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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.
1#include <stdio.h>
2
3int solveProblem(int n) {
4 int dp[n+1];
5 dp[0] = 1; // Base case
6 for (int i = 1; i <= n; i++) {
7 dp[i] = dp[i-1] * 2; // Hypothetical subproblem solution
8 }
9 return dp[n];
10}
11
12int main() {
13 int n = 5;
14 printf("Solution: %d\n", solveProblem(n));
15 return 0;
16}The provided C solution uses a dynamic programming array to store the results of intermediate calculations. The base case is initialized, and subsequent entries are computed based on the previous value, iterating from 1 to n, where n is the given input.
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
The recursive approach in Java involves calling the function recursively with decrementing the problem size until the function reaches the defined base case.