A short description of your algorithm, where you explain the dynamic programing approach (see the sketch of the Algorithm below). More precisely, you need to indicate how you compute d[0] (this is the initialization step), and how you compute for every i ≥ 1, the value of d[i] using the values of some of the previous d[j]'s, for j
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- The Binary Search algorithm works by testing a mid-point, then eliminating half of the list. In this exercise, you are going to take our binary search algorithm and add print statements so that you can track how the search executes. Inside of the recursive binary search function, add print statements to print out the starting, ending, and midpoint values each time. Then as you test a value, print out the results, either too high, too low, or a match. Sample Output Starting value: 0 Ending value: 9 Testing midpoint value: 4 Too high! Starting value: 0 Ending value: 3 Testing midpoint value: 1 Too low! Starting value: 2 Ending value: 3 Testing midpoint value: 2 Match!Flip a fair coin repeatedly until you get two heads in a row (HH). What is the probability of getting HH in at-most N (N > 1) tosses? Can you write a recursive function and implementation to calculate the probability?Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. Sierpinski.java When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle with the specified side length. public static double height(double length) // Draws a filled equilateral triangle with the specified side length // whose bottom vertex is (x, y). public static void filledTriangle(double x, double y, double length) // Draws a Sierpinski triangle of order n, such that the largest filled //…
- 1. Analyze the word finder with wild card characters scenario to form the algorithm and compute the time complexity. You are given a list of characters with size n, m. You need to read character data provided as input into this list. There is also a list of p words that you need to find in the given problem. You can only search in left, right, up and down direction from a position. There are two wild characters *' and '+' ,if there is any instance of wild card characters for example '+' appears you can match whatever character in your word that you are searching at this position (only one character). Similarly, if you got wildcard *' you can skip any number of characters ( A sequence of characters not necessary same in between the characters) but the last character should be matched in the given data. This means you are not allowed to match a first and last character with *' wildeard. Input: The first line of the input will give you two integers n and m. From the next line you will get…I need to write a recursive program to count the number of muck-free regions in a lagoon. The Lagoon is represented by a rectangle of N x M squares. Each square contains either muck ('M') or sand ('.'). A region is defined as a connected set of one of more squares with sand in it, where a square is considered to connect to all eight of its adjacent squares. Sample input/output is shown in picture attachedWrite in python programming language: The Longest Subsequence Problem is a well-studied problem in Computer Science, where given a sequence of distinct positive integers, the goal is to output the longest subsequence whose elements appear from smallest to largest, or from largest to smallest. For example, consider the sequence S= [9,7,4,10,6,8,2,1,3,5]. The longest increasing subsequence of S has length three ([4,6,8] or [2,3,5]), and the longest decreasing subsequence of S has length five([9,7,4,2,1] or [9,7,6,2,1]). And if we have the sequence S = [531,339,298,247,246,195,104,73,52,31], then the length of the longest increasing subsequence is 1 and the length of the longest decreasing subsequence is 10. Question: Find a sequence with nine distinct integers for which the length of the longest increasing subsequence is 3, and the length of the longest decreasing subsequence is 3. Briefly explain how youconstructed your sequence. Let S be a sequence with ten distinct integers. Prove by…
- The next question has to do with a bisection process, which is very common in mathematical software. For example, the bisection method for finding a root of a function starts with an interval, [a, b], where f(a) and f(b) have different signs. It then computes the midpoint of the interval, c = (a + b) / 2. It then replaces either a or b by c so that the signs of the new f(a) and f(b) are still different, thus guaranteeing that the new interval [a, b], which is either the left or right half of the previous interval, still brackets a root. In the next 2 questions, assume B = 2 and p = 24. 13. If a = 1 and b = 2, how many times can bisection occur before there are no floating-point numbers in the interval (a, b) (in other words, a and b are adjacent floating-point numbers)?I need to write a recursive Java program to count the number of muck-free regions in a lagoon. The Lagoon is represented by a rectangle of N x M squares. Each square contains either muck ('M') or sand ('.'). A region is defined as a connected set of one of more squares with sand in it, where a square is considered to connect to all eight of its adjacent squares. Sample input/output is shown in picture attachedPlease do this in JAVA PROGRAMMING. Given: List L of pairs of charactersString SOutput: TRUE if S is a valid string, FALSE otherwise. A string is considered valid if each character in the string can be paired with another character in the string, where the pair belongs to the input list L. Furthermore, two pairs cannot cross each other. In other words, a pair most completely enclose another, or be completely separate. Design and implement an efficient dynamic programming solution to this problem. Examples: Input L: (a b) (b c) (c d) (a a) Input S: aaba Output: True (pairs shown color-coded: aaba, "aa" fully encloses "ab") Input L: (a b) (b c) (c d) (a a) Input S: abcaad Output: True (pairs shown color-coded: abcaad, "ab" is separate from the other pairs) Input L: (a b) (b c) (c d) (a a) Input S: acbd Output: False (acbd is not valid because the pairs cross each other.) Input L: (a b) (b c) (c d) (a a) Input S: aaac Output: False
- In python, Problem Description:Sheldon and Leonard are physicists who are fixated on the BIG BANG theory. In order to exchange secret insights they have devised a code that encodes UPPERCASE words by shifting their letters forward. Shifting a letter by S positions means to go forward S letters in the alphabet. For example, shifting B by S = 3 positions gives E. However, sometimes this makes us go past Z, the last letter of the alphabet. Whenever this happens we wrap around, treating A as the letter that follows Z. For example, shifting Z by S = 2 positions gives B. Sheldon and Leonard’s code depends on a parameter K and also varies depending on the position of each letter in the word. For the letter at position P, they use the shift value of S = 3P + K. For example, here is how ZOOM is encoded when K = 3. The first letter Z has a shift valueof S = 3 × 1 + 3 = 6; it wraps around and becomes the letter F. The second letter, O, hasS = 3 × 2 + 3 = 9 and becomes X. The last two letters…Let n be a positive integer and let MaxCrossing(n) be a function that returns the maximum number of line crossings that you can create by drawing n straight lines. Write down a recursive formula for MaxCrossing(n) and analyze the time complexity of the corresponding recursive algorithm. You must write a formal recursive formula including the base case and general recursive step.I just need the method they are asking for Write a recursive function that takes a start index, array of integers, and a target sum. Your goal is to find whether a subset of the array of integers adds up to the target sum. The start index is initially 0.A target sum of 0 is true for any array. Examples: subsetSum(0, {2, 4, 8}, 10) -> true public boolean subsetSum(int start, int[] nums, int target) { }