search DII Algorithm
The Search Directed Interpolation and Integration Algorithm (DII algorithm) is a powerful and efficient technique for solving optimization problems in complex systems, particularly in the field of engineering and operations research. This algorithm combines the strengths of both interpolation and integration methods to build a more accurate and precise search model for optimization problems. It is designed to handle problems with multiple objectives, constraints, and uncertainties, making it well-suited for a wide range of applications, such as structural design, process control, and resource allocation.
The DII algorithm works by constructing a search model that adapts itself to the underlying problem's landscape, successively refining the model as more information is gathered during the search process. It starts with an initial set of sample points, which are evaluated to determine their objective function values and constraints. These points are then used to create an interpolation model that approximates the problem's true objective function and constraints. The algorithm then integrates the interpolation model to compute an optimal solution and a set of search directions to guide the exploration of the solution space. The search directions are used to generate new sample points, which are evaluated and used to update the interpolation model. This iterative process continues until a termination criterion is met, such as convergence to an optimal solution or reaching a maximum number of iterations. The DII algorithm's adaptive nature allows it to efficiently explore the solution space and converge to an optimal or near-optimal solution, even in the presence of complex constraints and uncertainties.
/**
* Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:
* Integers in each row are sorted in ascending from left to right.
* Integers in each column are sorted in ascending from top to bottom.
*/
#include <iostream>
#include <vector>
bool searchMatrix( std::vector<std::vector<int>> matrix, int target ) {
int M = matrix.size();
int N = matrix[0].size();
if ( target < matrix[0][0] || target > matrix[M-1][N-1] ) {
return false;
}
int row = 0;
int col = N - 1;
while ( row <= M -1 && col >= 0 ) {
if ( matrix[row][col] == target ) {
return true;
} else if ( matrix[row][col] > target ) {
col--;
} else {
row++;
}
}
return false;
}
int main() {
std::vector<std::vector<int>> matrix = {
{1, 4, 7, 11, 15},
{2, 5, 8, 12, 19},
{3, 6, 9, 16, 22},
{10, 13, 14, 17, 24},
{18, 21, 23, 26, 30}
};
std::cout << searchMatrix(matrix, 5) << std::endl;
std::cout << searchMatrix(matrix, 20) << std::endl;
return 0;
}
