132 lines
4.8 KiB
Plaintext
132 lines
4.8 KiB
Plaintext
//¾ØÕóÀà
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template<typename T> struct mat {
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vector<T> a; int h, w;
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mat(): a(), h(), w() {}
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mat(const mat &v): a(v.a), h(v.h), w(v.w) {}
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mat(const int &_h, const int &_w): a(_h * _w), h(_h), w(_w) { }
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void init() { a.clear(); a.resize(h * w); }
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static mat e(const int &_h, const int &_w) {
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mat res(_h, _w);
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for (int i = 0, n = min(_h, _w); i < n; i++) { res[i][i] = 1; }
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return res;
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}
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static mat e(const mat &b) { return e(b.h, b.w); }
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T *operator[](const int &v) { return &a[v * w]; }
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const T *operator[](const int &v)const { return &a[v * w]; }
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mat &operator+=(const mat &b) {
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for (int i = 0, n = h * w; i < n; i++) { a[i] += b.a[i]; }
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return *this;
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}
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mat &operator-=(const mat &b) { return *this += -b; }
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mat &operator*=(const mat &b) {
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mat c(h, b.w);
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for (int i = 0; i < h; i++) {
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for (int k = 0; k < w; k++) {
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const T &tmp = (*this)[i][k];
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if (isZero(tmp)) { continue; }
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for (int j = 0; j < b.w; j++) { c[i][j] = (c[i][j] + tmp * b[k][j])/*%M*/; }
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}
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}
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swap(a, c.a); h = c.h; w = c.w; return *this;
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}
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mat operator-()const {
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mat ret(*this);
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for (int i = 0, n = h * w; i < n; i++) { ret.a[i] = -ret.a[i]; }
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return ret;
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}
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mat operator+(const mat &b)const { return mat(*this) += b; }
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mat operator-(const mat &b)const { return mat(*this) -= b; }
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mat operator*(const mat &b)const { return mat(*this) *= b; }
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mat operator^(const ll &v)const {
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mat ret(e(*this)), t(*this);
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for (ll b = v; b; b >>= 1) { if (b & 1) { ret *= t; } t *= t; }
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return ret;
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}
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bool operator==(const mat &b)const {
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if (h != b.h || w != b.w) { return false; }
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for (int i = 0, n = h * w; i < n; i++) { if (!isZero(a[i] - b.a[i])) { return false; } }
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return true;
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}
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bool operator!=(const mat &b)const { return !(*this == b); }
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T abs(const T &v)const { return v < 0 ? -v : v; }
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bool isZero(const T &v)const { return abs(v) < 1e-9; }
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void input() { for (int i = 0, n = h * w; i < n; i++) { scanf("%I64d", &a[i]); } }
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void print()const {
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for (int i = 0, n = h * w; i < n; i++) { printf("%I64d%c", a[i], i % w == w - 1 ? '\n' : ' '); }
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}
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mat trans()const {
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mat ret(w, h);
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for (int i = 0; i < w; i++) { for (int j = 0; j < h; j++) { ret[i][j] = a[j][i]; } }
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return ret;
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}
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//ÇóÄæ¾ØÕó ÏÞdouble ¿ÉÄæÔò·µ»Øtrue ½á¹ûÔÚ²ÎÊývÖÐ
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bool inv(mat &v)const {
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if (h != w) { return false; }
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int is[N], js[N]; v = *this;
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for (int k = 0; k < h; k++) {
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double t = 0;
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for (int i = k; i < h; i++) {
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for (int j = k; j < h; j++) {
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if (abs(v[i][j]) > t) { t = abs(v[is[k] = i][js[k] = j]); }
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}
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}
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if (isZero(t)) { return false; }
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if (is[k] != k) { for (int j = 0; j < h; j++) { swap(v[k][j], v[is[k]][j]); } }
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if (js[k] != k) { for (int i = 0; i < h; i++) { swap(v[i][k], v[i][js[k]]); } }
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v[k][k] = 1.0 / v[k][k];
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for (int j = 0; j < h; j++) { if (j != k) { v[k][j] *= v[k][k]; } }
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for (int i = 0; i < h; i++) {
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if (i != k) { for (int j = 0; j < h; j++) { if (j != k) { v[i][j] -= v[i][k] * v[k][j]; } } }
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}
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for (int i = 0; i < h; i++) { if (i != k) { v[i][k] *= -v[k][k]; } }
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}
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for (int k = h - 1; k >= 0; k--) {
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for (int j = 0; j < h; j++) { if (js[k] != k) { swap(v[k][j], v[js[k]][j]); } }
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for (int i = 0; i < h; i++) { if (is[k] != k) { swap(v[i][k], v[i][is[k]]); } }
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}
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return true;
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}
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//ÇóÐÐÁÐʽģM ÐèÄæÔª
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ll detmod()const {
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if (h != w) { return 0; }
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ll res = 1; mat c(*this);
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for (int i = 0; i < h; i++) {
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for (int j = 0; j < h; j++) { c[i][j] = (c[i][j] % M + M) % M; }
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}
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for (int i = 0; i < h; i++) {
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for (int j = i; j < h; j++) {
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if (c[j][i] != 0) {
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for (int k = i; k < h; k++) { swap(c[i][k], c[j][k]); }
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if (i != j) { res = (-res + M) % M; }
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break;
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}
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}
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if (c[i][i] == 0) { res = -1; break; }
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for (int j = i + 1; j < h; j++) {
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//int mul = (c[j][i] * Inv[c[i][i]]) % M; //´ò±íÄæÔª
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ll mul = (c[j][i] * inv(c[i][i], M)) % M;
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for (int k = i; k < h; k++) { c[j][k] = (c[j][k] - (c[i][k] * mul) % M + M) % M; }
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}
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res = (res * c[i][i]) % M;
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}
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return res;
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}
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//ÇóÐÐÁÐʽ ÏÞdouble
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double det()const {
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if (h != w) { return 0; }
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int sign = 0; double ret = 1.0; mat c(*this);
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for (int i = 0, j, k; i < h; i++) {
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if (isZero(c[i][i])) {
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for (j = i + 1; j < h && isZero(c[j][i]); j++);
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if (j == h) { return 0; }
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for (k = i; k < h; k++) { swap(c[i][k], c[j][k]); }
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sign++;
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}
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ret *= c[i][i];
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for (k = i + 1; k < h; k++) { c[i][k] /= c[i][i]; }
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for (j = i + 1; j < h; j++) { for (k = i + 1; k < h; k++) { c[j][k] -= c[j][i] * c[i][k]; } }
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}
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return sign & 1 ? -ret : ret;
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}
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};
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