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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 <stdio.h>
2
3void solveSubProblem(int *data, int start, int end) {
4 if (start >= end) return;
5 int mid = (start + end) / 2;
6 solveSubProblem(data, start, mid);
7 solveSubProblem(data, mid + 1, end);
8 // Combine results
9 ...
10}
11
12void divideAndConquer(int *data, int size) {
13 solveSubProblem(data, 0, size - 1);
14}
15
16int main() {
17 int data[] = { /* Your data here */ };
18 int size = sizeof(data) / sizeof(data[0]);
19 divideAndConquer(data, size);
20 return 0;
21}This C program uses a divide and conquer strategy to solve the problem. The solveSubProblem function is called recursively to divide the data array until each subproblem reaches a base case (when start is greater than or equal to end). After each recursion, it combines results of the subproblems to form a contiguous solution. You will need to fill in the logic to solve your specific problem within the 'Combine results' section.
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#include <vector>
void solveIteratively(std::vector<int> &data) {
// Implement logic here
...
}
int main() {
std::vector<int> data = { /* Your data here */ };
solveIteratively(data);
return 0;
}In this C++ solution, the use of std::vector allows for dynamic manipulation of the data as subproblems are iteratively processed.