neet-code-top-150-python-visual/visual/0053_maximum_subarray.html at main · kimtth/neet-code-top-150-python-visual · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>LC 53: Maximum Subarray - Algorithm Visualization</title>
    <link rel="stylesheet" href="styles.css">
    <script src="https://d3js.org/d3.v7.min.js"></script>
</head>
<body>
    <div class="container">
        <div class="problem-info">
            <h1><span class="problem-number">#53</span> Maximum Subarray</h1>
            <p>Given an integer array, find the contiguous subarray with the largest sum and return its sum.</p>
            <div class="problem-meta">
                <span class="meta-tag">🤑 Greedy</span>
                <span class="meta-tag">📈 Kadane's Algorithm</span>
                <span class="meta-tag">⏱️ O(n)</span>
                <span class="meta-tag">💾 O(1)</span>
            </div>
            <div class="file-ref">
                📄 Python: <code>python/0053_maximum_subarray/0053_maximum_subarray.py</code>
            </div>
            </div>

        <div class="explanation-panel">
            <h4>🧠 How It Works (Layman's Terms)</h4>
            <p>At each position, ask yourself: <strong>"Should I keep adding to my current streak, or start fresh?"</strong></p>
            <ul>
                <li><strong>curr_sum:</strong> Best sum ending at current position</li>
                <li><strong>max_sum:</strong> Best sum seen so far (the answer)</li>
                <li><strong>Key insight:</strong> If current sum is negative, it's better to start fresh!</li>
                <li><strong>Decision:</strong> max(start fresh, keep going) = max(num, curr_sum + num)</li>
            </ul>
        </div>


        <div class="visualization-section">
            <h3>🎬 Step-by-Step Visualization</h3>

            <div class="controls">
                <button class="btn btn-primary" id="stepBtn" onclick="step()">Step</button>
                <button class="btn btn-success" id="autoBtn" onclick="toggleAuto()">Auto Run</button>
                <button class="btn btn-warning" onclick="reset()">Reset</button>
            </div>

            <div class="info-box secondary" style="margin-bottom: 20px;">
                📊 Array: <strong>[-2, 1, -3, 4, -1, 2, 1, -5, 4]</strong>
            </div>

            <div class="status-message" id="statusMessage">
                Click "Step" or "Auto Run" to start visualization
            </div>

            <div class="array-section">
                <div class="array-label">📊 Array:</div>
                <div class="array-container" id="arrayContainer"></div>
            </div>

            <div class="variable-section" style="margin: 20px 0; display: flex; gap: 30px; justify-content: center; flex-wrap: wrap;">
                <div class="variable" style="background: #e3f2fd;">
                    <span class="var-name">curr_sum</span>
                    <span class="var-value" id="currSumValue">-2</span>
                    <span class="var-desc">best ending here</span>
                </div>
                <div class="variable" style="background: #e8f5e9;">
                    <span class="var-name">max_sum</span>
                    <span class="var-value" id="maxSumValue">-2</span>
                    <span class="var-desc">overall best</span>
                </div>
            </div>

            <div class="explanation-panel" style="margin-top: 20px;">
                <h4>📝 Current Decision</h4>
                <div id="decisionDisplay" style="font-size: 1.1em; padding: 10px;">
                    Waiting to start...
                </div>
            </div>

            <div id="chartContainer" style="width: 100%; height: 200px; margin-top: 20px;"></div>
        </div>

        <div class="code-section">
            <h3>💻 Python Solution (Kadane's Algorithm)</h3>
            <div class="code-block">
                <pre><span class="keyword">def</span> <span class="function">max_sub_array</span>(self, nums: <span class="class-name">List</span>[<span class="class-name">int</span>]) -> <span class="class-name">int</span>:
    curr_sum = max_sum = nums[<span class="number">0</span>]

    <span class="keyword">for</span> num <span class="keyword">in</span> nums[<span class="number">1</span>:]:
        <span class="comment"># Either start fresh or extend</span>
        curr_sum = <span class="function">max</span>(num, curr_sum + num)
        max_sum = <span class="function">max</span>(max_sum, curr_sum)

    <span class="keyword">return</span> max_sum</pre>
            </div>
        </div>
    </div>

    <script>
        const nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4];
        let currSum = nums[0];
        let maxSum = nums[0];
        let currentIdx = 0;
        let subarrayStart = 0;
        let bestStart = 0;
        let bestEnd = 0;
        let autoInterval = null;
        let history = [{idx: 0, currSum: nums[0], maxSum: nums[0]}];

        function init() {
            renderArray();
            renderChart();
            updateVariables();
        }

        function renderArray() {
            const container = document.getElementById('arrayContainer');
            container.innerHTML = '';

            nums.forEach((val, i) => {
                const box = document.createElement('div');
                box.className = 'array-box';
                box.id = `num-${i}`;
                box.innerHTML = `${val}<span class="index-label">${i}</span>`;

                // Color the current subarray
                if (i >= subarrayStart && i <= currentIdx) {
                    box.style.background = '#bbdefb';
                    box.style.borderColor = '#2196f3';
                }

                // Highlight best subarray found so far
                if (i >= bestStart && i <= bestEnd) {
                    box.style.background = '#c8e6c9';
                    box.style.borderColor = '#4caf50';
                }

                // Current position
                if (i === currentIdx) {
                    box.classList.add('highlight');
                }

                container.appendChild(box);
            });
        }

        function renderChart() {
            d3.select('#chartContainer').selectAll('*').remove();

            const margin = {top: 20, right: 30, bottom: 40, left: 50};
            const width = document.getElementById('chartContainer').offsetWidth - margin.left - margin.right;
            const height = 160 - margin.top - margin.bottom;

            const svg = d3.select('#chartContainer')
                .append('svg')
                .attr('width', width + margin.left + margin.right)
                .attr('height', height + margin.top + margin.bottom)
                .append('g')
                .attr('transform', `translate(${margin.left},${margin.top})`);

            const xScale = d3.scaleLinear()
                .domain([0, nums.length - 1])
                .range([0, width]);

            const minVal = Math.min(...history.map(h => Math.min(h.currSum, h.maxSum)), -5);
            const maxVal = Math.max(...history.map(h => Math.max(h.currSum, h.maxSum)), 10);

            const yScale = d3.scaleLinear()
                .domain([minVal - 1, maxVal + 1])
                .range([height, 0]);

            // Zero line
            svg.append('line')
                .attr('x1', 0)
                .attr('x2', width)
                .attr('y1', yScale(0))
                .attr('y2', yScale(0))
                .attr('stroke', '#999')
                .attr('stroke-dasharray', '3,3');

            // curr_sum line
            const currLine = d3.line()
                .x(d => xScale(d.idx))
                .y(d => yScale(d.currSum));

            svg.append('path')
                .datum(history)
                .attr('fill', 'none')
                .attr('stroke', '#2196f3')
                .attr('stroke-width', 2)
                .attr('d', currLine);

            // max_sum line
            const maxLine = d3.line()
                .x(d => xScale(d.idx))
                .y(d => yScale(d.maxSum));

            svg.append('path')
                .datum(history)
                .attr('fill', 'none')
                .attr('stroke', '#4caf50')
                .attr('stroke-width', 3)
                .attr('d', maxLine);

            // Axes
            svg.append('g')
                .attr('transform', `translate(0,${height})`)
                .call(d3.axisBottom(xScale).ticks(nums.length));

            svg.append('g')
                .call(d3.axisLeft(yScale));

            // Legend
            svg.append('line').attr('x1', width - 100).attr('y1', 5).attr('x2', width - 80).attr('y2', 5).attr('stroke', '#2196f3').attr('stroke-width', 2);
            svg.append('text').attr('x', width - 75).attr('y', 8).text('curr_sum').style('font-size', '11px');
            svg.append('line').attr('x1', width - 100).attr('y1', 20).attr('x2', width - 80).attr('y2', 20).attr('stroke', '#4caf50').attr('stroke-width', 3);
            svg.append('text').attr('x', width - 75).attr('y', 23).text('max_sum').style('font-size', '11px');
        }

        function updateVariables() {
            document.getElementById('currSumValue').textContent = currSum;
            document.getElementById('maxSumValue').textContent = maxSum;
        }

        function step() {
            currentIdx++;

            if (currentIdx >= nums.length) {
                document.getElementById('statusMessage').className = 'status-message success';
                document.getElementById('statusMessage').textContent =
                    `✅ Done! Maximum subarray sum: ${maxSum} (indices ${bestStart} to ${bestEnd})`;
                document.getElementById('stepBtn').disabled = true;
                stopAuto();
                return;
            }

            const num = nums[currentIdx];
            const extendSum = currSum + num;
            const startFresh = num;

            let decision;
            if (startFresh > extendSum) {
                currSum = startFresh;
                subarrayStart = currentIdx;
                decision = 'START FRESH';
            } else {
                currSum = extendSum;
                decision = 'EXTEND';
            }

            if (currSum > maxSum) {
                maxSum = currSum;
                bestStart = subarrayStart;
                bestEnd = currentIdx;
            }

            document.getElementById('statusMessage').textContent =
                `Index ${currentIdx}: num = ${num}, extend (${extendSum}) vs start fresh (${startFresh}) → ${decision}`;

            document.getElementById('decisionDisplay').innerHTML =
                `<strong>At index ${currentIdx} (value: ${num}):</strong><br>` +
                `Option 1 (Extend): ${currSum - num < 0 ? '' : '+'}${currSum - num} + ${num} = ${extendSum}<br>` +
                `Option 2 (Start Fresh): ${num}<br>` +
                `<strong>Decision: ${decision}</strong> → curr_sum = ${currSum}<br>` +
                (currSum === maxSum && currentIdx === bestEnd ?
                    `<span style="color: #4caf50;">✨ New max_sum = ${maxSum}!</span>` :
                    `max_sum stays at ${maxSum}`);

            history.push({idx: currentIdx, currSum, maxSum});

            updateVariables();
            renderArray();
            renderChart();
        }

        function toggleAuto() {
            if (autoInterval) {
                stopAuto();
            } else {
                document.getElementById('autoBtn').textContent = 'Pause';
                autoInterval = setInterval(() => {
                    if (currentIdx >= nums.length - 1) {
                        step();
                        stopAuto();
                    } else {
                        step();
                    }
                }, 1200);
            }
        }

        function stopAuto() {
            if (autoInterval) {
                clearInterval(autoInterval);
                autoInterval = null;
            }
            document.getElementById('autoBtn').textContent = 'Auto Run';
        }

        function reset() {
            stopAuto();
            currSum = nums[0];
            maxSum = nums[0];
            currentIdx = 0;
            subarrayStart = 0;
            bestStart = 0;
            bestEnd = 0;
            history = [{idx: 0, currSum: nums[0], maxSum: nums[0]}];
            document.getElementById('stepBtn').disabled = false;
            document.getElementById('statusMessage').className = 'status-message';
            document.getElementById('statusMessage').textContent = 'Click "Step" or "Auto Run" to start visualization';
            document.getElementById('decisionDisplay').textContent = 'Waiting to start...';
            init();
        }

        init();
    </script>
</body>
</html>