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fix errors in matrix_exponentiation

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Krishna Vedala 2020-06-24 18:27:01 -04:00
parent 46854f516e
commit a190674131
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1 changed files with 26 additions and 29 deletions
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55
others/matrix_exponentiation.cpp
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@ -36,21 +36,18 @@ using std::vector;
#define endl std::endl #define endl std::endl
/*! shorthand definition for `int64_t` */ /*! shorthand definition for `int64_t` */
#define pb push_back #define pb push_back
#define MOD 1000000007 #define MOD 1000000007
/** returns absolute value */ /** global variable mat_size
inline ll ab(ll x) { return x > 0LL ? x : -x; }
/** global variable k
* @todo @stepfencurryxiao add documetnation * @todo @stepfencurryxiao add documetnation
*/ */
ll k; ll mat_size;
/** global vector variables /** global vector variables used in the ::ans function.
* @todo @stepfencurryxiao add documetnation * @todo @stepfencurryxiao add documetnation
*/ */
vector<ll> a, b, c; vector<ll> fib_b, fib_c;
/** To multiply 2 matrices /** To multiply 2 matrices
* \param [in] A matrix 1 of size (m\f$\times\f$n) * \param [in] A matrix 1 of size (m\f$\times\f$n)
@ -59,10 +56,10 @@ vector<ll> a, b, c;
*/ */
vector<vector<ll>> multiply(const vector<vector<ll>> &A, vector<vector<ll>> multiply(const vector<vector<ll>> &A,
const vector<vector<ll>> &B) { const vector<vector<ll>> &B) {
vector<vector<ll>> C(k + 1, vector<ll>(k + 1)); vector<vector<ll>> C(mat_size + 1, vector<ll>(mat_size + 1));
for (ll i = 1; i <= k; i++) { for (ll i = 1; i <= mat_size; i++) {
for (ll j = 1; j <= k; j++) { for (ll j = 1; j <= mat_size; j++) {
for (ll z = 1; z <= k; z++) { for (ll z = 1; z <= mat_size; z++) {
C[i][j] = (C[i][j] + (A[i][z] * B[z][j]) % MOD) % MOD; C[i][j] = (C[i][j] + (A[i][z] * B[z][j]) % MOD) % MOD;
} }
} }
@ -94,24 +91,24 @@ vector<vector<ll>> power(const vector<vector<ll>> &A, ll p) {
ll ans(ll n) { ll ans(ll n) {
if (n == 0) if (n == 0)
return 0; return 0;
if (n <= k) if (n <= mat_size)
return b[n - 1]; return fib_b[n - 1];
// F1 // F1
vector<ll> F1(k + 1); vector<ll> F1(mat_size + 1);
for (ll i = 1; i <= k; i++) F1[i] = b[i - 1]; for (ll i = 1; i <= mat_size; i++) F1[i] = fib_b[i - 1];
// Transpose matrix // Transpose matrix
vector<vector<ll>> T(k + 1, vector<ll>(k + 1)); vector<vector<ll>> T(mat_size + 1, vector<ll>(mat_size + 1));
for (ll i = 1; i <= k; i++) { for (ll i = 1; i <= mat_size; i++) {
for (ll j = 1; j <= k; j++) { for (ll j = 1; j <= mat_size; j++) {
if (i < k) { if (i < mat_size) {
if (j == i + 1) if (j == i + 1)
T[i][j] = 1; T[i][j] = 1;
else else
T[i][j] = 0; T[i][j] = 0;
continue; continue;
} }
T[i][j] = c[k - j]; T[i][j] = fib_c[mat_size - j];
} }
} }
// T^n-1 // T^n-1
@ -119,7 +116,7 @@ ll ans(ll n) {
// T*F1 // T*F1
ll res = 0; ll res = 0;
for (ll i = 1; i <= k; i++) { for (ll i = 1; i <= mat_size; i++) {
res = (res + (T[1][i] * F1[i]) % MOD) % MOD; res = (res + (T[1][i] * F1[i]) % MOD) % MOD;
} }
return res; return res;
@ -133,19 +130,19 @@ int main() {
cin >> t; cin >> t;
ll i, j, x; ll i, j, x;
while (t--) { while (t--) {
cin >> k; cin >> mat_size;
for (i = 0; i < k; i++) { for (i = 0; i < mat_size; i++) {
cin >> x; cin >> x;
b.pb(x); fib_b.pb(x);
} }
for (i = 0; i < k; i++) { for (i = 0; i < mat_size; i++) {
cin >> x; cin >> x;
c.pb(x); fib_c.pb(x);
} }
cin >> x; cin >> x;
cout << ans(x) << endl; cout << ans(x) << endl;
b.clear(); fib_b.clear();
c.clear(); fib_c.clear();
} }
return 0; return 0;
} }