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This approach involves breaking down the problem into smaller subproblems. Each subproblem is solved independently, and the solutions to these subproblems are combined to solve the original problem. This is typically implemented through recursive functions.
Time Complexity: O(n log n) due to the divide and conquer methodology where the problem is divided into two halves.
Space Complexity: O(log n) due to the recursive stack depth.
#include <vector>
void solveSubProblem(std::vector<int> &data, int start, int end) {
if (start >= end) return;
int mid = (start + end) / 2;
solveSubProblem(data, start, mid);
solveSubProblem(data, mid + 1, end);
// Combine results
...
}
void divideAndConquer(std::vector<int> &data) {
solveSubProblem(data, 0, data.size() - 1);
}
int main() {
std::vector<int> data = { /* Your data here */ };
divideAndConquer(data);
return 0;
}This C++ program mirrors the C solution but utilizes std::vector for dynamic array management. The solveSubProblem is invoked recursively, and the algorithm solves subproblems similarly by splitting and combining sub-arrays.
This approach avoids recursion by iteratively solving subproblems. It may use data structures as stacks or queues to keep track of subproblems, or directly manipulate indices to iterate over sections of the data.
Time Complexity: O(n), if the problem can be iteratively solved in linear time.
Space Complexity: O(1), if no extra storage apart from input data is used.
1public class IterativeSolution {
2
3 public static void solveIteratively(int[] data) {
4 // Implement iterative logic
5 ...
6 }
7
8 public static void main(String[] args) {
9 int[] data = { /* Your data here */ };
10 solveIteratively(data);
11 }
12}The Java version uses a main method solveIteratively that encompasses the iterative logic necessary to replace recursion, systematically solving the problem for defined subproblems.