Course Content
Dynamic Programming
Dynamic Programming
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.
Task
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
Task
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
Switch to desktop for real-world practiceContinue from where you are using one of the options belowEverything was clear?
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.
Task
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
Task
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
Switch to desktop for real-world practiceContinue from where you are using one of the options belowEverything was clear?
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.
Task
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
Task
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
Switch to desktop for real-world practiceContinue from where you are using one of the options belowEverything was clear?
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.
Task
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
Switch to desktop for real-world practiceContinue from where you are using one of the options belowSwitch to desktop for real-world practiceContinue from where you are using one of the options below