algorithm-neet-code-top-150-python-visual/visual/0118_pascals_triangle.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>118 - Pascal's Triangle</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">#118</span> Pascal's Triangle</h1>
            <p>
                Given an integer numRows, return the first numRows of Pascal's triangle.
                In Pascal's triangle, each number is the sum of the two numbers directly above it.
            </p>
            <h3>Key Pattern</h3>
            <p>
                Each row starts and ends with 1. For middle elements:
                <strong>triangle[row][col] = triangle[row-1][col-1] + triangle[row-1][col]</strong>
            </p>
            <div class="problem-meta">
                <span class="meta-tag">📝 Algorithm</span>
                <span class="meta-tag">⏱️ O(n)</span>
            </div>
            <div class="file-ref">
                📄 Python: <code>python/0118_pascal's_triangle/0118_pascal's_triangle.py</code>
            </div>

        </div>

        <div class="explanation-panel">
            <h4>🧠 How It Works (Layman's Terms)</h4>
            <p>This algorithm solves the problem <strong>step by step</strong>:</p>
            <ul>
                <li><strong>Understand:</strong> Parse the input data</li>
                <li><strong>Process:</strong> Apply the core logic</li>
                <li><strong>Optimize:</strong> Use efficient data structures</li>
                <li><strong>Return:</strong> Output the computed result</li>
            </ul>
        </div>


        <section class="visualization-section">
            <h3>🎬 Step-by-Step Visualization</h3>
            <div class="controls">
                <button id="autoRunBtn" class="btn">▶ Auto Run</button>
                <button id="stepBtn" class="btn btn-success">Step</button>
                <button id="resetBtn" class="btn btn-danger">Reset</button>
                <label style="margin-left: 20px;">
                    Rows: <input type="range" id="rowSlider" min="1" max="10" value="6">
                    <span id="rowCount">6</span>
                </label>
            </div>
            <div class="status" id="status">Click Auto Run to build Pascal's Triangle row by row</div>
            <svg id="visualization"></svg>
        </section>

        <section class="code-section">
            <h3>💻 Python Solution</h3>
            <div class="code-block">
                <pre>from typing import List, Optional

"""
LeetCode 118. Pascal's Triangle

Problem from LeetCode: https://leetcode.com/problems/pascals-triangle/

Description:
Given an integer numRows, return the first numRows of Pascal's triangle.

In Pascal's triangle, each number is the sum of the two numbers directly above it.

Example 1:
Input: numRows = 5
Output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]

Example 2:
Input: numRows = 1
Output: [[1]]

Constraints:
- 1 &lt;= numRows &lt;= 30
"""

class Solution:

    def generate(self, numRows):
        result = []
        if numRows &gt;= 1:
            result.append([1])
        for row in range(1, numRows):
            current_row = [1]
            prev_row = result[row - 1]
            for j in range(1, row):
                current_row.append(prev_row[j - 1] + prev_row[j])
            current_row.append(1)
            result.append(current_row)
        return result


if __name__ == '__main__':
    # Example usage based on LeetCode sample
    solution = Solution()

    # Example 1
    numRows = 5
    result = solution.generate(numRows)
    print(f"Input: numRows = {numRows}")
    print(f"Output: {result}")
    # Expected output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]

    # Example 2
    numRows = 1
    result = solution.generate(numRows)
    print(f"Input: numRows = {numRows}")
    print(f"Output: {result}")
    # Expected output: [[1]]
</pre>
            </div>
        </section>
    </div>

    <script>
        const width = 900;
        const height = 600;

        const svg = d3.select("#visualization")
            .attr("width", width)
            .attr("height", height);

        let numRows = 6;
        let triangle = [];
        let currentRow = 0;
        let currentCol = 0;
        let phase = "init";
        let animationTimer = null;
        let highlighting = null;

        document.getElementById("rowSlider").addEventListener("input", (e) => {
            numRows = parseInt(e.target.value);
            document.getElementById("rowCount").textContent = numRows;
            reset();
        });

        function reset() {
            triangle = [];
            currentRow = 0;
            currentCol = 0;
            phase = "init";
            highlighting = null;

            if (animationTimer) clearInterval(animationTimer);
            animationTimer = null;
            document.getElementById("autoRunBtn").textContent = "▶ Auto Run";
            document.getElementById("status").textContent =
                `Building Pascal's Triangle with ${numRows} rows`;
            render();
        }

        function render() {
            svg.selectAll("*").remove();

            const cellSize = 55;
            const startY = 50;
            const centerX = width / 2;

            // Title
            svg.append("text")
                .attr("x", 30)
                .attr("y", 25)
                .attr("font-size", "14px")
                .attr("font-weight", "bold")
                .attr("fill", "#1e293b")
                .text(`Pascal's Triangle (${numRows} rows)`);

            // Draw the triangle
            for (let row = 0; row < triangle.length; row++) {
                const rowValues = triangle[row];
                const rowWidth = rowValues.length * cellSize;
                const startX = centerX - rowWidth / 2;

                for (let col = 0; col < rowValues.length; col++) {
                    const x = startX + col * cellSize;
                    const y = startY + row * 55;
                    const value = rowValues[col];

                    const isCurrentCell = row === currentRow && col === currentCol && phase !== "done";
                    const isHighlighted = highlighting &&
                        ((row === highlighting.row && col === highlighting.col1) ||
                         (row === highlighting.row && col === highlighting.col2));
                    const isNewCell = row === currentRow && phase === "building";
                    const isJustAdded = row === currentRow && col < currentCol;

                    // Draw hexagon-like shape for visual appeal
                    const hexPath = `M${x + cellSize/2},${y}
                                    L${x + cellSize - 5},${y + 15}
                                    L${x + cellSize - 5},${y + 40}
                                    L${x + cellSize/2},${y + 55}
                                    L${x + 5},${y + 40}
                                    L${x + 5},${y + 15} Z`;

                    svg.append("path")
                        .attr("d", hexPath)
                        .attr("fill", () => {
                            if (isCurrentCell) return "#fef3c7";
                            if (isHighlighted) return "#dbeafe";
                            if (isJustAdded) return "#d1fae5";
                            return "#f0fdf4";
                        })
                        .attr("stroke", () => {
                            if (isCurrentCell) return "#f59e0b";
                            if (isHighlighted) return "#3b82f6";
                            if (isJustAdded) return "#10b981";
                            return "#86efac";
                        })
                        .attr("stroke-width", isCurrentCell || isHighlighted ? 3 : 2);

                    svg.append("text")
                        .attr("x", x + cellSize / 2)
                        .attr("y", y + 32)
                        .attr("text-anchor", "middle")
                        .attr("font-size", value > 99 ? "14px" : "16px")
                        .attr("font-weight", "bold")
                        .attr("fill", "#1e293b")
                        .text(value);
                }
            }

            // Draw arrows showing current computation
            if (highlighting && triangle.length > 1 && currentRow > 0) {
                const prevRow = currentRow - 1;
                const prevRowValues = triangle[prevRow];
                const prevRowWidth = prevRowValues.length * cellSize;
                const prevStartX = centerX - prevRowWidth / 2;

                const currRowWidth = (triangle[currentRow] ? triangle[currentRow].length : currentCol) * cellSize;
                const currStartX = centerX - currRowWidth / 2;

                // Arrow from left parent
                if (highlighting.col1 >= 0 && highlighting.col1 < prevRowValues.length) {
                    const fromX = prevStartX + highlighting.col1 * cellSize + cellSize / 2;
                    const fromY = startY + prevRow * 55 + 55;
                    const toX = currStartX + currentCol * cellSize + cellSize / 2 - 10;
                    const toY = startY + currentRow * 55;

                    svg.append("path")
                        .attr("d", `M${fromX},${fromY} Q${fromX},${(fromY + toY) / 2} ${toX},${toY}`)
                        .attr("fill", "none")
                        .attr("stroke", "#3b82f6")
                        .attr("stroke-width", 2)
                        .attr("stroke-dasharray", "5,3");
                }

                // Arrow from right parent
                if (highlighting.col2 >= 0 && highlighting.col2 < prevRowValues.length) {
                    const fromX = prevStartX + highlighting.col2 * cellSize + cellSize / 2;
                    const fromY = startY + prevRow * 55 + 55;
                    const toX = currStartX + currentCol * cellSize + cellSize / 2 + 10;
                    const toY = startY + currentRow * 55;

                    svg.append("path")
                        .attr("d", `M${fromX},${fromY} Q${fromX},${(fromY + toY) / 2} ${toX},${toY}`)
                        .attr("fill", "none")
                        .attr("stroke", "#3b82f6")
                        .attr("stroke-width", 2)
                        .attr("stroke-dasharray", "5,3");
                }
            }

            // Calculation display
            if (highlighting && phase === "building") {
                const calcY = height - 130;
                svg.append("rect")
                    .attr("x", 30)
                    .attr("y", calcY)
                    .attr("width", 400)
                    .attr("height", 50)
                    .attr("rx", 10)
                    .attr("fill", "#eff6ff")
                    .attr("stroke", "#3b82f6");

                svg.append("text")
                    .attr("x", 230)
                    .attr("y", calcY + 32)
                    .attr("text-anchor", "middle")
                    .attr("font-size", "14px")
                    .attr("fill", "#1e293b")
                    .text(highlighting.text);
            }

            // Algorithm explanation
            const algoY = height - 70;
            svg.append("text")
                .attr("x", 30)
                .attr("y", algoY)
                .attr("font-size", "12px")
                .attr("fill", "#64748b")
                .text("Pattern: Each number = sum of two numbers above it");

            svg.append("text")
                .attr("x", 30)
                .attr("y", algoY + 20)
                .attr("font-size", "12px")
                .attr("fill", "#64748b")
                .text("First and last elements of each row are always 1");

            // Completion message
            if (phase === "done") {
                svg.append("rect")
                    .attr("x", width / 2 - 200)
                    .attr("y", height - 70)
                    .attr("width", 400)
                    .attr("height", 55)
                    .attr("rx", 10)
                    .attr("fill", "#d1fae5")
                    .attr("stroke", "#10b981")
                    .attr("stroke-width", 2);

                svg.append("text")
                    .attr("x", width / 2)
                    .attr("y", height - 35)
                    .attr("text-anchor", "middle")
                    .attr("font-size", "16px")
                    .attr("font-weight", "bold")
                    .attr("fill", "#10b981")
                    .text(`✓ Pascal's Triangle with ${numRows} rows complete!`);
            }
        }

        function step() {
            if (phase === "done") return;

            if (phase === "init") {
                // Start with first row
                triangle.push([1]);
                currentRow = 0;
                phase = "row_complete";
                document.getElementById("status").textContent = "Row 1: [1] - First row always just contains 1";
                render();
                return;
            }

            if (phase === "row_complete") {
                currentRow++;
                if (currentRow >= numRows) {
                    phase = "done";
                    document.getElementById("status").textContent = `✓ Complete! Generated ${numRows} rows.`;
                    render();
                    return;
                }
                currentCol = 0;
                triangle.push([]);
                phase = "building";
            }

            if (phase === "building") {
                const row = currentRow;
                const col = currentCol;
                const prevRow = triangle[row - 1];

                if (col === 0 || col === row) {
                    // First or last element is always 1
                    triangle[row].push(1);
                    highlighting = {
                        row: row - 1,
                        col1: col > 0 ? col - 1 : -1,
                        col2: col < row ? col : -1,
                        text: `Position [${row}][${col}]: Edge element = 1`
                    };
                    document.getElementById("status").textContent =
                        `Row ${row + 1}, Position ${col}: Edge element, value = 1`;
                } else {
                    // Middle element = sum of two above
                    const val = prevRow[col - 1] + prevRow[col];
                    triangle[row].push(val);
                    highlighting = {
                        row: row - 1,
                        col1: col - 1,
                        col2: col,
                        text: `Position [${row}][${col}]: ${prevRow[col-1]} + ${prevRow[col]} = ${val}`
                    };
                    document.getElementById("status").textContent =
                        `Row ${row + 1}, Position ${col}: ${prevRow[col-1]} + ${prevRow[col]} = ${val}`;
                }

                currentCol++;

                if (currentCol > row) {
                    phase = "row_complete";
                    highlighting = null;
                    document.getElementById("status").textContent =
                        `Row ${row + 1} complete: [${triangle[row].join(', ')}]`;
                }

                render();
            }
        }

        function autoRun() {
            if (animationTimer) {
                clearInterval(animationTimer);
                animationTimer = null;
                document.getElementById("autoRunBtn").textContent = "▶ Auto Run";
                return;
            }

            document.getElementById("autoRunBtn").textContent = "⏸ Pause";
            animationTimer = setInterval(() => {
                if (phase === "done") {
                    clearInterval(animationTimer);
                    animationTimer = null;
                    document.getElementById("autoRunBtn").textContent = "▶ Auto Run";
                    return;
                }
                step();
            }, 600);
        }

        document.getElementById("autoRunBtn").addEventListener("click", autoRun);
        document.getElementById("stepBtn").addEventListener("click", step);
        document.getElementById("resetBtn").addEventListener("click", reset);

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