Searcha2 D Matrix Algorithm
The Searcha2 D Matrix Algorithm is an advanced search algorithm designed to efficiently search through two-dimensional matrices. It is commonly used in various fields, such as computer science, data analysis, and image processing, where large-scale datasets or images are being processed and specific patterns or elements need to be identified. The algorithm takes advantage of the inherent structure of the matrix to optimize the search process, resulting in faster and more effective search results compared to traditional linear search methods.
The key principle behind the Searcha2 D Matrix Algorithm is the efficient traversal of the matrix by systematically searching through rows and columns in a sorted manner. Typically, the matrix is sorted in ascending order, both row-wise and column-wise, allowing the algorithm to make informed decisions on where to search next. Starting at a specific corner of the matrix, the algorithm compares the target value to the current element and, based on the comparison, decides to either move to the next row or column. This process is repeated until the target value is found or the search space is exhausted. By leveraging the sorting of the matrix, the algorithm can eliminate large portions of the search space in each step, resulting in a highly efficient search process.
class Solution {
public:
bool searchMatrix(vector<vector<int>>& matrix, int target) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
if (matrix.empty()) return false;
int lf = 0;
int rt = matrix.size() - 1;
int column = matrix[0].size();
while (lf <= rt) {
int m = (lf + rt) / 2;
if (target < matrix[m][0]) {
rt = m - 1;
}
else if (target > matrix[m][column-1]) {
lf = m + 1;
}
else {
return isValid(matrix[m], target);
}
}
return false;
}
bool isValid(vector<int>& row, int target) {
int lf = 0;
int rt = row.size() - 1;
while (lf <= rt) {
int m = (lf + rt) / 2;
if (target == row[m]) {
return true;
}
else if (target > row[m]) {
lf = m + 1;
}
else {
rt = m - 1;
}
}
return false;
}
};
