/**
 * @file
 * @brief Implementation of [Saddleback
 * Algorithm](https://www.geeksforgeeks.org/saddleback-search-algorithm-in-a-2d-array)
 * for 2D arrays.
 *
 * @details
 * Saddleback Algorithm is an algorithm that searches 2D array in linear time,
 * i.e, O(m + n), where m is number of rows and n is number of columns of 2D
 * array. Also, each row and column of the matrix should be sorted beforehand
 * for this algorithm to work.
 *
 * @author [Hashir Niazi](https://github.com/HashirGJ8842)
 */
#include <cassert>   /// for assert
#include <cstdint>
#include <iostream>  /// for io operations, and std::pair
#include <vector>    /// for std::vector

/** \namespace search
 * \brief Algorithms for searching
 */
namespace search {
/** \namespace saddleback
 * \brief Function for implementing [Saddleback
 * Algorithm](https://www.geeksforgeeks.org/saddleback-search-algorithm-in-a-2d-array).
 */
namespace saddleback {
/**
 * This function implements [Saddleback
 * Algorithm](https://www.geeksforgeeks.org/saddleback-search-algorithm-in-a-2d-array),
 * on a sorted 2D array, and finds the location of the element needed to search
 * @param matrix 2D matrix which is sorted on the basis of rows and columns
 * @param element element to be searched
 * @return An std::pair of with row and column populated within it, if the
 * element is present.
 * @return An std::pair with (0, 0), if the element is not present.
 */
std::pair<uint32_t, uint32_t> saddleback(
    std::vector<std::vector<int32_t>> matrix, int32_t element) {
    uint32_t left_index = 0;
    uint32_t right_index = matrix[0].size() - 1;  // Start from top right corner
    while (left_index <
           matrix.size()) {  // Exit once the value of indexes get out of range.
        if (element ==
            matrix[left_index]
                  [right_index]) {  // If value on this position of matrix is
                                    // equal to element, return (row, column).
            return std::make_pair(left_index + 1, right_index + 1);
        } else if (element >
                   matrix[left_index]
                         [right_index]) {  // Else if value on this position of
                                           // matrix is less than the element,
                                           // move left.
            ++left_index;
        } else if (element <
                   matrix[left_index]
                         [right_index]) {  // Else if value on this position of
                                           // matrix is greater than the
                                           // element, move down.
            if (!right_index)
                break;
            else
                --right_index;
        }
    }
    return std::make_pair(
        0, 0);  // If the program reaches here, that means one of the index
                // went out of index, hence no element present.
}
}  // namespace saddleback
}  // namespace search

/**
 * @brief Test implementations
 * @returns void
 */
static void test() {
    std::vector<std::vector<int32_t>> matrix = {{1, 10, 100, 1000, 10000},
                                                {2, 20, 200, 2000, 20000},
                                                {3, 30, 300, 3000, 30000},
                                                {4, 40, 400, 4000, 40000},
                                                {5, 50, 500, 5000, 50000}};

    std::pair<uint32_t, uint32_t> not_found = std::make_pair(0, 0);
    std::pair<uint32_t, uint32_t> test_answer;
    // Test 1
    std::pair<uint32_t, uint32_t> answer1 =
        search::saddleback::saddleback(matrix, 123);
    assert(not_found == answer1);
    // Test 2
    answer1 = search::saddleback::saddleback(matrix, 0);
    assert(not_found == answer1);
    // Test 3
    answer1 = search::saddleback::saddleback(matrix, 1);
    test_answer = std::make_pair(1, 1);
    assert(test_answer == answer1);
    // Test 4
    answer1 = search::saddleback::saddleback(matrix, 50000);
    test_answer = std::make_pair(5, 5);
    assert(test_answer == answer1);
    // Test 5
    answer1 = search::saddleback::saddleback(matrix, 300);
    test_answer = std::make_pair(3, 3);
    assert(test_answer == answer1);
}

/**
 * @brief Main function
 * @returns 0 on exit
 */
int main() {
    test();  // execute the tests
    return 0;
}