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This approach involves breaking down the problem into overlapping subproblems, solving each subproblem only once, and storing their solutions - typically in a table. This can help reduce redundant calculations and improve efficiency.
Time Complexity: O(n), as each subproblem from 1 to n is solved once.
Space Complexity: O(n), due to the storage of results in the dp array.
1function solveProblem(n) {
2 let dp = new Array(n + 1).fill(1);
3 for (let i = 1; i <= n; i++) {
4 dp[i] = dp[i - 1] * 2;
5 }
6 return dp[n];
7}
8
9let n = 5;
10console.log("Solution:", solveProblem(n));In JavaScript, an array is initialized and filled with a default value to store the results of each subproblem. Iteration over the array to update each element based on the previous is similar to other language implementations.
A recursive approach solves the problem by solving smaller instances of the same problem. While this is a straightforward approach, it may lead to inefficiencies without memoization or optimizations because it can repeatedly solve the same subproblems.
Time Complexity: O(2^n), due to many duplicate subproblem calculations without memoization.
Space Complexity: O(n), considering the call stack.
1
class Solution {
static int SolveProblem(int n) {
if (n == 0) return 1;
return 2 * SolveProblem(n - 1);
}
static void Main() {
int n = 5;
Console.WriteLine("Solution: " + SolveProblem(n));
}
}In this C# solution, the recursive function invokes itself with smaller arguments until a base case of n equals zero is met.