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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Question
Chapter 8.3, Problem 5E
Program Plan Intro
To find the number of sorting passes needed to sort d digit decimal number in the worst case. Also, find the number of piles of cards for an operator to keep track of in the worst case.
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Chapter 8 Solutions
Introduction to Algorithms
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- Design a top-down algorithm (based on dynamic programming and recursion; i.e. memory function) for checking the existence of a winning strategy for the “Rocks” game. Hints: • Give it the name: RocksMF(n,m) where n,m are the number of rocks on the two piles • Use recursion to call the algorithm itself to solve smaller subproblems • Use a global variable for the two-dimensional tablearrow_forwardStarting with the first Fibonacci number, Fib(1) = 1, and the second Fibonacci number, Fib(2) = 1, what is the sum of Fib(8) and Fib(10)?arrow_forwardA task is given to generate matrix A from matrix B. 1 200 000 01 340 0 000 0 001 20 0 0 0 0 03 4 00 00 000 1 20 0 0 00340 0 000 0 0 1 2 B = 0 0 0 Lo 0 0 0 0 0 3 4 However, the program generates inaccurate matrix A where you need to debug. Analyze the program below to debug the syntax errors or violations of rules. Copy the Table Q4(b) and Paste it into your answer script. Replace with the corrected codes. Line No Program Codes 1 int n = 2; int B[n] = {{1, 2}, {3, 4}}; int P= 5; int A[2*P] [2*P] = {}; int col, row, j; for (int block = 0; block <= P; block++) ( (b) A = 13 2 3 4 5 6 7 8 9 coln (block+1) n; //col = 0, 2, 4, 6 row col; 10 11 for (int ii = 0; ii <= n; ii++) 12 ( 13 for (int jj = 0; jj <-(n-1); jj++) 14 { 15 16 } 17 18 Line No. Corrections A[row+ii] [col+jj] = B[ii+1] [jj+1]; Table Q4(b):arrow_forward
- 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?arrow_forwardInstrument FrequencyCounter to use Stopwatch and StdDraw to make a plot where the x-axis is the number of calls on get() or put() and the y-axis is the total running time, with a point plotted of the cumulative time after each call. Run your program for Tale of Two Cities using SequentialSearchST and again using BinarySearchST and discuss the results. Note : Sharp jumps in the curve may be explained by caching, which is beyond the scope of this question.arrow_forwardThe 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! public class BinaryExplorer { public static void main(String[] args) {int[] testArray = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; binaryRec(testArray, 8, 0, testArray.length - 1); } /*** Add Print statements to the binaryRec method:* * Print Starting, ending, and midpoint values.* * Print when you find a match* * Print if you are…arrow_forward
- 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!arrow_forwardCarl is sitting in a chair that is next to a table. Carl’s cell phone is on top of the table. Your task is to direct Carl to pick up his cell phone. Does the solution to this problem require a repetition structure? If so, what needs to be repeated?arrow_forwardFrom a list of participants’ ids, find which id is missing from the list. The participant ids sorted in ascending order with a certain difference. Output explanation: the difference for each id is 12, from the list the missing number Is 120073 which is after 120061 and before 120085. Design an algorithm using C language! (PS: use divide and conquer algorithm)arrow_forward
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