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If there is a problem like this: Give $$$4$$$ integer $$$a, b, c, d$$$ and $$$u_n=au_{n-1}+bv_{n-1}, v_n=cu_{n-1}+dv_{n-1}$$$, we knew $$$u_0, v_0$$$. We need to calculate $$$u_n$$$ with $$$n\le 10^9$$$. This problem can be solved by using matrix exponentiation, we have $$$u_n=(a+d)u_n-(ad-bc)u_{n-1}$$$ with $$$n>1$$$.
sorry for my bad english
Auto comment: topic has been updated by i_loveMaiPhuong (previous revision, new revision, compare).
Auto comment: topic has been updated by i_loveMaiPhuong (previous revision, new revision, compare).