Problem A. Binomial Coefficient
The tasks in this section contain test function calls. Please do not change this code; otherwise, the assignment may not be accepted.
In previous sections, we solved the problems that can be described as functions with 1 parameter (fib(n), rabbit(n)). Sometimes, the function depends on 2 or more parameters, for example, this one.
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Create the program to calculate Binomial coefficient C(n, k) using dynamic programming. Since the function contains two parameters, the problem requires a two-dimensional array dp[n+1][n+1] to store the values.
- Define the base cases:
C(n,0) = C(n,n) = 1 - Use the rule:
C(n,k) = C(n-1,k-1) + C(n-1,k).
Use Optimal Substructure and Overlapping Subproblems principles. If you’re unsure about how to store sub-solutions, open Hint.
Example 1. n=3, k=2 -> res = 3
Example2. n=10, k=4 -> res = 210
Soluzione
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