274 lines
11 KiB
HTML
274 lines
11 KiB
HTML
<!DOCTYPE html>
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<html lang="zh-Hans">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>074. 数组中的第K个最大元素 – 图解</title>
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<link rel="stylesheet" href="../shared/style.css">
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<style>
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.vis-area { min-height: 120px; padding: 16px 0; }
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.code-section { margin-top: 16px; }
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.heap-row { display:flex; justify-content:center; gap:6px; margin:6px 0; flex-wrap:wrap; }
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.heap-cell {
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min-width:36px; height:32px; display:inline-flex; align-items:center; justify-content:center;
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border-radius:8px; font-weight:700; font-size:14px; font-family:monospace;
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transition: all 0.25s ease; padding:2px 8px;
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}
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.heap-cell.default { background:#e2e8f0; color:#0f172a; }
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.heap-cell.top { background:#fef3c7; color:#92400e; border:2px solid #f59e0b; box-shadow:0 0 0 3px rgba(245,158,11,0.2); }
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.heap-cell.new { background:#dcfce7; color:#166534; border:2px solid #16a34a; }
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.heap-cell.ejected { background:#fee2e2; color:#991b1b; border:2px dashed #ef4444; opacity:0.5; }
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.heap-cell.in-heap { background:#dbeafe; color:#1e40af; border:1px solid #3b82f6; }
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.arrow-down { text-align:center; color:#94a3b8; font-size:18px; margin:2px 0; }
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</style>
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</head>
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<body>
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<div class="container">
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<h1>🟡 074. 数组中的第K个最大元素 <span class="badge medium">中等</span></h1>
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<p class="subtitle">分类：堆 ｜ LeetCode Hot 100</p>
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<div class="controls" id="controls">
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<label for="inputArea">输入：</label>
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<input type="text" id="inputArea" value="nums=[3,2,1,5,6,4], k=2" placeholder="nums=[...], k=N">
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<button id="applyBtn" class="primary">生成图解</button>
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<select id="exampleSelect"></select>
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<span style="flex:1"></span>
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<button id="prevBtn">◀ 上一步</button>
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<button id="nextBtn">下一步 ▶</button>
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<button id="jumpBtn">⏭ 跳到结果</button>
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<button id="autoBtn">自动播放</button>
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<button id="resetBtn">重置</button>
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</div>
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<div class="pipeline" id="pipeline"></div>
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<div class="hint info" id="hintBox">
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<span id="stepInfo"></span><br>
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<span id="hintText"></span>
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</div>
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<div class="panels">
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<div class="panel" id="mainPanel">
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<h3>📊 可视化</h3>
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<div class="vis-area" id="vizArea">点击「生成图解」开始</div>
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</div>
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<div class="panel-grid">
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<div class="panel" id="detailPanel">
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<h3>📝 当前步骤详情</h3>
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<div id="detailContent">等待开始...</div>
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</div>
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<div class="panel" id="resultPanel">
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<h3>✅ 结果</h3>
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<div id="resultContent">等待完成...</div>
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</div>
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</div>
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</div>
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<div class="panel code-section">
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<h3>💻 参考代码（Python）</h3>
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<div id="codeArea"></div>
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</div>
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<footer>Powered by QwenPaw · 图解算法 · LeetCode Hot 100</footer>
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</div>
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<script src="../shared/algo-viz.js"></script>
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<script>
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"use strict";
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(function() {
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const examples = [
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{nums:[3,2,1,5,6,4], k:2, label:'示例1: [3,2,1,5,6,4], k=2'},
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{nums:[3,2,3,1,2,4,5,5,6], k:4, label:'示例2: [3,2,3,1,2,4,5,5,6], k=4'},
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];
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let nums, k, steps, stepCtrl;
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// Min-heap utilities
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function heapPush(heap, val) {
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heap.push(val);
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let i = heap.length - 1;
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while (i > 0) {
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const parent = (i - 1) >> 1;
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if (heap[parent] > heap[i]) {
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[heap[parent], heap[i]] = [heap[i], heap[parent]];
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i = parent;
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} else break;
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}
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}
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function heapPop(heap) {
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const top = heap[0];
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const last = heap.pop();
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if (heap.length > 0) {
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heap[0] = last;
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let i = 0;
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while (true) {
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let smallest = i;
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const l = 2*i+1, r = 2*i+2;
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if (l < heap.length && heap[l] < heap[smallest]) smallest = l;
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if (r < heap.length && heap[r] < heap[smallest]) smallest = r;
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if (smallest !== i) { [heap[i], heap[smallest]] = [heap[smallest], heap[i]]; i = smallest; }
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else break;
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}
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}
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return top;
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}
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function buildSteps(arr, kVal) {
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nums = arr.slice(); k = kVal;
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steps = [];
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// Stage 1: Show initial array
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steps.push({stage:'init', msg:`输入数组长度=${arr.length}，找第 ${k} 大元素。用小顶堆维护前 K 大：堆顶 = 当前第 K 大`, arrHL:{}, heap:[], idx:-1, popped:null});
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// Stage 2: Build initial heap with first k elements
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const heap = [];
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for (let i = 0; i < kVal; i++) {
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heapPush(heap, arr[i]);
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const arrHL = {};
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for (let j = 0; j <= i; j++) arrHL[j] = 'blue';
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steps.push({stage:'build', msg:`将 nums[${i}]=${arr[i]} 加入小顶堆，堆大小=${heap.length}`, arrHL, heap:heap.slice(), idx:i, popped:null});
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}
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steps.push({stage:'heap-ready', msg:`初始小顶堆构建完成，堆顶=${heap[0]} 即当前第 ${k} 大`, arrHL:{}, heap:heap.slice(), idx:-1, popped:null});
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// Stage 3: Process remaining elements
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for (let i = kVal; i < arr.length; i++) {
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const arrHL = {};
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// Mark heap elements blue, current element orange
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for (let j = 0; j < kVal; j++) arrHL[j] = 'blue';
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arrHL[i] = 'orange';
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steps.push({stage:'compare', msg:`检查 nums[${i}]=${arr[i]}，与堆顶 ${heap[0]} 比较`, arrHL, heap:heap.slice(), idx:i, popped:null});
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if (arr[i] > heap[0]) {
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const popped = heapPop(heap);
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heapPush(heap, arr[i]);
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const arrHL2 = {};
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for (let j = 0; j < kVal; j++) arrHL2[j] = 'blue';
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arrHL2[i] = 'green';
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steps.push({stage:'replace', msg:`${arr[i]} > ${popped}，弹出堆顶 ${popped}，压入 ${arr[i]}，新堆顶=${heap[0]}`, arrHL:arrHL2, heap:heap.slice(), idx:i, popped});
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} else {
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const arrHL2 = {};
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for (let j = 0; j < kVal; j++) arrHL2[j] = 'blue';
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arrHL2[i] = 'red';
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steps.push({stage:'skip', msg:`${arr[i]} ≤ ${heap[0]}，跳过，堆不变`, arrHL:arrHL2, heap:heap.slice(), idx:i, popped:null});
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}
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}
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// Stage 4: Result
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steps.push({stage:'done', msg:`遍历结束，小顶堆堆顶 ${heap[0]} 即为第 ${k} 大元素`, arrHL:{}, heap:heap.slice(), idx:-1, popped:null, result:heap[0]});
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}
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function renderHeap(heap, topHighlight) {
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if (heap.length === 0) return '<div style="color:#94a3b8;font-style:italic;">空堆</div>';
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let html = '<div style="text-align:center;padding:8px 0;">';
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// Level order display
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let level = 0, idx = 0;
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while (idx < heap.length) {
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const count = Math.pow(2, level);
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html += '<div class="heap-row">';
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for (let j = 0; j < count && idx < heap.length; j++, idx++) {
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let cls = 'in-heap';
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if (idx === 0 && topHighlight) cls = 'top';
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html += `<span class="heap-cell ${cls}">${heap[idx]}</span>`;
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}
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html += '</div>';
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if (idx < heap.length) html += '<div class="arrow-down">↓</div>';
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level++;
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}
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html += '</div>';
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return html;
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}
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function render(step) {
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const s = steps[step];
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// Main visualization
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let viz = '<div style="margin-bottom:12px;"><b>原始数组：</b></div>';
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viz += renderArray(nums, {highlights: s.arrHL});
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if (s.popped !== null) {
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viz += `<div style="margin-top:8px;color:#991b1b;">弹出: <span class="heap-cell ejected" style="display:inline-flex;min-width:30px;">${s.popped}</span></div>`;
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}
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viz += '<div style="margin:12px 0;"><b>小顶堆 (size=' + s.heap.length + ')：</b></div>';
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viz += renderHeap(s.heap, s.stage === 'heap-ready' || s.stage === 'done');
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if (s.heap.length > 0) {
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viz += `<div style="margin-top:6px;font-size:13px;color:#64748b;">堆顶(最小值) = <code>${s.heap[0]}</code></div>`;
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}
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$('vizArea').innerHTML = viz;
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// Detail
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let detail = '<div class="calc-block">' + s.msg + '</div>';
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if (s.stage === 'compare') {
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detail += `<div style="margin-top:8px;">比较: nums[${s.idx}]=<b>${nums[s.idx]}</b> vs 堆顶=<b>${s.heap[0]}</b></div>`;
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}
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$('detailContent').innerHTML = detail;
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// Result
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if (s.stage === 'done') {
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$('resultContent').innerHTML = `<div class="final-answer">第 <b>${k}</b> 大元素 = <b>${s.result}</b><br><br>小顶堆始终保持 K 个最大元素，堆顶即第 K 大。<br>时间 O(nlogk)，空间 O(k)</div>`;
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}
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$('hintText').textContent = s.msg;
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// Pipeline
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const stages = ['init→初始化','build→建堆','heap-ready→堆就绪','compare→比较','replace→替换','skip→跳过','done→完成'];
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$('pipeline').innerHTML = stages.map(st => {
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const [key, label] = st.split('→');
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return `<span class="pipe-step ${s.stage===key?'active':''}">${label}</span>`;
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}).join('<i>→</i>');
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}
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function init() {
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const sel = $('exampleSelect');
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examples.forEach((e,i) => { sel.innerHTML += `<option value="${i}">${e.label}</option>`; });
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buildSteps(examples[0].nums, examples[0].k);
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stepCtrl = new StepController({onStep: render});
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stepCtrl.setSteps(steps.map((_,i) => i));
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$('stepInfo').textContent = `步骤 1 / ${steps.length}`;
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stepCtrl.onStep = (idx) => { render(idx); $('stepInfo').textContent = `步骤 ${idx+1} / ${steps.length}`; };
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$('applyBtn').onclick = () => {
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const m = $('inputArea').value.match(/nums=\[([^\]]+)\]\s*,\s*k=(\d+)/);
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if (!m) { alert('格式: nums=[3,2,1,5,6,4], k=2'); return; }
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const arr = m[1].split(',').map(Number);
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const kVal = parseInt(m[2]);
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buildSteps(arr, kVal);
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stepCtrl.setSteps(steps.map((_,i) => i));
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render(0);
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$('stepInfo').textContent = `步骤 1 / ${steps.length}`;
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};
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$('exampleSelect').onchange = () => {
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const e = examples[parseInt($('exampleSelect').value)];
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$('inputArea').value = `nums=[${e.nums}], k=${e.k}`;
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buildSteps(e.nums, e.k);
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stepCtrl.setSteps(steps.map((_,i) => i));
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render(0);
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$('stepInfo').textContent = `步骤 1 / ${steps.length}`;
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};
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$('prevBtn').onclick = () => stepCtrl.prev();
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$('nextBtn').onclick = () => stepCtrl.next();
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$('jumpBtn').onclick = () => stepCtrl.jumpToEnd();
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$('autoBtn').onclick = () => { const on = stepCtrl.toggleAuto(); $('autoBtn').textContent = on ? '暂停' : '自动播放'; };
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$('resetBtn').onclick = () => { stepCtrl.reset(); $('autoBtn').textContent = '自动播放'; };
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}
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init();
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$('codeArea').innerHTML = renderCode(`import heapq
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def findKthLargest(nums, k):
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# 用小顶堆维护前 K 大元素
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heap = []
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for num in nums:
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if len(heap) < k:
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heapq.heappush(heap, num) # 堆未满，直接加入
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elif num > heap[0]:
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heapq.heapreplace(heap, num) # 比堆顶大，替换堆顶
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return heap[0] # 堆顶即第 K 大
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# 复杂度：O(n log k) 时间，O(k) 空间`, {lang:'Python'});
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})();
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</script>
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</body>
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</html>
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