Pascal triangle logic

#1

please anyone can explain logic for this ,i am not able to get it.

#2

@DiwyanshuPascal’s triangle is the triangular array of the binomial coefficients.The number of entries in a given line is equal to the line number.Every entry in the line is the value of a binomial coefficient. The value of ith entry in the number line is C(line,i)(i.e apply mathematical combination formula ).
Where C(line,i)=line!/((line-i)!*i!).

Given pattern can be seen as first spaces then numbers and can be formed using 3 approches:
1.A simple method is to run two loops and calculate the value of binomial coefficient in inner loop. Complexity: O(N3).
2.O(N2) time and O(n2) space complexity.In this method store the previously generated values in 2-D array. Use these values to generate value in a line.
3.O(N2) time and O(1) space complexity. In this method calculate C(line,i) using C(line,i-1). It can be calculated in O(1) time as follows:

C(line,i-1)=line !/ ( ( line-i+1 ) ! * ( i-1) ! )
C(line,i)=line ! /( ( line-i ) ! * i ! )
C(line,i)=C(line,i-1) * ( line-i+1 )/ i .

#3

thanks for help i able to do it…
@jaiskid can you help in this
chewbba and number

i got correct answer but unable to pass test case…

#4

@Diwyanshu hey diwanyshu your code is not working for the case 9555 it should give 9444 but your code giving 4440