep, 5); i++) {const stepCard = document.getElementById(`step-${i}`);if (stepCard) {stepCard.classList.remove('hidden');if (i === currentStep) {stepCard.classList.remove('bg-gray-100');stepCard.classList.add('bg-primary/10');}}}// 更新按钮状态document.getElementById('prev-btn').disabled = currentStep === 1;document.getElementById('next-btn').disabled = currentStep === totalSteps;// 更新路径节点状态for (let i = 0; i < 6; i++) {if (i < currentStep - 1) {pathNodes[i].classList.remove('bg-gray-200');pathNodes[i].classList.add('bg-secondary');} else if (i === currentStep - 1) {pathNodes[i].classList.remove('bg-gray-200');pathNodes[i].classList.add('bg-accent');pathNodes[i].classList.add('animate-pulse');} else {pathNodes[i].classList.remove('bg-secondary', 'bg-accent', 'animate-pulse');pathNodes[i].classList.add('bg-gray-200');}}// 更新方向箭头document.querySelectorAll('.direction-arrow').forEach(arrow => {arrow.classList.remove('direction-arrow-active');});// 更新调用栈updateCallStack();// 更新状态文本和网格状态updateStatusText();}// 更新调用栈function updateCallStack() {const callStack = document.getElementById('call-stack');callStack.innerHTML = '';// 根据当前步骤构建调用栈let stackItems = [];switch(currentStep) {case 1:case 2:case 3:stackItems = ['backtrack(0,0,0)'];break;case 4:case 5:stackItems = ['backtrack(0,0,0)', 'backtrack(0,1,1)'];break;case 6:case 7:stackItems = ['backtrack(0,0,0)', 'backtrack(0,1,1)', 'backtrack(0,2,2)'];break;case 8:stackItems = ['backtrack(0,0,0)', 'backtrack(0,1,1)', 'backtrack(0,2,2)', 'backtrack(1,2,3)'];break;case 9:stackItems = ['backtrack(0,0,0)', 'backtrack(0,1,1)', 'backtrack(0,2,2)', 'backtrack(1,2,3)', 'backtrack(2,2,4)'];break;case 10:stackItems = ['backtrack(0,0,0)', 'backtrack(0,1,1)', 'backtrack(0,2,2)', 'backtrack(1,2,3)', 'backtrack(2,2,4)', 'backtrack(2,1,5)'];break;}// 添加到DOMstackItems.forEach((item, index) => {const stackItem = document.createElement('div');stackItem.className = 'stack-item';stackItem.textContent = item;// 高亮当前调用if (index === stackItems.length - 1) {stackItem.classList.add('bg-accent/20');stackItem.classList.add('text-accent');stackItem.classList.add('font-bold');}callStack.appendChild(stackItem);});}// 更新状态文本function updateStatusText() {const statusText = document.getElementById('status-text');directionArrow.classList.add('invisible');// 重置所有单元格样式for (let i = 0; i < 3; i++) {for (let j = 0; j < 4; j++) {const cellId = `${i}-${j}`;cells[cellId].classList.remove('grid-cell-current', 'grid-cell-visited', 'grid-cell-failed');// 恢复原始值if (i === 0 && j === 0) cells[cellId].textContent = 'A';if (i === 0 && j === 1) cells[cellId].textContent = 'B';if (i === 0 && j === 2) cells[cellId].textContent = 'C';if (i === 1 && j === 2) cells[cellId].textContent = 'C';if (i === 2 && j === 2) cells[cellId].textContent = 'E';if (i === 2 && j === 1) cells[cellId].textContent = 'D';}}switch(currentStep) {case 1:statusText.innerHTML = `正在检查 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][0]</code> 是否匹配 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">word[0]='A'</code>...`;cells['0-0'].classList.add('grid-cell-current');cells['0-0'].classList.remove('grid-cell-start');break;case 2:statusText.innerHTML = `匹配成功！标记 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][0]</code> 为已访问`;cells['0-0'].classList.remove('grid-cell-current');cells['0-0'].classList.add('grid-cell-visited');cells['0-0'].textContent = '#';break;case 3:statusText.innerHTML = `正在检查 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">board[0][0]</code> 的四个方向：`;cells['0-0'].classList.add('grid-cell-current');cells['0-0'].classList.remove('grid-cell-visited');cells['0-0'].textContent = 'A';// 激活右侧箭头document.getElementById('arrow-right').classList.add('direction-arrow-active');document.getElementById('path-arrow-1').classList.add('direction-arrow-active');// 显示方向箭头positionDirectionArrow(0, 0, 'right');break;case 4:statusText.innerHTML = `递归调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,1,1)</code>`;cells['0-1'].classList.add('grid-cell-current');cells['0-0'].classList.add('grid-cell-visited');cells['0-0'].textContent = '#';break;case 5:statusText.innerHTML = `在 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,1,1)</code> 中检查四个方向：`;cells['0-1'].classList.add('grid-cell-current');cells['0-0'].classList.add('grid-cell-visited');cells['0-0'].textContent = '#';// 激活右侧箭头document.getElementById('arrow-right-2').classList.add('direction-arrow-active');// 显示方向箭头positionDirectionArrow(0, 1, 'right');break;case 6:statusText.innerHTML = `递归调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,2,2)</code>`;cells['0-2'].classList.add('grid-cell-current');cells['0-1'].classList.add('grid-cell-visited');cells['0-1'].textContent = '#';break;case 7:statusText.innerHTML = `在 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(0,2,2)</code> 中检查四个方向：`;cells['0-2'].classList.add('grid-cell-current');cells['0-1'].classList.add('grid-cell-visited');cells['0-1'].textContent = '#';// 激活下侧箭头document.getElementById('arrow-down').classList.add('direction-arrow-active');// 显示方向箭头positionDirectionArrow(0, 2, 'down');break;case 8:statusText.innerHTML = `递归调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(1,2,3)</code>`;cells['1-2'].classList.add('grid-cell-current');cells['0-2'].classList.add('grid-cell-visited');cells['0-2'].textContent = '#';break;case 9:statusText.innerHTML = `递归调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(2,2,4)</code>`;cells['2-2'].classList.add('grid-cell-current');cells['1-2'].classList.add('grid-cell-visited');cells['1-2'].textContent = '#';// 显示方向箭头positionDirectionArrow(1, 2, 'down');break;case 10:statusText.innerHTML = `递归调用 <code class="bg-primary/20 px-1 py-0.5 rounded text-primary">backtrack(2,1,5)</code> - <span class="text-accent font-bold">找到最后一个字符 'D'！</span>`;cells['2-1'].classList.add('grid-cell-current');cells['2-2'].classList.add('grid-cell-visited');cells['2-2'].textContent = '#';// 显示方向箭头positionDirectionArrow(2, 2, 'left');// 激活所有路径箭头document.querySelectorAll('.direction-arrow').forEach(arrow => {arrow.classList.add('direction-arrow-active');});// 高亮所有路径节点for (let i = 0; i < 6; i++) {pathNodes[i].classList.remove('bg-gray-200', 'bg-primary');pathNodes[i].classList.add('bg-accent');pathNodes[i].classList.add('animate-pulse');}break;}}// 定位方向箭头function positionDirectionArrow(i, j, direction) {const cell = cells[`${i}-${j}`];const cellRect = cell.getBoundingClientRect();const container = document.querySelector('.grid');const containerRect = container.getBoundingClientRect();const cellSize = cellRect.width;const arrowSize = 30;let top, left, rotate;switch(direction) {case 'right':top = cellRect.top - containerRect.top + cellSize/2 - arrowSize/2;left = cellRect.right - containerRect.left;rotate = 0;break;case 'down':top = cellRect.bottom - containerRect.top;left = cellRect.left - containerRect.left + cellSize/2 - arrowSize/2;rotate = 90;break;case 'left':top = cellRect.top - containerRect.top + cellSize/2 - arrowSize/2;left = cellRect.left - containerRect.left - arrowSize;rotate = 180;break;case 'up':top = cellRect.top - containerRect.top - arrowSize;left = cellRect.left - containerRect.left + cellSize/2 - arrowSize/2;rotate = 270;break;}// 设置箭头位置和旋转directionArrow.style.top = `${top}px`;directionArrow.style.left = `${left}px`;directionArrow.style.transform = `rotate(${rotate}deg)`;directionArrow.classList.remove('invisible');}// 重新开始function restartVisualization() {// 重置所有状态currentStep = 1;// 重置路径节点for (let i = 0; i < 6; i++) {pathNodes[i].classList.remove('bg-secondary', 'bg-accent', 'animate-pulse');pathNodes[i].classList.add('bg-gray-200');}// 重置方向箭头document.querySelectorAll('.direction-arrow').forEach(arrow => {arrow.classList.remove('direction-arrow-active');});// 更新显示updateStepDisplay();}// 初始化页面document.addEventListener('DOMContentLoaded', function() {// 初始化显示updateStepDisplay();// 设置按钮事件document.getElementById('prev-btn').addEventListener('click', function() {if (currentStep > 1) {currentStep--;updateStepDisplay();}});document.getElementById('next-btn').addEventListener('click', function() {if (currentStep < totalSteps) {currentStep++;updateStepDisplay();}});// 添加重新开始按钮事件document.getElementById('restart-btn').addEventListener('click', restartVisualization);// 添加键盘导航document.addEventListener('keydown', function(e) {if (e.key === 'ArrowLeft' && currentStep > 1) {currentStep--;updateStepDisplay();} else if (e.key === 'ArrowRight' && currentStep < totalSteps) {currentStep++;updateStepDisplay();} else if (e.key === 'r' || e.key === 'R') {restartVisualization();}});});</script>
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