Compute det in inv

Author: adamant-pwn

cp-algo/linalg/matrix.hpp

@@ -182,16 +182,18 @@ namespace cp_algo::linalg {
             return res;
         }
 
-        std::optional<matrix> inv() const {
+        std::pair<base, matrix> inv() const {
             assert(n() == m());
             matrix b = *this | eye(n());
             if(size(b.echelonize<reverse>(n())[0]) < n()) {
-                return std::nullopt;
+                return {0, {}};
             }
+            base det = 1;
             for(size_t i = 0; i < n(); i++) {
+                det *= b[i][i];
                 b[i] *= base(1) / b[i][i];
             }
-            return b.submatrix(std::slice(0, n(), 1), std::slice(n(), n(), 1));
+            return {det, b.submatrix(std::slice(0, n(), 1), std::slice(n(), n(), 1))};
         }
 
         // Can also just run gauss on T() | eye(m)

verify/linalg/adj.test.cpp

@@ -24,12 +24,11 @@ void solve() {
         A[i][n] = cp_algo::random::rng();
         A[n][i] = cp_algo::random::rng();
     }
-    auto Ai = A.inv();
-    auto D = A.det();
+    auto [D, Ai] = A.inv();
     for(int i: views::iota(0, n)) {
         for(int j: views::iota(0, n)) {
             if(D != 0) {
-                auto res = (*Ai)[n][n] * (*Ai)[i][j] - (*Ai)[i][n] * (*Ai)[n][j];
+                auto res = Ai[n][n] * Ai[i][j] - Ai[i][n] * Ai[n][j];
                 cout << res * D << " \n"[j + 1 == n];
             } else {
                 cout << 0 << " \n"[j + 1 == n];

verify/linalg/inv.test.cpp

@@ -15,11 +15,11 @@ void solve() {
     cin >> n;
     matrix<modint<mod>> a(n, n);
     a.read();
-    auto ai = a.inv();
-    if(!ai) {
+    auto [d, ai] = a.inv();
+    if(d == 0) {
         cout << -1 << "\n";
     } else {
-        ai->print();
+        ai.print();
     }
 }
 

verify/linalg/tutte.test.cpp

@@ -32,17 +32,17 @@ void solve() {
             B[i][j] = T[pivots[i]][pivots[j]];
         }
     }
-    B = *B.inv();
+    auto [d, Bi] = B.inv();
     vector<pair<int, int>> ans;
     for(size_t i = 0; i < size(pivots); i++) {
         for(size_t j = 0; j < size(pivots); j++) {
-            if(T[pivots[i]][pivots[j]] != 0 && B[i][j] != 0) {
+            if(T[pivots[i]][pivots[j]] != 0 && Bi[i][j] != 0) {
                 ans.emplace_back(pivots[i], pivots[j]);
-                B.eliminate<gauss_mode::reverse>(i, j);
-                B.eliminate<gauss_mode::reverse>(j, i);
-                B.normalize();
-                B[i] *= 0;
-                B[j] *= 0;
+                Bi.eliminate<gauss_mode::reverse>(i, j);
+                Bi.eliminate<gauss_mode::reverse>(j, i);
+                Bi.normalize();
+                Bi[i] *= 0;
+                Bi[j] *= 0;
             }
         }
     }