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508. Get specific row K in a Pascal Triangle
Given a row index K, write a program to print the Kth of the Pascal triangle.
Note: The row index starts from 0.
Pascal Triangle:
Example:
K = 2 Output: 1, 1 K= 5 Output: 1, 4, 6, 4, 1
Simple Approach:
As we discussed here  Pascal triangle, start calculating the rows from 1 to K and then print the Kth row.
Output:
[1, 7, 21, 35, 35, 21, 7, 1]
Better Solution:
We do not need to calculate all the k rows to know the kth row. We can find the pattern followed in all the rows and then use that pattern to calculate only the kth row and print it.
Pattern: Let's take K = 7
Output: 1, 7, 21, 35, 35, 21, 7, 1 Index 0 = 1 Index 1 = 7/1 = 7 Index 2 = 7x6/1x2 = 21 Index 3 = 7x6x5/1x2x3 = 35 Index 4 = 7x6x5x4/1x2x3x4 = 35 Index 5 = 7x6x5x4x3/1x2x3x4x5 = 21 Index 6 = 7x6x5x4x3x2/1x2x3x4x5x6 = 21 Index 7 = 7x6x5x4x3x2x1/1x2x3x4x5x6x7 = 1
Have start=1, end = 7. So take a variable current = 1. Iterate from i = 1 to 7 and for each iteration do current = current * end and then current = current / start, then current will be ith element of the row. Do end and start++.
Output:
[1, 7, 21, 35, 35, 21, 7, 1]
Reference: Leetcode