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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.
1using System;
2
3class Solution {
4 static int SolveProblem(int n) {
5 int[] dp = new int[n + 1];
6 dp[0] = 1;
7 for (int i = 1; i <= n; i++) {
8 dp[i] = dp[i - 1] * 2;
9 }
10 return dp[n];
11 }
12
13 static void Main() {
14 int n = 5;
15 Console.WriteLine("Solution: " + SolveProblem(n));
16 }
17}The C# solution makes use of an integer array for storing subproblem results. The algorithm iterates over the range, updating each array entry based on its predecessor, similar to solutions in other languages.
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
JavaScript uses recursion in a straightforward manner, calling itself with progressively smaller subproblems until the base case is reached.