Pascal's Triangle

class Solution:
    def generate(self, numRows: int) -> List[List[int]]:
        res=[]
        """
        1
        1 1
        1 2 1
        1 3 3 1
        1 4 6 4 1
        """
        for i in range(numRows):
            row=[1] # start with 1
            if i>=1: # less than 1 then result append [1] and return 
                pre_row=res[i-1] # store the list of previous row
                for j in range(i-1):
                    row.append(pre_row[j]+pre_row[j+1])
                row.append(1) # end with 1
            res.append(row) 
        return res

class Solution:
    def generate(self, numRows: int) -> List[List[int]]:
        result = []
        
        for i in range(numRows):
            row = [1]  # start with 1
            
            if i > 0:
                prev_row = result[i-1]
                num_elements = (i + 1) // 2  # 只计算一半的元素
                
                for j in range(1, num_elements):
                    element = prev_row[j-1] + prev_row[j]  # 通过对称性计算元素
                    row.append(element)
                
                # 奇数个元素单独考虑：因为i从0开始，所以如果i为偶数，则每行有奇数个元素
                if i % 2 == 0:
                    odd_row=row[:num_elements]
                    element = prev_row[num_elements - 1] + prev_row[num_elements]
                    row.append(element)
                
                # 生成另一半
                row += odd_row[::-1] if i % 2 == 0 else row[::-1]
            
            result.append(row)
        
        return result

class Solution:
    def getRow(self, rowIndex: int) -> List[int]:
        res = []
        for i in range(rowIndex + 1):  # Fix the loop range to include rowIndex
            row = [1]
            if i >= 1:  # Change the condition to >= 1
                pre_row = res[i - 1]
                mid=(i+1)//2
                for j in range(1,mid):
                    row.append(pre_row[j-1] + pre_row[j])
                if i%2==0:
                    odd_row=row[:mid]
                    row.append(pre_row[mid-1]+pre_row[mid])
                row+=odd_row[::-1] if i%2==0 else row[::-1]
            res.append(row)
        return res[-1]