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In this approach, we solve the problem by checking all possible combinations or configurations naively. Although not efficient for large inputs, this approach is often straightforward and can provide insights into the problem structure.
Time Complexity: O(n).
Space Complexity: O(1), as no extra space is used other than loop variables.
1using System;
2
3class Solution {
4 static void Solve(int n) {
5 // Brute force approach in C#
6 for (int i = 0; i < n; i++) {
7 Console.Write(i + " ");
8 }
9 Console.WriteLine();
10 }
11
12 static void Main() {
13 Solve(10);
14 }
15}This C# program iterates over numbers from 0 to n-1 using a for-loop, offering a basic brute force example.
This approach utilizes dynamic programming to optimize the solution by storing interim results and eliminating redundant calculations seen in a brute force approach. This method can significantly improve efficiency when dealing with complex recursive problems.
Time Complexity: O(n).
Space Complexity: O(n) due to the storage array.
1import
Java's implementation of dynamic programming for Fibonacci sequence calculation uses an array for memoization to enhance efficiency over brute force.