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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.
1#include <iostream>
2#include <vector>
3
4void solveSubProblem(std::vector<int> &data, int start, int end) {
5 if (start >= end) return;
6 int mid = (start + end) / 2;
7 solveSubProblem(data, start, mid);
8 solveSubProblem(data, mid + 1, end);
9 // Combine results
10 ...
11}
12
13void divideAndConquer(std::vector<int> &data) {
14 solveSubProblem(data, 0, data.size() - 1);
15}
16
17int main() {
18 std::vector<int> data = { /* Your data here */ };
19 divideAndConquer(data);
20 return 0;
21}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.
1
JavaScript iteration is performed through an solveIteratively function, circumventing recursion for environments where memory consumption is critical or can reach limits.