Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 4.1, Problem 1E
Program Plan Intro
To find the elements of array
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illustrate the operation of BUCKET-SORT on the ten-elementarray A = {0.22, 0.93, 0.08, 0.94, 0.91, 0.40, 0.48, 0.03, 0.23, 0.35}.
When we apply the mergesort on a 12-element array, how many comparisons do we need for the worst case? Ans:
Run mergesort for large random arrays, and make an empirical determination of the average length of the other subarray when the first subarray exhausts, as a function of N (the sum of the two subarray sizes for a given merge).
Chapter 4 Solutions
Introduction to Algorithms
Ch. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5E
Ch. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6P
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- Use elements of {[0,0,0] [0,0,1] [ 1,0,2]} and write a SciPy program for Spare Matrix.arrow_forwardQUESTION 5 Given A=(nez: In| <2} and B-P(A), how many permutations of the elements in B start with (1 )? Answer:arrow_forwardWhat is the worst case time complexity for binary search on a BST with n elements? Explainarrow_forward
- For x[5] = {1,2,3,4,5}, use cout << x; in order to show all elements of x?arrow_forwardWhy doesn't SparseVector's dot() function accept a SparseVector object as a parameter and return a SparseVector object?arrow_forwardRun mergesort for huge random arrays and determine empirically, as a function of N (the total of the two subarray sizes for a given merge), the average length of the other subarray when the first subarray exhausts.arrow_forward
- Q6: Find result of adding (A38), and (1356)o?arrow_forwarduse change of variable to solve this recurrence . find the best case for quick sort .arrow_forwarddef weighted_mse_grad(w, X, y, V):"""Calculate gradient of the weight MSE loss in the given point w Parameters----------w: array_likeCurrent point, in which we want to evaluate gradient (vector with k+1 elements)X: array_likeDesign matrix with N rows and k+1 columnsy: array_likeVector with N observations of the target variableV: array_likeDiagonal matrix N x N, with the weightsReturns----------out: ndarrayvector of gradient, k+1"""# your code here # TEST weighted_mse_grad()w = np.zeros(5)X = np.random.randn(10, 5)y = np.ones(10)V = np.diag(np.ones(10)) L_grad = weighted_mse_grad(w, X, y, V)assert(L_grad.shape == (5,)) w = np.zeros(5)X = np.eye(5)y = np.ones(5)V = np.diag(np.ones(5))L_grad = weighted_mse_grad(w, X, y, V)assert(L_grad.shape == (5,)), 'The shape of the output on the test case is wrong'assert(np.allclose(5 * L_grad,- y * 2)), 'The values of the output on the test case is wrong'arrow_forward
- What is the obvious limit-to the problem of finding the median of a given array of n-elements? Is this obvious lower bound a TIGHT lower bound, why?arrow_forwardYou are running radix sort (base 10) on values 123, 322, 311, 332, 312, 132, 213, 321, 323. Unfortunately, the counting-sort implementation that your radix-sort calls is "anti-stable", that is, in case of a tie, it always reverses the order of two keys. What is the final order you get? Show the array after each pass.arrow_forwardConsider ID as an array of 9 elements,Please follow this ID (201920090) in this solution for importance and only solve the part (d, e, f), thanks.arrow_forward
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