FLOPS of Kalman and particle filters

Consider the following linear Gaussian state space model: $x_k=([1,1$; $0,1])x_{k-1}+q_{k-1}$

$y_k=([1,0])x_k+r_k$

where $x_k=(x_k,x_k^{})$ is the state, $y_k$ is the measurement, and $q_{k}N(0,$diag$(\frac{1}{{10}^2},1^2))$

and $r_{k}N(0,{10}^2)$ are white Gaussian noise processes.

$($a$)$ Write down the Kalman filter equations for this model step$-$by$-$step.

$($b$)$ Derive an expression for the optimal importance distribution for the model step$-$by$-$step:

$(x_k)=p(x_k|x_{k-1},y_{1\text{:}k})$

$($c$)$ Write pseudo$-$code for the corresponding particle filter algorithm $($sequential importance resampling algorithm$)$ step$-$by$-$step. Also write down the equations for the weight update step$-$by$-$step.

$($d$)$ Compare the number of CPU steps $($multiplications and additions$)$ needed by the particle filter and Kalman filter step$-$by$-$step. Which implementation would you choose for a real implementation?