Description:
Given an integer rowIndex, return the rowIndexth (0-indexed) row of the Pascal’s triangle.
In Pascal’s triangle, each number is the sum of the two numbers directly above it as shown:
Examples:
Example 1:
Input: rowIndex = 3
Output: [1,3,3,1]
Example 2:
Input: rowIndex = 0
Output: [1]
Example 3:
Input: rowIndex = 1
Output: [1,1]Solution in Python:
To solve this problem, we need to generate the rowIndex-th row of Pascal’s Triangle. Each element in the triangle is the sum of the two elements directly above it in the previous row.
Here’s a step-by-step explanation of the approach we’ll use:
- Initialization: Start with the first row, which is
[1]. - Iteration: For each subsequent row up to
rowIndex, generate the next row based on the current row. - Row Generation: The new row can be generated by adding pairs of adjacent elements from the current row. For instance, if the current row is
[1, 3, 3, 1], the next row starts and ends with1, and the middle elements are sums of adjacent elements from the current row (i.e.,1+3,3+3,3+1). - Edge Case: If
rowIndexis0, return[1]immediately.
Python
class Solution:
def getRow(self, rowIndex: int) -> list[int]:
# Initialize the first row of Pascal's Triangle
row = [1]
# Generate rows until we reach the desired rowIndex
for _ in range(rowIndex):
# Create the next row
new_row = [1] # Start with 1
for j in range(1, len(row)):
# Each new element is the sum of the two elements above it
new_row.append(row[j - 1] + row[j])
new_row.append(1) # End with 1
row = new_row # Move to the next row
return row
# Example usage:
# sol = Solution()
# print(sol.getRow(3)) # Output: [1, 3, 3, 1]
# print(sol.getRow(0)) # Output: [1]
# print(sol.getRow(1)) # Output: [1, 1]Explanation of the Code:
- Initialization:
- Start with the first row,
[1].
- Start with the first row,
- Loop to Generate Rows:
- Use a loop to generate each row from the previous row.
- For each new row, start with
[1]. - Use another loop to compute the inner elements by summing pairs of adjacent elements from the previous row.
- Append
1at the end of the new row. - Update the current row to the new row.
- Return the Desired Row:
- After completing the iterations, the
rowvariable will contain therowIndex-th row of Pascal’s Triangle.
- After completing the iterations, the
This approach ensures that we efficiently build the row we need without constructing the entire Pascal’s Triangle up to that row.
Solution in Javascript:
JavaScript
/**
* @param {number} rowIndex
* @return {number[]}
*/
var getRow = function(rowIndex) {
// Initialize the first row of Pascal's Triangle
let row = [1];
// Generate rows until we reach the desired rowIndex
for (let i = 0; i < rowIndex; i++) {
// Create the next row
let newRow = [1]; // Start with 1
for (let j = 1; j < row.length; j++) {
// Each new element is the sum of the two elements above it
newRow.push(row[j - 1] + row[j]);
}
newRow.push(1); // End with 1
row = newRow; // Move to the next row
}
return row;
};
// Example usage:
console.log(getRow(3)); // Output: [1, 3, 3, 1]
console.log(getRow(0)); // Output: [1]
console.log(getRow(1)); // Output: [1, 1]Solution in Java:
Java
import java.util.ArrayList;
import java.util.List;
class Solution {
public List<Integer> getRow(int rowIndex) {
// Initialize the first row of Pascal's Triangle
List<Integer> row = new ArrayList<>();
row.add(1);
// Generate rows until we reach the desired rowIndex
for (int i = 0; i < rowIndex; i++) {
// Create the next row
List<Integer> newRow = new ArrayList<>();
newRow.add(1); // Start with 1
// Each new element is the sum of the two elements above it
for (int j = 1; j < row.size(); j++) {
newRow.add(row.get(j - 1) + row.get(j));
}
newRow.add(1); // End with 1
row = newRow; // Move to the next row
}
return row;
}
// Example usage
public static void main(String[] args) {
Solution sol = new Solution();
System.out.println(sol.getRow(3)); // Output: [1, 3, 3, 1]
System.out.println(sol.getRow(0)); // Output: [1]
System.out.println(sol.getRow(1)); // Output: [1, 1]
}
}Solution in C#:
C#
using System;
using System.Collections.Generic;
public class Solution {
public IList<int> GetRow(int rowIndex) {
// Initialize the first row of Pascal's Triangle
List<int> row = new List<int> { 1 };
// Generate rows until we reach the desired rowIndex
for (int i = 0; i < rowIndex; i++) {
// Create the next row
List<int> newRow = new List<int> { 1 }; // Start with 1
// Each new element is the sum of the two elements above it
for (int j = 1; j < row.Count; j++) {
newRow.Add(row[j - 1] + row[j]);
}
newRow.Add(1); // End with 1
row = newRow; // Move to the next row
}
return row;
}
}