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- 10. Apply Djikstra's Algorithm to find a shortest path from A to Z. Be sure to show each step of the algoriothm on a separate picture as discussed in class. Work carefully and pay attention to details. You need to clearly show how you are applying the algorithm. Also be sure to clearly name the verticies of a final shortest path BGiven is a strictly increasing function, f(x). Strictly increasing meaning: f(x)< f(x+1). (Refer to the example graph of functions for a visualization.) Now, define an algorithm that finds the smallest positive integer, n, at which the function, f(n), becomes positive. The things left to do is to: Describe the algorithm you came up with and make it O(log n).**MATLAB** Write a MATLAB program to generate and plot a Bezier curve. Construct the pro- ´ gram so that it accepts sets of control points as N × 2 matrices. The first and second columns of the matrix should correspond to the x- and y-coordinates of the control points. The program should be able to handle the cases N = 3, 4, and 5.
- I am trying to work with some generic search algorithms in a coding homework, and I am having trouble understanding some of it. Here are my questions: 1. For this linear search algorithm below I am trying to send an array of x and y cordinate points into it and search to see if a specific x, y point is in the array, but I don't know how to send the points into the linear search function. By the way, I am using a struct point type for the array of points and the point I am looking for. (The below code is an exact example from our teacher during a lecture.) void* linearSearchG(void* key, void* arr, int size, int elemSize, int(*compare)(void* a, void* b)) { for (int i = 0; i < size; i++) { void* elementAddress = (char*)arr + i * elemSize; if (compare(elementAddress, key) == 0) return elementAddress; } return NULL; } 2. I forgot what this line of code specifically does: void* elementAddress = (char*)arr + i * elemSize; I need to code this myself, so if you could explain…You are given a 2 by n grid, where the cell on row i column j contains a non-negative number ai,j . You can start at either cell in the lefttmost column, and your goal is to reach either cell in the rightmost column by a sequence of moves. You can move to an adjacent cell (if it exists) in each of the 4 cardinal directions (up,down, left and right). A path achieves a score equal to the sum of values in its cells. Note that a cell which is used twice in a path only counts its value once to the score of that path.Design an algorithm which runs in O(n) time and finds a path of minimum score from the leftmost column to the rightmost column.Q. Given a 2d grid map of '1's (land) and '0's (water),count the number of islands.An island is surrounded by water and is formed byconnecting adjacent lands horizontally or vertically.You may assume all four edges of the grid are all surrounded by water. Example 1: 11110110101100000000Answer: 1 Example 2: 11000110000010000011Answer: 3""" def num_islands(grid): count = 0 for i in range(len(grid)): for j, col in enumerate(grid[i]): if col == 1: dfs(grid, i, j) count += 1 Please code it. .
- 5. You are given a set of n positive numbers A = {a₁,..., an} and a positive integer t. Design a dynamic programming algorithm running in O(nt) time that decides whether there exists a subset A' CA such that Σ x = t. Note that each element of A can be xЄA' used at most once. Is the run-time of your algorithm polynomial with respect to the size of the input?Help the lazy mountain climber. Assume that a mountain climber wants to cross a mountain range by limiting the change in elevation (i.e., the climber does not want to climb up or down more often than necessary). The elevation of the terrain is given in a m by n matrix. The climber needs to start in the first column and end in the last column. Each move can be to the right, to the right and up, or to the right and down. Construct an algorithm to determine the minimum change in altitude that is possible for crossing the mountain range. State the time efficiency of your approachSuppose that you have a maze search problem. From each numbered square in the maze, youmay move that exact number of squares horizontally or vertically in a straight line. Startingat a particular square (e.g. the top-left corner), find a path to the goal square marked "G".3 4 1 3 1 3 3 3 G 2 3 1 2 2 3 4 2 3 3 3 4 1 4 3 2 Describe the State Space components of this problem. Then solve the problem using breadthirst search and the depth first search. Hint: Indicate the changes to the Open and ClosedQueues in solving this problem for each type of search.
- Recall that the dot product of two vectors (1d matrices) produces a scalar value. The dot product is slightly confusing as the scalar value produced can have an arbitrary meaning that simply represents the mathematical operations of multiplying and summing. In other words, the dot product can simply represent the linear projection of vector onto the number line. This interpretation will be used repeatedly throughout machine learning as our main goal will be to take some features dotted with some weights/parameters. Once again, this can be though of as projecting our features onto a number line where the projection acts as our prediction! Keep this idea in mind as it might not make complete sense as of yet. It also important to know that the dot product can additionally take on other meanings such as a geometric meaning which represents how similar any two vectors are when projected onto one another. Meaning, how much one vector points in the direction of another. Given the following…Let f RR be continuous. Which of the following statements about the bisection, secant, and Newton methods is/are correct? If f(a) 0, the error of the bisection method starting from [a, b] decreases exponentially with the number of iterations. For a starting interval [a, b], the bisection method fails if f(a) > f(b). If initialized sufficiently close to a simple root of a smooth (infinitely differentiable) function, the order of convergence of the secant method is approximately 1.618. The secant method cannot be applied with a starting interval [a, b] such that f(a) = f(b). The order of convergence of the Newton method is 1. If f is smooth (infinitely differentiable) on the starting interval [a, b] and contains exactly one root x Є [a, b], then the bisection method will converge to this root. If f contains exactly one root in the starting interval [a, b] with ƒ(a)f (b) < 0, then the secant method will converge to this root.Write a python code that implements the Forward Euler method to solve thedifferential equation. The slope function depends on the unknown solution y(t). Define your slope function so that the model parameters, b, PM, h areinput variables in your function definition. Complete your code by writing a loop that calculates the solution foreach time point and can plot your final approximate solution.