Pascals Triangle

                                            
class Solution {
public:
    vector<vector<int>> generate(int numRows) {
        vector<vector<int>> result(numRows);

        for (int i = 0; i < numRows; i++) {
            result[i].resize(i + 1);
            result[i][0] = result[i][i] = 1;

            for (int j = 1; j < i; j++) {
                result[i][j] = result[i - 1][j - 1] + result[i - 1][j];
            }
        }

        return result;
    }
};

                                            
class Solution {
    public List<List<Integer>> generate(int numRows) {
        List<List<Integer>> triangle = new ArrayList<>();
        
        if (numRows == 0) {
            return triangle;
        }
        
        triangle.add(new ArrayList<>());
        triangle.get(0).add(1);
        
        for (int i = 1; i < numRows; i++) {
            List<Integer> row = new ArrayList<>();
            List<Integer> prevRow = triangle.get(i - 1);
            
            row.add(1);
            
            for (int j = 1; j < i; j++) {
                row.add(prevRow.get(j - 1) + prevRow.get(j));
            }
            
            row.add(1);
            triangle.add(row);
        }
        
        return triangle;
    }
}

                                            
class Solution(object):
    def generate(self, numRows):
        """
        :type numRows: int
        :rtype: List[List[int]]
        """
        if numRows == 0:
            return []
        
        triangle = [[1]]
        
        for i in range(1, numRows):
            prev_row = triangle[i - 1]
            new_row = [1]
            for j in range(1, i):
                new_row.append(prev_row[j - 1] + prev_row[j])
            new_row.append(1)
            triangle.append(new_row)
        
        return triangle

                                            
/**
 * Return an array of arrays of size *returnSize.
 * The sizes of the arrays are returned as 
*returnColumnSizes array.
*/

int** generate(int numRows, int* returnSize, int** returnColumnSizes){
    *returnSize = numRows;
    int **result = (int **)malloc(numRows * sizeof(int *));
    *returnColumnSizes = (int *)malloc(numRows * sizeof(int));
    
    for(int i = 0; i < numRows; i++){
        result[i] = (int *)malloc((i + 1) * sizeof(int));
        (*returnColumnSizes)[i] = i + 1;
        result[i][0] = 1;
        result[i][i] = 1;
        
        for(int j = 1; j < i; j++){
            result[i][j] = result[i - 1][j - 1] + result[i - 1][j];
        }
    }
    
    return result;
}

                                            
public class Solution {
    public IList<IList<int>> Generate(int numRows) {
        IList<IList<int>> triangle = new List<IList<int>>();
        
        if(numRows == 0){
            return triangle;
        }
        
        List<int> firstRow = new List<int>();
        firstRow.Add(1);
        triangle.Add(firstRow);
        
        for(int i = 1; i < numRows; i++){
            List<int> prevRow = new List<int>(triangle[i - 1]);
            List<int> row = new List<int>();
            
            row.Add(1);
            for(int j = 1; j < i; j++){
                row.Add(prevRow[j - 1] + prevRow[j]);
            }
            row.Add(1);
            
            triangle.Add(row);
        }
        
        return triangle;
    }
}

                                            
/**
 * @param {number} numRows
 * @return {number[][]}
 */
var generate = function(numRows) {
    const result = [];
    
    for (let i = 0; i < numRows; i++) {
        const row = new Array(i + 1).fill(1);
        
        for (let j = 1; j < row.length - 1; j++) {
            row[j] = result[i - 1][j - 1] + result[i - 1][j];
        }
        
        result.push(row);
    }
    
    return result;
};

                                            
function generate(numRows: number): number[][] {
    const result: number[][] = [];
    
    for (let i = 0; i < numRows; i++) {
        const row: number[] = new Array(i + 1).fill(1);
        
        for (let j = 1; j < row.length - 1; j++) {
            row[j] = result[i - 1][j - 1] + result[i - 1][j];
        }
        
        result.push(row);
    }
    
    return result;
};

                                            
class Solution {
    /**
     * @param Integer $numRows
     * @return Integer[][]
     */
    function generate($numRows) {
        $triangle = array();
        for ($i = 0; $i < $numRows; $i++) {
            $triangle[$i] = array_fill(0, $i + 1, 0);
            $triangle[$i][0] = 1;
            $triangle[$i][$i] = 1;
            for ($j = 1; $j < $i; $j++) {
                $triangle[$i][$j] = $triangle[$i - 1][$j - 1] + $triangle[$i - 1][$j];
            }
        }
        return $triangle;
    }
}

                                            
class Solution {
    func generate(_ numRows: Int) -> [[Int]] {
        var triangle = [[Int]]()

        if numRows == 0 {
            return triangle
        }

        triangle.append([1])

        for i in 1..<numRows {
            var row = [1]

            for j in 1..<i {
                row.append(triangle[i-1][j-1] + triangle[i-1][j])
            }

            row.append(1)
            triangle.append(row)
        }

        return triangle
    }
}

                                            
class Solution {
    fun generate(numRows: Int): List<List<Int>> {
        val result = mutableListOf<MutableList<Int>>()
        if (numRows == 0) return result
        
        result.add(mutableListOf(1))
        
        for (i in 1 until numRows) {
            val prevRow = result[i - 1]
            val row = mutableListOf<Int>()
            row.add(1)
            
            for (j in 1 until i) {
                row.add(prevRow[j - 1] + prevRow[j])
            }
            
            row.add(1)
            result.add(row)
        }
        
        return result
    }
}

                                            
class Solution {
  List<List<int>> generate(int numRows) {
    List<List<int>> triangle = [];

    for (int i = 0; i < numRows; i++) {
      List<int> row = List<int>.filled(i + 1, 1);

      for (int j = 1; j < row.length - 1; j++) {
        row[j] = triangle[i - 1][j - 1] + triangle[i - 1][j];
      }

      triangle.add(row);
    }

    return triangle;
  }
}

                                            
func generate(numRows int) [][]int {
    result := make([][]int, numRows)
    
    for i := 0; i < numRows; i++ {
        row := make([]int, i+1)
        row[0], row[i] = 1, 1
        
        for j := 1; j < i; j++ {
            row[j] = result[i-1][j-1] + result[i-1][j]
        }
        
        result[i] = row
    }
    
    return result
}

                                            
# @param {Integer} num_rows
# @return {Integer[][]}
def generate(num_rows)
    triangle = Array.new(num_rows) { |i| Array.new(i+1) }
    
    (0...num_rows).each do |i|
        triangle[i][0] = triangle[i][-1] = 1
        
        (1...i).each do |j|
            triangle[i][j] = triangle[i-1][j-1] + triangle[i-1][j]
        end
    end
    
    triangle
end

                                            
object Solution {
    def generate(numRows: Int): List[List[Int]] = {
        if (numRows == 0) return List()
        else if (numRows == 1) return List(List(1))
        else {
            val res = collection.mutable.ListBuffer[List[Int]]()
            res += List(1)
            for (i <- 1 until numRows) {
                val prev = res(i - 1)
                val curr = (0 until i + 1).map(j => if (j == 0 || j == i) 1 else prev(j - 1) + prev(j)).toList
                res += curr
            }
            res.toList
        }
    }
}

                                            
impl Solution {
    pub fn generate(num_rows: i32) -> Vec<Vec<i32>> {
        let mut triangle: Vec<Vec<i32>> = Vec::new();
        
        for i in 0..num_rows as usize {
            let mut row = Vec::new();
            for j in 0..=i {
                if j == 0 || j == i {
                    row.push(1);
                } else {
                    row.push(triangle[i - 1][j - 1] + triangle[i - 1][j]);
                }
            }
            triangle.push(row);
        }
        
        triangle
    }
}

To solve this coding challenge, we need to generate Pascal's Triangle with a given number of rows,

numRows

. Pascal's Triangle is a triangular array where each element is the sum of the two elements directly above it from the previous row.

Explanation

Understanding the Base Case :

If
numRows

is 1, the triangle contains just one row:
[1]

.

Building the Triangle :

Start with the first row, which is
[1]

.
For subsequent rows, begin and end with
1

.
Each element in between the
1

s is formed by the sum of the two elements above it from the previous row.

Iterative Construction :

Initialize the triangle with the first row
[1]

.
For each new row, calculate each element using the previous row.
Continue this process until
numRows

rows are constructed.

Edge Cases :

Ensure that the input
numRows

adheres to the constraint 1 <= numRows <= 30.
If
numRows

is 0 explicitly, return an empty list, though it's not required as per the constraints.

Detailed Steps in Pseudocode

The pseudocode described here provides a detailed step-by-step approach to solving the challenge:

Initialize the Triangle :

If
numRows

is less than 1, return an empty list (though this edge case isn't necessary as per constraints).

Base Case :

Initialize the triangle with the first row:
triangle = [[1]]

.

Generate Rows Iteratively :

                                            
# Loop from the second row to the numRows
for i from 1 to numRows - 1:
# Get the previous row from the triangle
previous_row = triangle[i - 1]

# Start the new row with 1
new_row = [1]

# Fill in the middle elements
for j from 1 to i - 1:
# Calculate the new element as the sum of two elements from the previous row
new_element = previous_row[j - 1] + previous_row[j]
new_row.append(new_element)

# End the new row with 1
new_row.append(1)

# Append the new row to the triangle
triangle.append(new_row)

# Return the complete triangle
return triangle

Result :

Return the constructed
triangle

.

Detailed Explanation

Initialize the Triangle :

By starting with
triangle = [[1]]

, we establish the first, and the simplest, row of Pascal's Triangle.

Iterate to Form Each Row :

We use a loop to create from the second row up to the
numRows

-th row.
In each iteration, we prepare to form a new row based on the last row in
triangle

.

Forming the New Row :

Each new row starts and ends with
1

, which are fixed.
The elements in between are computed as the sum of two adjacent elements directly above in the previous row.

Appending the Row :

Each newly formed row is appended to
triangle

, thereby building the structure iteratively.

By following these steps, we can construct Pascal's Triangle incrementally row by row until we reach the desired number of rows. This method ensures clarity, simplicity, and adherence to the basic principles of Pascal's Triangle generation.