595 lines
21 KiB
HTML
595 lines
21 KiB
HTML
<!DOCTYPE html>
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<html>
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<head>
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<meta charset="UTF-8">
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<title>Morris Post‑Order Traversal Animation & Code Display</title>
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<style>
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html, body { margin: 0; padding: 0; font-family: Arial, sans-serif; }
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h1 { text-align: center; margin-top: 10px; margin-bottom: 5px; }
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p { text-align: center; margin: 5px 0 15px; }
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.visualization-container {
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display: flex;
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justify-content: space-between;
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max-width: 1200px;
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margin: 0 auto;
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height: 88vh;
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}
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.code-container {
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background-color: #f0f0f0;
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border-radius: 10px;
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padding: 15px;
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width: 48%;
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overflow-y: auto;
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height: 88vh;
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font-size: 15px;
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}
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pre {
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margin: 0;
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background-color: #f0f0f0;
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overflow-x: auto;
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}
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code {
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font-family: Consolas, "Courier New", monospace;
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white-space: pre;
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}
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.line-number {
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color: #666;
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display: inline-block;
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min-width: 30px;
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}
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.tree-container {
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background-color: #f0f0f0;
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border-radius: 10px;
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padding: 15px;
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width: 48%;
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height: 88vh;
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position: relative;
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display: flex;
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flex-direction: column;
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}
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#nextStep {
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margin: 10px auto;
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padding: 8px 15px;
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font-size: 16px;
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width: fit-content;
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cursor: pointer;
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background-color: #4CAF50;
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color: white;
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border: none;
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border-radius: 4px;
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display: block;
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}
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#nextStep:hover { background-color: #45a049; }
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#nextStep:disabled { background-color: #cccccc; cursor: not-allowed; }
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#container { flex-grow: 1; width: 100%; }
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.explanation {
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margin-top: 10px;
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font-size: 14px;
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padding: 10px;
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background-color: #e8e8e8;
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border-radius: 5px;
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}
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.color-key {
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display: flex;
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flex-wrap: wrap;
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gap: 8px;
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margin-bottom: 5px;
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padding: 8px;
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background-color: #e8e8e8;
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border-radius: 5px;
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}
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.color-item {
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display: flex;
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align-items: center;
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margin-right: 10px;
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font-size: 13px;
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}
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.color-box {
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width: 16px;
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height: 16px;
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border-radius: 3px;
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margin-right: 4px;
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border: 1px solid #888;
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}
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.color-arrow {
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position: relative;
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width: 24px;
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height: 3px;
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margin-right: 4px;
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}
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.color-arrow:after {
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content: "";
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position: absolute;
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right: -2px;
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top: -4px;
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border-left: 6px solid;
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border-top: 4px solid transparent;
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border-bottom: 4px solid transparent;
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}
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.dotted-line {
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width: 24px;
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height: 0;
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border-top: 2px dashed #ff5722;
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margin-right: 4px;
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}
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</style>
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<!-- Load Konva.js -->
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<script src="https://cdn.jsdelivr.net/npm/konva@8.3.13/konva.min.js"></script>
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</head>
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<body>
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<h1>Morris Post-Order Traversal Visualization</h1>
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<p>This animation shows how the Morris post-order traversal algorithm works without using a stack or recursion. Click the "Next Step" button to run the animation.</p>
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<div class="visualization-container">
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<div class="code-container">
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<pre><code><span class="line-number">0.</span> <span style="color:blue">void</span> postorderTraversal(<span style="color:blue">TreeNode</span>* root) {
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<span class="line-number">1.</span> <span style="color:blue">TreeNode</span>* current = root;
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<span class="line-number">2.</span> <span style="color:blue">TreeNode</span>* rightmost;
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<span class="line-number">3.</span> <span style="color:blue">while</span> (current != <span style="color:blue">nullptr</span>) {
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<span class="line-number">4.</span> <span style="color:blue">if</span> (current->left != <span style="color:blue">nullptr</span>) {
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<span class="line-number">5.</span> rightmost = current->left;
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<span class="line-number">6.</span> <span style="color:blue">while</span> (rightmost->right != <span style="color:blue">nullptr</span> && rightmost->right != current) {
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<span class="line-number">7.</span> rightmost = rightmost->right;
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<span class="line-number">8.</span> }
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<span class="line-number">9.</span> <span style="color:blue">if</span> (rightmost->right == <span style="color:blue">nullptr</span>) {
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<span class="line-number">10.</span> rightmost->right = current;
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<span class="line-number">11.</span> current = current->left;
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<span class="line-number">12.</span> } <span style="color:blue">else</span> {
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<span class="line-number">13.</span> rightmost->right = <span style="color:blue">nullptr</span>;
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<span class="line-number">14.</span> reverseTraverseRightEdge(current->left);
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<span class="line-number">15.</span> current = current->right;
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<span class="line-number">16.</span> }
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<span class="line-number">17.</span> } <span style="color:blue">else</span> {
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<span class="line-number">18.</span> current = current->right;
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<span class="line-number">19.</span> }
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<span class="line-number">20.</span> }
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<span class="line-number">21.</span> reverseTraverseRightEdge(root); <span style="color:green">// final right edge</span>
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<span class="line-number">22.</span> <span style="color:blue">return</span>;
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<span class="line-number">23.</span> }
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<span class="line-number">24.</span>
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<span class="line-number">25.</span> <span style="color:blue">TreeNode</span>* reverse(<span style="color:blue">TreeNode</span>* head) {
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<span class="line-number">26.</span> <span style="color:blue">TreeNode</span>* prev = <span style="color:blue">nullptr</span>;
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<span class="line-number">27.</span> <span style="color:blue">TreeNode</span>* next = <span style="color:blue">nullptr</span>;
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<span class="line-number">28.</span> <span style="color:blue">while</span> (head != <span style="color:blue">nullptr</span>) {
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<span class="line-number">29.</span> next = head->right;
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<span class="line-number">30.</span> head->right = prev;
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<span class="line-number">31.</span> prev = head;
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<span class="line-number">32.</span> head = next;
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<span class="line-number">33.</span> }
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<span class="line-number">34.</span> <span style="color:blue">return</span> prev;
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<span class="line-number">35.</span> }
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<span class="line-number">36.</span>
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<span class="line-number">37.</span> <span style="color:blue">void</span> reverseTraverseRightEdge(<span style="color:blue">TreeNode</span>* head) {
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<span class="line-number">38.</span> <span style="color:blue">TreeNode</span>* tail = reverse(head);
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<span class="line-number">39.</span> <span style="color:blue">TreeNode</span>* current = tail;
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<span class="line-number">40.</span> <span style="color:blue">while</span> (current != <span style="color:blue">nullptr</span>) {
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<span class="line-number">41.</span> std::cout << current->val << " ";
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<span class="line-number">42.</span> current = current->right;
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<span class="line-number">43.</span> }
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<span class="line-number">44.</span> reverse(tail); <span style="color:green">// restore structure</span>
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<span class="line-number">45.</span> }</code></pre>
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</div>
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<div class="tree-container">
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<div class="color-key">
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<div class="color-item">
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<div class="color-box" style="background-color: #ffeb3b;"></div>
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<span>Current Node</span>
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</div>
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<div class="color-item">
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<div class="color-box" style="background-color: #2196f3;"></div>
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<span>Rightmost Node</span>
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</div>
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<div class="color-item">
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<div class="color-box" style="background-color: #4caf50;"></div>
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<span>Visited Node</span>
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</div>
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<div class="color-item">
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<div class="color-box" style="background-color: #03a9f4;"></div>
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<span>Thread Created</span>
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</div>
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<div class="color-item">
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<div class="color-arrow" style="background-color: #888;"></div>
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<span>Tree Edge</span>
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</div>
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<div class="color-item">
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<div class="dotted-line"></div>
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<span>Thread Edge</span>
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</div>
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<div class="color-item">
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<div class="color-arrow" style="background-color: #e91e63;"></div>
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<span>Reversed Edge</span>
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</div>
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</div>
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<button id="nextStep">Next Step</button>
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<div id="container"></div>
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<div class="explanation" id="treeExplanation">
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Post-order traversal output: <span id="output"></span>
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</div>
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</div>
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</div>
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<script>
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// Wait for the "Next Step" button click.
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function waitForNext() {
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return new Promise(resolve => {
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const btn = document.getElementById('nextStep');
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btn.disabled = false;
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btn.onclick = () => {
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btn.disabled = true;
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resolve();
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};
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});
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}
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// Append text to the output.
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function appendOutput(text) {
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const out = document.getElementById('output');
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out.innerText += text;
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}
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// Update the explanation text.
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function updateExplanation(text) {
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document.getElementById('treeExplanation').innerHTML =
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'Post-order traversal output: <span id="output">' +
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document.getElementById('output').innerText + '</span><br>' + text;
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}
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// Tree node class using Konva for visualization.
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class TreeNode {
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constructor(val, x, y) {
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this.val = val;
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this.left = null;
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this.right = null;
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this.x = x;
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this.y = y;
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this.shape = new Konva.Rect({
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x: x - 20,
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y: y - 20,
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width: 40,
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height: 40,
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fill: 'white',
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stroke: '#888',
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strokeWidth: 2,
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cornerRadius: 4
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});
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this.label = new Konva.Text({
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x: x - 7,
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y: y - 10,
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text: String(val),
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fontSize: 20,
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fontFamily: 'Arial',
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fill: 'black'
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});
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this.leftEdge = null;
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this.rightEdge = null;
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this.threadEdge = null;
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this.reversedEdges = [];
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}
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}
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// Initialize Konva stage and layer.
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const stage = new Konva.Stage({
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container: 'container',
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width: document.querySelector('.tree-container').clientWidth - 30,
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height: document.querySelector('.tree-container').clientHeight - 140
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});
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const layer = new Konva.Layer();
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stage.add(layer);
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// Calculate connection points for arrow drawing.
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function calculateConnectionPoints(fromNode, toNode) {
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const nodeRadius = 20;
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const dx = toNode.x - fromNode.x;
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const dy = toNode.y - fromNode.y;
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const angle = Math.atan2(dy, dx);
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return {
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fromX: fromNode.x + nodeRadius * Math.cos(angle),
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fromY: fromNode.y + nodeRadius * Math.sin(angle),
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toX: toNode.x - nodeRadius * Math.cos(angle),
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toY: toNode.y - nodeRadius * Math.sin(angle)
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};
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}
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// Create an arrow between two nodes.
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function createArrow(fromNode, toNode, color = '#888', dashed = false) {
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const points = calculateConnectionPoints(fromNode, toNode);
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const arrow = new Konva.Arrow({
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points: [points.fromX, points.fromY, points.toX, points.toY],
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pointerLength: 10,
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pointerWidth: 8,
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fill: color,
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stroke: color,
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strokeWidth: dashed ? 1 : 2,
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dashEnabled: dashed,
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dash: dashed ? [5, 5] : null
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});
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layer.add(arrow);
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return arrow;
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}
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// Draw an edge between two nodes.
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function drawEdge(parent, child, isLeft = true) {
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const arrow = createArrow(parent, child);
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layer.add(arrow);
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if (isLeft) { parent.leftEdge = arrow; }
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else { parent.rightEdge = arrow; }
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arrow.moveToBottom();
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return arrow;
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}
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// Create and remove thread edges.
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function createThreadEdge(fromNode, toNode) {
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if (fromNode.threadEdge) { fromNode.threadEdge.destroy(); }
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const threadArrow = createArrow(fromNode, toNode, '#ff5722', true);
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fromNode.threadEdge = threadArrow;
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threadArrow.moveToTop();
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layer.draw();
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return threadArrow;
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}
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function removeThreadEdge(node) {
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if (node && node.threadEdge) {
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node.threadEdge.destroy();
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node.threadEdge = null;
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layer.draw();
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}
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}
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// Highlight and unhighlight a node.
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function highlightNode(node, color = '#8bc34a') {
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if (node && node.shape) { node.shape.to({ fill: color, duration: 0.25 }); }
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}
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function unhighlightNode(node, color = 'white') {
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if (node && node.shape) { node.shape.to({ fill: color, duration: 0.25 }); }
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}
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// Calculate tree layout.
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const stageWidth = stage.width();
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const stageHeight = stage.height();
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const centerX = stageWidth / 2;
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const topY = 40;
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const levelHeight = stageHeight / 4;
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// Build the 9-node binary tree.
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const node1 = new TreeNode(1, centerX, topY);
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const node2 = new TreeNode(2, centerX - stageWidth/4, topY + levelHeight);
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const node3 = new TreeNode(3, centerX + stageWidth/4, topY + levelHeight);
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const node4 = new TreeNode(4, centerX - stageWidth/3, topY + 2*levelHeight);
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const node5 = new TreeNode(5, centerX - stageWidth/6, topY + 2*levelHeight);
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const node6 = new TreeNode(6, centerX - stageWidth/4, topY + 3*levelHeight);
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const node7 = new TreeNode(7, centerX - stageWidth/12, topY + 3*levelHeight);
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const node8 = new TreeNode(8, centerX + stageWidth/3, topY + 2*levelHeight);
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const node9 = new TreeNode(9, centerX + stageWidth/4, topY + 3*levelHeight);
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node1.left = node2;
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node1.right = node3;
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node2.left = node4;
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node2.right = node5;
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node5.left = node6;
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node5.right = node7;
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node3.right = node8;
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node8.left = node9;
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const nodes = [node1, node2, node3, node4, node5, node6, node7, node8, node9];
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nodes.forEach(n => {
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layer.add(n.shape);
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layer.add(n.label);
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});
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drawEdge(node1, node2, true);
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drawEdge(node1, node3, false);
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drawEdge(node2, node4, true);
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drawEdge(node2, node5, false);
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drawEdge(node5, node6, true);
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drawEdge(node5, node7, false);
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drawEdge(node3, node8, false);
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drawEdge(node8, node9, true);
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nodes.forEach(n => {
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n.shape.moveToTop();
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n.label.moveToTop();
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});
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layer.draw();
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// Visualize the reversal process.
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async function visualizeReversal(head) {
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const connections = [];
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let current = head;
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while (current !== null && current.right !== null) {
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connections.push({ from: current, to: current.right });
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current = current.right;
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}
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for (const conn of connections) {
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if (conn.from.rightEdge) {
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conn.from.rightEdge.destroy();
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conn.from.rightEdge = null;
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}
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}
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let prev = null;
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current = head;
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while (current !== null) {
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const next = current.right;
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if (prev !== null) {
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const reversedEdge = createArrow(current, prev, '#e91e63');
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current.reversedEdges.push(reversedEdge);
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reversedEdge.moveToTop();
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}
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prev = current;
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current = next;
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layer.draw();
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await waitForNext();
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}
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return prev;
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}
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// Restore the original tree structure.
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async function visualizeRestore(head) {
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nodes.forEach(node => {
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if (node.reversedEdges) {
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node.reversedEdges.forEach(edge => edge.destroy());
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node.reversedEdges = [];
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}
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});
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let current = head;
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while (current !== null && current.right !== null) {
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if (!current.rightEdge) {
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current.rightEdge = createArrow(current, current.right, '#888');
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current.rightEdge.moveToBottom();
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}
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current = current.right;
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}
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nodes.forEach(n => {
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n.shape.moveToTop();
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n.label.moveToTop();
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});
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layer.draw();
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}
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// Reverse a chain of right pointers.
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async function reverseChain(head) {
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updateExplanation("Visualizing the reversal of pointers");
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await waitForNext();
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const reversedHead = await visualizeReversal(head);
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let prev = null, curr = head, next;
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while (curr !== null) {
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next = curr.right;
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curr.right = prev;
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prev = curr;
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curr = next;
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}
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return prev;
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}
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// Restore the chain.
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async function restoreChain(head) {
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updateExplanation("Visualizing the restoration of original pointers");
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await waitForNext();
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await visualizeRestore(head);
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let prev = null, curr = head, next;
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while (curr !== null) {
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next = curr.right;
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curr.right = prev;
|
||
prev = curr;
|
||
curr = next;
|
||
}
|
||
return prev;
|
||
}
|
||
|
||
// Reverse traverse the right edge of a subtree.
|
||
async function reverseTraverseRightEdge(head) {
|
||
if (!head) return;
|
||
updateExplanation("Reversing the right edge starting from node " + head.val);
|
||
await waitForNext();
|
||
let tail = await reverseChain(head);
|
||
layer.draw();
|
||
updateExplanation("Visiting nodes along the reversed right edge");
|
||
let cur = tail;
|
||
while (cur !== null) {
|
||
highlightNode(cur, '#4caf50');
|
||
layer.draw();
|
||
appendOutput(cur.val + " ");
|
||
updateExplanation("Visited node: " + cur.val);
|
||
await waitForNext();
|
||
unhighlightNode(cur, 'white');
|
||
layer.draw();
|
||
cur = cur.right;
|
||
}
|
||
updateExplanation("Restoring the original right edge");
|
||
await waitForNext();
|
||
await restoreChain(tail);
|
||
layer.draw();
|
||
}
|
||
|
||
// Morris Post‑Order Traversal Animation.
|
||
async function postorderTraversal(root) {
|
||
let current = root;
|
||
while (current !== null) {
|
||
highlightNode(current, '#ffeb3b');
|
||
layer.draw();
|
||
if (current.left !== null) {
|
||
updateExplanation("Current: " + current.val + " - Has left child, finding rightmost in left subtree");
|
||
await waitForNext();
|
||
let rightmost = current.left;
|
||
highlightNode(rightmost, '#2196f3');
|
||
layer.draw();
|
||
while (rightmost.right !== null && rightmost.right !== current) {
|
||
updateExplanation("Moving to right: " + rightmost.val);
|
||
await waitForNext();
|
||
unhighlightNode(rightmost, 'white');
|
||
rightmost = rightmost.right;
|
||
highlightNode(rightmost, '#2196f3');
|
||
layer.draw();
|
||
}
|
||
if (rightmost.right === null) {
|
||
updateExplanation("Rightmost: " + rightmost.val + " - Creating thread to current: " + current.val);
|
||
await waitForNext();
|
||
createThreadEdge(rightmost, current);
|
||
rightmost.right = current;
|
||
highlightNode(rightmost, '#03a9f4');
|
||
layer.draw();
|
||
await waitForNext();
|
||
unhighlightNode(rightmost, 'white');
|
||
unhighlightNode(current, 'white');
|
||
current = current.left;
|
||
} else {
|
||
updateExplanation("Thread detected at rightmost: " + rightmost.val + " - Removing thread and processing subtree");
|
||
await waitForNext();
|
||
removeThreadEdge(rightmost);
|
||
rightmost.right = null;
|
||
unhighlightNode(rightmost, 'white');
|
||
layer.draw();
|
||
await reverseTraverseRightEdge(current.left);
|
||
unhighlightNode(current, 'white');
|
||
current = current.right;
|
||
}
|
||
} else {
|
||
updateExplanation("Current: " + current.val + " - No left child, moving right");
|
||
await waitForNext();
|
||
unhighlightNode(current, 'white');
|
||
current = current.right;
|
||
}
|
||
}
|
||
updateExplanation("Processing final right edge");
|
||
await waitForNext();
|
||
await reverseTraverseRightEdge(root);
|
||
updateExplanation("Morris Post-Order Traversal complete");
|
||
await waitForNext();
|
||
updateExplanation("Final post-order traversal result: " + document.getElementById('output').innerText);
|
||
nodes.forEach(n => {
|
||
n.shape.moveToTop();
|
||
n.label.moveToTop();
|
||
});
|
||
layer.draw();
|
||
}
|
||
|
||
window.addEventListener('resize', function() {
|
||
stage.width(document.querySelector('.tree-container').clientWidth - 30);
|
||
stage.height(document.querySelector('.tree-container').clientHeight - 140);
|
||
layer.draw();
|
||
});
|
||
|
||
window.onload = function() {
|
||
document.getElementById('nextStep').disabled = false;
|
||
postorderTraversal(node1);
|
||
};
|
||
</script>
|
||
</body>
|
||
</html>
|