
May 1st, 2014, 08:26 PM
#1
Pascal Triangle Problem  Please help
Pascal’s triangle looks as follows:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
...
The first entry in a row is 1 and the last entry is 1 (except for the first row which contains only 1), and every other entry in Pascal’s triangle is equal to the sum of the two entries: the entry that is in the previous row and the same column, and the entry that is in the previous row and previous column.
(a) Give a recursive definition for the entry C[i, j] at row i and column j of Pascal’s triangle. Make sure that you distinguish the base case(s).
(b) Give a recursive algorithm to compute C[i, j], i > j > 1. Illustrate by drawing a diagram (tree) the steps that your algorithm performs to compute C[6, 4]. Does your algorithm perform overlapping computations?
(c) Use dynamic programming to design an O(n2) time algorithm that computes the first n rows in Pascal’s triangle. Does the dynamic programming algorithm performs better than the recursive
algorithm? Explain.

May 2nd, 2014, 05:06 AM
#2
Re: Pascal Triangle Problem  Please help
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C++17 Compiler: Microsoft VS2017 (15.5.0)

May 2nd, 2014, 05:46 AM
#3
Re: Pascal Triangle Problem  Please help
Originally Posted by BlueBir86
Pascal’s triangle looks as follows:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
...
The first entry in a row is 1 and the last entry is 1 (except for the first row which contains only 1), and every other entry in Pascal’s triangle is equal to the sum of the two entries: the entry that is in the previous row and the same column, and the entry that is in the previous row and previous column.
(a) Give a recursive definition for the entry C[i, j] at row i and column j of Pascal’s triangle. Make sure that you distinguish the base case(s).
(b) Give a recursive algorithm to compute C[i, j], i > j > 1. Illustrate by drawing a diagram (tree) the steps that your algorithm performs to compute C[6, 4].
You could start from wiki to solve (a) and (b)
Victor Nijegorodov

May 2nd, 2014, 03:42 PM
#4
Re: Pascal Triangle Problem  Please help
Originally Posted by BlueBir86
(c) Use dynamic programming to design an O(n2) time algorithm that computes the first n rows in Pascal’s triangle. Does the dynamic programming algorithm performs better than the recursive
algorithm? Explain.
Being presented with the question it strikes me that,
recursion + memoization == dynamic programming
Remember you read it here first
Last edited by zizz; May 2nd, 2014 at 05:29 PM.
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