CP-codes/Math/matrix_expo.cpp at master · hemant2132/CP-codes · GitHub

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/*
    -> Matrix Exponentiation
    -> ref: http://zobayer.blogspot.com/2010/11/matrix-exponentiation.html
    -> further reading:
        1. https://codeforces.com/blog/entry/43225
        2. https://codeforces.com/blog/entry/80195
*/

const int SZ = 4;

void display(int mat[SZ][SZ]) {
    for (int i = 0; i < SZ; ++i) {
        for (int j = 0; j < SZ; ++j)
            cout << mat[i][j] << " ";
        cout << "\n";
    }
}

void multiply(int a[SZ][SZ], int b[SZ][SZ]) {
    int res[SZ][SZ];
    for (int i = 0; i < SZ; ++i) {
        for (int j = 0; j < SZ; ++j) {
            res[i][j] = 0;
            for (int k = 0; k < SZ; ++k)
                res[i][j] = add(res[i][j], mul(a[i][k] % MOD, b[k][j] % MOD));
        }
    }

    for (int i = 0; i < SZ; ++i) {
        for (int j = 0; j < SZ; ++j)
            a[i][j] = res[i][j];
    }
}

void power(int x[SZ][SZ], int n) {
    int res[SZ][SZ];
    mem(res, 0);

    for (int i = 0; i < SZ; ++i)
        res[i][i] = 1;

    for (; n; n /= 2) {
        if (n % 2)
            multiply(res, x);

        multiply(x, x);
    }

    for (int i = 0; i < SZ; ++i) {
        for (int j = 0; j < SZ; ++j)
            x[i][j] = res[i][j];
    }
}

int NthTerm(int n) {
    if (n == 0) return 1;
    if (n == 1) return 2;

    //transformation matrix
    int trans[SZ][SZ] = {};

    //initial case
    int base[SZ][1] = {};

    power(trans, n - 1);

    int res = 0;
    for (int i = 0; i < SZ; ++i)
        res = add(res, mul(trans[0][i], base[i][0]));

    return res;
}