[dynamic programming] Yang Hui triangle

Given a nonnegative integer *numRows,* Generate 「 Yang hui triangle 」 Before numRows That's ok .

stay 「 Yang hui triangle 」 in , Each number is the sum of the numbers at the top left and right of it .

link ：https://leetcode-cn.com/problems/pascals-triangle/

Definition ：$dp[i][j]$​​​ Indicates the index position $i,j$ Value

The boundary conditions ：$dp[0][0]=1,dp[1][0]=dp[1][1]=1$​​​

State transition equation ：$dp[i][j]=dp[i-1][j-1]+dp[i-1][j],i$​ Not a boundary , The boundary is 1

class Solution:
    def generate(self, numRows: int) -> List[List[int]]:
        # dp[i][j] = dp[i-1][j]+dp[i-1][j-1]
        dp = []
        curRow = 0
        while curRow < numRows:               #  That's ok 
            if curRow==0:
                dp.append([1])
            elif curRow==1:
                dp.append([1,1])
            else:
                temp = []
                for i in range(curRow + 1):   #  Column 
                    if i==0 or i == curRow:   #  If a boundary is encountered 
                        temp.append(1)
                    else:
                        temp.append(dp[curRow-1][i]+dp[curRow-1][i-1])
                dp.append(temp)
            curRow += 1
        return dp

If you only need a sequence index of numRows（ Index from 0 Start ） Value , So based on the above code , Just make a simple change , relevant link

class Solution:
    def getRow(self, numRows: int) -> List[int]:
        dp = []
        curRow = 0
        while curRow < numRows+1:               #  That's ok 
            if curRow==0:
                dp=[1]
            elif curRow==1:
                dp=[1,1]
            else:
                temp = []
                for i in range(curRow + 1):   #  Column 
                    if i==0 or i == curRow:   #  If a boundary is encountered 
                        temp.append(1)
                    else:
                        temp.append(dp[i]+dp[i-1])
                dp=temp
            curRow += 1
        return dp