## C++, , minimax.cpp

``````/**
* @file
* @brief returns which is the longest/shortest number
* using [minimax](https://en.wikipedia.org/wiki/Minimax) algorithm
*
* @details
* Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in
* artificial intelligence, decision theory, game theory, statistics,
* and philosophy for minimizing the possible loss for a worst case (maximum
* loss) scenario. When dealing with gains, it is referred to as "maximin"—to
* maximize the minimum gain. Originally formulated for two-player zero-sum game
* theory, covering both the cases where players take alternate moves and those
* where they make simultaneous moves, it has also been extended to more complex
* games and to general decision-making in the presence of uncertainty.
*
* @author [Gleison Batista](https://github.com/gleisonbs)
* @author [David Leal](https://github.com/Panquesito7)
*/
#include <algorithm>  /// for std::max, std::min
#include <array>      /// for std::array
#include <cmath>      /// for log2
#include <iostream>   /// for IO operations

/**
* @namespace backtracking
* @brief Backtracking algorithms
*/
namespace backtracking {
/**
* @brief Check which is the maximum/minimum number in the array
* @param depth current depth in game tree
* @param node_index current index in array
* @param is_max if current index is the longest number
* @param scores saved numbers in array
* @param height maximum height for game tree
* @returns the maximum or minimum number
*/
template <size_t T>
int minimax(int depth, int node_index, bool is_max,
const std::array<int, T> &scores, double height) {
if (depth == height) {
return scores[node_index];
}

int v1 = minimax(depth + 1, node_index * 2, !is_max, scores, height);
int v2 = minimax(depth + 1, node_index * 2 + 1, !is_max, scores, height);

return is_max ? std::max(v1, v2) : std::min(v1, v2);
}
}  // namespace backtracking

/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
std::array<int, 8> scores = {90, 23, 6, 33, 21, 65, 123, 34423};
double height = log2(scores.size());

std::cout << "Optimal value: "
<< backtracking::minimax(0, 0, true, scores, height) << std::endl;
return 0;
}
``````