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 6.1, Problem 6E
Program Plan Intro
To decide whether the array with values
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numpy array([[-13,-38,22,-41,25], [-45,29,14,-34,-49], [26,21,-44,-25,0], [-30,-32,34,-39,-22], [-21,-36,0,18,37], [37,44,46,36,-37]])
extract the slices [[-30,-32,34,-39,-22], [-45,29,14,-34,-49], [-21,-36,0,18,37]]
extract the elements [25,34,46,-36]
extract the slices [14,-34,-49], [-44,-25,0], [34,-39,-22]
Mean of the numbers in each array of the first dimension
Sample standard deviation of numbers in each index position of the second dimension
Use a mask to find the mean of the negative numbers in the array
Prove that:
In the resizing array implementation of Stack the average number of array accesses for any sequence of operations starting from an empty data structure is constant in the worst case
Given the array:
63 53 86 35 99 34 75
Heapify into a max-heap.
Ex: 86, 75, 30
Chapter 6 Solutions
Introduction to Algorithms
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3E
Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3P
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- Python Fit a cubic to the following data set: x = array([ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.]) y = array([ -23.01372758, -98.68128886, -193.98575465, -278.72527151, -323.22426954, -298.42667233, -172.78799319, 82.63979118, 497.75672707, 1101.55912648]) What is the best-fit value of the y-intercept of this curve (i.e., the constant term in the polynomial)? Give your answer to at least eight decimal places.arrow_forwardPut the elements on the stack S in ascending order using one additional stack and some additional non-array variables.arrow_forwardShow that: In Stack's implementation of resizing arrays, the worst-case scenario average number of array accesses for any sequence of actions beginning with an empty data structure is constant.arrow_forward
- Study the function matrix_mult that takes two 2D arrays and performs a matrix multiplication and returns a new two-dimensional array. Each array should be represented as a list of lists. For example, A = [[1, 2, 3], [-2, 3, 7]] B = [[1,0,0],[0,1,O],[0,0,1]] matrix_mult(A, B) [[1, 2, 3], [-2, 3, 7]] Identify all lines that are in error - that is, select all answers that are correct. def matrix_mult(A, B): A_n = len(A) A_m = len(A[0]) B_n = len(B) B_m = len(B[0]) assert A_m = B_n R_n = A_n 1. 2. 3. 4. 5. 6. 7. 8. R_m = B_m R = [[0 for j in range (R_m)] fori in range(R_n)] def row(M, r): return v[c] for v in M def col(M, c): return M[r] def dot(v1, v2): return sum([x*y for x, y in zip(v1, v2)]) for i in range(R_n): for j in range (R_m): R[i][j] - dot(row(A,i), col(8,j)) return R 9. 10. 11. 12. 13. 14.arrow_forwardLet S be a stack with the following elements, 6,13,15,17,35,45,20,55. Implement the stack using an Array and Linked-listarrow_forwardData Structures and Algorithms is a course that teaches students about data structures and algorithms. Explain why you chose the choice. The worst-case scenario for deletion time complexity in an array-based stack is The letter O (log2 n) O. b. (n) o (1) d. None of the precedingarrow_forward
- You are going to be asked to make a singly-linked list of singly-linked lists. How are you designing your data structure to best facilitate this design? Be sure to explain how the data is internally stored within your linked list of linked lists. (PI 1.1/ABET[1], PI 6.1/ABET[6]) #Pythonarrow_forwardYou're given an array A[1...7] Heap-Insert(A, 8), what is the resulting A? (9, 7, 6, 4, 1, 5, 3). If you execute Max-arrow_forwardGiven array: (31,-1,-42, -77, 272) What is the array before the negative and non-negative buckets are built? (Ex: 1, 2, 3 After reversal, what integers are in the negative bucket?arrow_forward
- A := Matrix([[5, 3, 3, 1, 9, 1, 7, 4, 9, 3, 9], [4, 2, 9, 8, 7, 4, 7, 3, 9, 9, 3], [7, 9, 1, 6, 4, 5, 3, 6, 9, 7, 6], [5, 7, 9, 6, 6, 7, 2, 7, 5, 2, 3], [4, 8, 2, 1, 8, 8, 6, 7, 8, 4, 7], [6, 4, 6, 3, 1, 9, 7, 1, 3, 4, 2], [4, 8, 1, 2, 7, 2, 7, 4, 5, 2, 4], [5, 9, 6, 6, 2, 1, 5, 6, 5, 6, 7], [2, 9, 7, 9, 2, 7, 5, 7, 5, 7, 4], [8, 4, 8, 6, 8, 3, 6, 9, 9, 9, 1]]); This is the code. Thank u!arrow_forwardImplement an Array-Based ADT Stack and verify "isEmpty()", "isFull()" , "push()", "pop()", "popAll()", and "peak()" operations.arrow_forwardConsider an array: 4,2,9,1,7,8,6,3,5. Show all the steps of Heap sort.arrow_forward
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