algorithm-neet-code-top-150-python-visual/visual/0074_search_2d_matrix.html at main · kimtth/algorithm-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>Search a 2D Matrix - LeetCode 74</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">#74</span> Search a 2D Matrix</h1>
            <p>Search for a target in a sorted 2D matrix. Treat the matrix as a flattened 1D array and use binary search!</p>
            <div class="problem-meta">
                <span class="meta-tag">🔍 Binary Search</span>
                <span class="meta-tag">📊 Matrix</span>
                <span class="meta-tag">⏱️ O(log(m×n))</span>
            </div>
            <div class="file-ref">
                📄 Python: <a href="../python/0074_search_a_2d_matrix/0074_search_a_2d_matrix.py">0074_search_a_2d_matrix.py</a>
            </div>
            </div>

        <div class="explanation-panel">
            <h4>💡 How It Works (Layman's Terms)</h4>
            <ul>
                <li><strong>Key insight:</strong> The matrix is essentially a sorted 1D array arranged in rows</li>
                <li><strong>Flattening:</strong> We can treat it as a 1D array of size m×n</li>
                <li><strong>Index conversion:</strong> 1D index → row = index / cols, col = index % cols</li>
                <li><strong>Binary search:</strong> Standard binary search on the "virtual" 1D array</li>
                <li><strong>Why it works:</strong> Each row continues where the previous ended, so the whole matrix is sorted</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">
                Target = 3
            </div>

            <div class="status-message" id="statusMessage">
                Click "Step" or "Auto Run" to search the matrix using binary search
            </div>

            <div class="variable-display">
                <div class="variable-box">
                    <div class="variable-name">Left (1D index)</div>
                    <div class="variable-value" id="leftVal">0</div>
                </div>
                <div class="variable-box">
                    <div class="variable-name">Right (1D index)</div>
                    <div class="variable-value" id="rightVal">11</div>
                </div>
                <div class="variable-box">
                    <div class="variable-name">Mid (1D index)</div>
                    <div class="variable-value" id="midVal">-</div>
                </div>
                <div class="variable-box">
                    <div class="variable-name">Mid → [row, col]</div>
                    <div class="variable-value" id="coordVal">-</div>
                </div>
            </div>

            <div class="array-section">
                <div class="array-label">Matrix (each row sorted, first of each row > last of previous):</div>
                <div class="matrix-container" id="matrixContainer"></div>
            </div>

            <div class="array-section">
                <div class="array-label">Flattened View (how binary search sees it):</div>
                <div class="array-container" id="flatContainer"></div>
            </div>

            <div class="info-box" id="resultBox" style="display: none;"></div>
        </div>

        <div class="code-section">
            <h3>💻 Python Solution</h3>
            <div class="code-block">
                <pre><span class="keyword">def</span> <span class="function">searchMatrix</span>(self, matrix, target: <span class="class-name">int</span>) -> <span class="class-name">bool</span>:
    m, n = <span class="function">len</span>(matrix), <span class="function">len</span>(matrix[<span class="number">0</span>])

    <span class="comment"># Treat matrix as 1D sorted array</span>
    left, right = <span class="number">0</span>, m * n - <span class="number">1</span>

    <span class="keyword">while</span> left <= right:
        mid = (left + right) // <span class="number">2</span>

        <span class="comment"># Convert 1D index to 2D coordinates</span>
        row, col = mid // n, mid % n

        <span class="keyword">if</span> matrix[row][col] == target:
            <span class="keyword">return</span> <span class="class-name">True</span>
        <span class="keyword">elif</span> matrix[row][col] < target:
            left = mid + <span class="number">1</span>
        <span class="keyword">else</span>:
            right = mid - <span class="number">1</span>

    <span class="keyword">return</span> <span class="class-name">False</span></pre>
            </div>
        </div>
    </div>

    <script>
        const matrix = [
            [1, 3, 5, 7],
            [10, 11, 16, 20],
            [23, 30, 34, 60]
        ];
        const target = 3;
        const m = matrix.length;
        const n = matrix[0].length;

        let left = 0;
        let right = m * n - 1;
        let mid = -1;
        let phase = 'init';
        let autoInterval = null;

        function init() {
            left = 0;
            right = m * n - 1;
            mid = -1;
            renderMatrix();
            renderFlat();
            document.getElementById('leftVal').textContent = '0';
            document.getElementById('rightVal').textContent = (m * n - 1).toString();
            document.getElementById('midVal').textContent = '-';
            document.getElementById('coordVal').textContent = '-';
            document.getElementById('resultBox').style.display = 'none';
        }

        function renderMatrix() {
            const container = document.getElementById('matrixContainer');
            container.innerHTML = '';

            matrix.forEach((row, r) => {
                const rowDiv = document.createElement('div');
                rowDiv.className = 'matrix-row';

                row.forEach((val, c) => {
                    const cell = document.createElement('div');
                    cell.className = 'matrix-cell';
                    cell.id = `cell-${r}-${c}`;

                    const idx = r * n + c;
                    if (idx === mid) {
                        cell.classList.add('current');
                    }
                    if (idx < left || idx > right) {
                        cell.style.opacity = '0.3';
                    }
                    if (val === target && phase === 'done') {
                        cell.classList.add('visited');
                    }

                    cell.textContent = val;
                    rowDiv.appendChild(cell);
                });

                container.appendChild(rowDiv);
            });
        }

        function renderFlat() {
            const container = document.getElementById('flatContainer');
            container.innerHTML = '';

            for (let i = 0; i < m * n; i++) {
                const r = Math.floor(i / n);
                const c = i % n;
                const val = matrix[r][c];

                const box = document.createElement('div');
                box.className = 'array-box small';
                box.style.width = '45px';
                box.style.height = '45px';

                if (i === mid) {
                    box.classList.add('highlight');
                }
                if (i < left || i > right) {
                    box.style.opacity = '0.3';
                }
                if (i === left) {
                    box.style.borderLeftWidth = '3px';
                    box.style.borderLeftColor = '#4caf50';
                }
                if (i === right) {
                    box.style.borderRightWidth = '3px';
                    box.style.borderRightColor = '#f44336';
                }

                box.innerHTML = `${val}<span class="index-label">${i}</span>`;
                container.appendChild(box);
            }
        }

        function step() {
            if (phase === 'init') {
                phase = 'searching';
                document.getElementById('statusMessage').textContent =
                    'Starting binary search on the matrix (treated as 1D array)...';
            }

            if (phase === 'searching') {
                if (left > right) {
                    phase = 'done';
                    document.getElementById('resultBox').style.display = 'block';
                    document.getElementById('resultBox').className = 'info-box highlight';
                    document.getElementById('resultBox').textContent = `❌ Target ${target} not found in matrix`;
                    document.getElementById('statusMessage').textContent = 'Binary search complete. Target not found.';
                    document.getElementById('stepBtn').disabled = true;
                    stopAuto();
                    return;
                }

                mid = Math.floor((left + right) / 2);
                const row = Math.floor(mid / n);
                const col = mid % n;
                const val = matrix[row][col];

                document.getElementById('midVal').textContent = mid;
                document.getElementById('coordVal').textContent = `[${row}, ${col}]`;
                document.getElementById('leftVal').textContent = left;
                document.getElementById('rightVal').textContent = right;

                renderMatrix();
                renderFlat();

                if (val === target) {
                    phase = 'done';
                    document.getElementById('resultBox').style.display = 'block';
                    document.getElementById('resultBox').className = 'info-box secondary';
                    document.getElementById('resultBox').textContent = `✅ Found target ${target} at matrix[${row}][${col}] (1D index: ${mid})`;
                    document.getElementById('statusMessage').textContent =
                        `Found! matrix[${row}][${col}] = ${val} = target`;
                    document.getElementById('stepBtn').disabled = true;
                    stopAuto();
                } else if (val < target) {
                    document.getElementById('statusMessage').textContent =
                        `matrix[${row}][${col}] = ${val} < target ${target} → Search right half, left = ${mid + 1}`;
                    left = mid + 1;
                } else {
                    document.getElementById('statusMessage').textContent =
                        `matrix[${row}][${col}] = ${val} > target ${target} → Search left half, right = ${mid - 1}`;
                    right = mid - 1;
                }
            }
        }

        function toggleAuto() {
            if (autoInterval) {
                stopAuto();
            } else {
                document.getElementById('autoBtn').textContent = 'Pause';
                autoInterval = setInterval(() => {
                    if (phase === 'done') {
                        stopAuto();
                    } else {
                        step();
                    }
                }, 1200);
            }
        }

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

        function reset() {
            stopAuto();
            phase = 'init';
            document.getElementById('stepBtn').disabled = false;
            document.getElementById('statusMessage').textContent =
                'Click "Step" or "Auto Run" to search the matrix using binary search';
            init();
        }

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