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/**
 * Generate Full Triangle Approach
 * Time Complexity: O(rowIndex²) - We generate rowIndex rows with a total of O(rowIndex²) elements
 * Space Complexity: O(rowIndex) - We only store the current row
 * 
 * @param {number} rowIndex - The index of the row to return (0-indexed)
 * @return {number[]} - The rowIndex-th row of Pascal's Triangle
 */
function getRowFullTriangle(rowIndex) {
  // Initialize result with the first row
  let result = [1];
  
  // Generate each row based on the previous row
  for (let i = 1; i <= rowIndex; i++) {
    // Create a new row
    const row = [1];
    
    // Calculate middle elements
    for (let j = 1; j < i; j++) {
      row.push(result[j - 1] + result[j]);
    }
    
    // End with 1
    row.push(1);
    
    // Replace result with the new row
    result = row;
  }
  
  return result;
}
 
/**
 * Iterative In-Place Calculation Approach
 * Time Complexity: O(rowIndex²) - We still perform calculations for each element
 * Space Complexity: O(rowIndex) - We use a single array of size rowIndex+1
 * 
 * @param {number} rowIndex - The index of the row to return (0-indexed)
 * @return {number[]} - The rowIndex-th row of Pascal's Triangle
 */
function getRowInPlace(rowIndex) {
  // Initialize array with all 1s
  const row = new Array(rowIndex + 1).fill(1);
  
  // Update the array in-place
  for (let i = 2; i <= rowIndex; i++) {
    // Update from right to left
    for (let j = i - 1; j >= 1; j--) {
      row[j] = row[j] + row[j - 1];
    }
  }
  
  return row;
}
 
/**
 * Mathematical Formula (Binomial Coefficients) Approach
 * Time Complexity: O(rowIndex) - We calculate each element in the row once
 * Space Complexity: O(rowIndex) - We use a single array of size rowIndex+1
 * 
 * @param {number} rowIndex - The index of the row to return (0-indexed)
 * @return {number[]} - The rowIndex-th row of Pascal's Triangle
 */
function getRow(rowIndex) {
  // Initialize array
  const row = new Array(rowIndex + 1);
  
  // First element is always 1
  row[0] = 1;
  
  // Calculate remaining elements using the formula
  for (let j = 1; j <= rowIndex; j++) {
    row[j] = row[j - 1] * (rowIndex - j + 1) / j;
  }
  
  return row;
}
 
// Test cases
console.log(getRow(3));  // [1, 3, 3, 1]
console.log(getRow(0));  // [1]
console.log(getRow(1));  // [1, 1]
console.log(getRow(4));  // [1, 4, 6, 4, 1]