Added determinant calculation

Author: fredbr

math/determinant.cpp

@@ -0,0 +1,81 @@
+#include <iostream>
+#include <vector>
+
+#include <gmpxx.h>
+
+template<typename T>
+void divide_row(std::vector<T> &A, T ratio) {
+    for (auto& num : A) {
+        num /= ratio;
+    }
+}
+
+template<typename T>
+void equalize_row(std::vector<T> const& A, std::vector<T> &B, T ratio) {
+    int32_t n = A.size();
+    for (int32_t i = 0; i < n; i++) {
+        B[i] += A[i]*ratio;
+    }
+}
+
+template<typename T>
+void print_matrix(std::vector<std::vector<T>> const& A) {
+    for (auto const& row : A) {
+        for (auto const& num : row) {
+            std::cout << num << " ";
+        }
+        std::cout << "\n";
+    }
+}
+
+template<typename T>
+T determinant(std::vector<std::vector<T>> A) {
+    T ans = 1;
+
+    int32_t n = A.size();
+    for (int32_t i = 0; i < n; i++) {
+        int32_t best = i;
+
+        for (int32_t j = i+1; j < n; j++) {
+            if (abs(A[best][i]) < abs(A[j][i])) {
+                best = j;
+            }
+        }
+
+        if (best != i) {
+            ans = -ans;
+            std::swap(A[best], A[i]);
+        }
+
+        ans *= T(A[i][i]);
+        divide_row<T>(A[i], A[i][i]);
+
+        for (int32_t j = i+1; j < n; j++) {
+            equalize_row<T>(A[i], A[j], -A[j][i]);
+        }
+    }
+
+    for (int32_t i = 0; i < n; i++) {
+        ans *= A[i][i];
+    }
+
+    return ans;
+}
+
+int main() {
+    using rational = mpq_class;
+
+    int32_t n;
+    std::cin >> n;
+
+    auto M = std::vector<std::vector<rational>>(n, std::vector<rational>(n));
+    for (auto& row : M) {
+        for (auto& x : row) {
+            std::cin >> x;
+        }
+    }
+
+    auto x = determinant<rational>(M);
+
+    std::cout << x << "\n";
+}