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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.
1function solve(n) {
2 // Brute force in JavaScript
3 for (let i = 0; i < n; i++) {
4 process.stdout.write(i + ' ');
5 }
6 console.log();
7}
8
9solve(10);This JavaScript solution uses a simple for-loop to iterate and print numbers from 0 to n-1, illustrating a brute force technique.
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.
1#include <vector>
std::vector<int> dp(1000, -1);
int solve(int n) {
if (n <= 1) return n;
if (dp[n] != -1) return dp[n];
return dp[n] = solve(n-1) + solve(n-2);
}
int main() {
std::cout << solve(10) << std::endl;
return 0;
}This C++ solution uses a vector to implement dynamic programming for computing Fibonacci numbers, preventing redundant computations by storing results.