1. Implement the Forward algorithm in Python. Your task is to write code for the following prototype: def Forward(A,B,Pi,O) : Evaluation of Discrete Models Instructions return forwardProbability # P(O|^) Test this implementation using the hand-calculated results for question 1. The results produced by your Python code must match the hand-calculated results. Create your own 3 observation vector and calculate P(O|2) by hand. Test your forward algorithm implementation using this vector. The results produced by your code must match the hand- calculated results. 4. Create an observation vector of at least 7 elements. Test your forward algorithm using this vector. 2. 3.

1. Consider the following dynamic programming implementation of the Knapsack problem:   #include int find_max(int a, int b) {       if(a > b)          return a;       return b; } int knapsack(int W, int *wt, int *val,int n) {      int ans[n + 1][W + 1];      int itm,w;      for(itm = 0; itm <= n; itm++)          ans[itm][0] = 0;      for(w = 0;w <= W; w++)         ans[0][w] = 0;      for(itm = 1; itm <= n; itm++)      {           for(w = 1; w <= W; w++)           {                if(wt[itm - 1] <= w)                   ans[itm][w] = ______________;                else                   ans[itm][w] = ans[itm - 1][w];           }      }      return ans[n][W]; } int main() {      int w[] = {10,20,30}, v[] = {60, 100, 120}, W = 50;      int ans = knapsack(W, w, v, 3);      printf("%d",ans);      return 0; }   Which of the following lines completes the above code? A. find_max(ans[itm – 1][w – wt[itm – 1]] + val[itm – 1], ans[itm – 1][w]) B. find_max(ans[itm – 1][w –…

Write the PYTHON programming to solve with breadth-first search and build node-arcs with python code for the attached problem:

We can implement requests to the waiter as either a queue of requests or as a periodic retry of a request. With a queue, requests are handled in the order they are received. Th e problem with using the queue is that we may not always be able to service the philosopher whose request is at the head of the queue (due to the unavailability of resources). Describe a scenario with 5 philosophers where a queue is provided, but service is not granted even though there are forks available for another philosopher (whose request is deeper in the queue) to eat.If we implement requests to the waiter by periodically repeating our request until the resources become available, will this solve the problem described in the above Exercise? Explain.

All businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs.  This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions: There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it. One car arrives at the entrance every 10 seconds.  It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars.  Written in java, Your Tasks:  Design class CarInLine, with the following specifications: The class has two instance variables: arrivalTime and DepartureTime, stored as integers. Define a constructor that accepts an integer as an argument representing the arrival time, in…