Overlapping Subproblems Property: Tabulation
Tabulation
"First, solve all necessary subproblems, and then solve the main problem."
Such a principle is called the Bottom-Up approach. We start with trivial subproblems and move from the bottom to the answer. This principle also uses additional tables to store solutions.
Example
Let’s create an array dp to store the solutions. (dp can be a common name for data structure in a class of DP problems).
1234567891011121314def fib(n): # Array declaration dp = [0]*(n+1) # Base case assignment dp[0] = 0 dp[1] = 1 # Calculating and storing the values for trivial cases for i in range(2 , n+1): dp[i] = dp[i-1] + dp[i-2] return dp[n]
Since we know how to calculate the next element using the previous two elements, let's move from the pre-defined first two elements (base case) and figure out the solution for the 3rd sub-problem. After that, solve the 4th sub-problem using the 2nd and 3rd, and so on, until the last element.
Swipe to start coding
Look at the following task code for the Fibonacci problem.
- Fix it to make the solution correct.
- Call the function for
n = 16and output the 16th Fibonacci number.
Solution
Merci pour vos commentaires !
single
Demandez à l'IA
Demandez à l'IA
Posez n'importe quelle question ou essayez l'une des questions suggérées pour commencer notre discussion
Résumer ce chapitre
Expliquer le code dans file
Expliquer pourquoi file ne résout pas la tâche
Awesome!
Completion rate improved to 8.33Overlapping Subproblems Property: Tabulation
Glissez pour afficher le menu
Tabulation
"First, solve all necessary subproblems, and then solve the main problem."
Such a principle is called the Bottom-Up approach. We start with trivial subproblems and move from the bottom to the answer. This principle also uses additional tables to store solutions.
Example
Let’s create an array dp to store the solutions. (dp can be a common name for data structure in a class of DP problems).
1234567891011121314def fib(n): # Array declaration dp = [0]*(n+1) # Base case assignment dp[0] = 0 dp[1] = 1 # Calculating and storing the values for trivial cases for i in range(2 , n+1): dp[i] = dp[i-1] + dp[i-2] return dp[n]
Since we know how to calculate the next element using the previous two elements, let's move from the pre-defined first two elements (base case) and figure out the solution for the 3rd sub-problem. After that, solve the 4th sub-problem using the 2nd and 3rd, and so on, until the last element.
Swipe to start coding
Look at the following task code for the Fibonacci problem.
- Fix it to make the solution correct.
- Call the function for
n = 16and output the 16th Fibonacci number.
Solution
Passez à un bureau pour une pratique réelleContinuez d'où vous êtes en utilisant l'une des options ci-dessousMerci pour vos commentaires !
Awesome!
Completion rate improved to 8.33single
