ALGORITHMS Lecture Notes - Erik Demaine, Insertion Sort, Binary Search Algorithm

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oualiyacine1995

24 Oct 2022

School

MIT

Department

Mathematics

Course

ALGORITHMS

Professor

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Document Summary

Instructors: erik demaine, jason ku, and justin solomon. Faster nd min/max (at rst and last index of array) Faster nds via binary search: o(log n) Order find prev(k) delete(k) find max() find next(k) Sorted array n n log n n log n n n n. Sorting: given a sorted array, we can leverage binary search to make an ef cient set data structure, input: (static) array a of n numbers, output: (static) array b which is a sorted permutation of a. Permutation: array with same elements in a different order. Sorted: b[i 1] b[i] for all i {1, . Correct by case analysis: try all possibilities (brute force) Solving recurrences: substitution: guess a solution, replace with representative function, recurrence holds true, recurrence tree: draw a tree representing the recursive calls and sum computation at nodes, master theorem: a formula to solve many recurrences (r03)

Related Questions

1.Create a list that contains 10 successive integers starting with the value in the variable start. For example, if start is 7, the resulting list should be [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. Store the list in a variable named my_list. Assume that the value of start has already been set.

2.Create a list that is made up of the first half of the elements of a list called original_list. Store the new list in a variable called half_list. Assume that the original list has already been initialized and contains an even number of elements.

3. Write a predicate function called same_ends that accepts a list of integers and an integer (n) as arguments. Return True if the first n numbers in the list are the same as the last n numbers in the list, and False otherwise. For example, if the list was [1, 2, 3, 4, 99, 1, 2, 3, 4], the function would return True if n is 4 and False if n is 3. Assume that n is between 1 and the length of the list, inclusive.

4.Write a function called highest_values that accepts as arguments a list of numeric values and a single integer (n). The function should return a list made up of the largest n values from the argument list in order from lowest to highest. For example, if the argument list is [46, 82, 25, 61, 70, 33, 54] and n is 3, the return value should be [61, 70, 82]. Assume that the argument list contains at least n elements.

5.Assume that a list of integers stored in a variable named original contains exactly two elements that are zero. Write code that creates a separate list that contains the elements from original that are between the two zeros. Do not include the zeros in the new list. Store the list in a variable named between_zeros.

6. Write a function called price_range that accepts a list of floating-point numbers representing prices as an argument and returns the the difference between the highest price and the lowest price. Do NOT use the built-in functions max or min in your solution. Assume that all prices are positive values and that none of them exceed 10,000.00.

7. Write a function called count_vowels that accepts a string argument that represents a word and returns the number of vowels that are in the word. The vowels are A, E, I, O, and U (ignore the 'sometimes Y' rule). Count both uppercase and lowercase vowels.

Assume that the variable table holds a two-dimensional list of integers. Write code that computes the sum of all elements in the table, assigning the result to the variable table_sum.

emeraldhorse214

you have the following statements define the class dataType.h to implement the date in a program:

class dateType

{

public:

void setDate(int month, int day, int year);

//Function to set the date.

//The member variables dMonth, dDay, and dYear are set

//according to the parameters

//Postcondition: dMonth = month; dDay = day;

// dYear = year

int getDay() const;

//Function to return the day.

//Postcondition: The value of dDay is returned.

int getMonth() const;

//Function to return the month.

//Postcondition: The value of dMonth is returned.

int getYear() const;

//Function to return the year.

//Postcondition: The value of dYear is returned.

void printDate() const;

//Function to output the date in the form mm-dd-yyyy.

bool isLeapYear();

//Function to determine whether the year is a leap year.

dateType(int month = 1, int day = 1, int year = 1900);

//Constructor to set the date

//The member variables dMonth, dDay, and dYear are set

//according to the parameters

//Postcondition: dMonth = month; dDay = day;

// dYear = year

//If no values are specified, the default values are

//used to initialize the member variables.

private:

int dMonth; //variable to store the month

int dDay; //variable to store the day

int dYear; //variable to store the year

};

Further, the definitions of the member functions are as follows:

#include <iostream>

#include "dateType.h"

using namespace std;

void dateType::setDate(int month, int day, int year)

{

if (year >= 1)

dYear = year;

else

dYear = 1900;

if (1 <= month && month <= 12)

dMonth = month;

else

dMonth = 1;

switch (dMonth)

{

case 1:

case 3:

case 5:

case 7:

case 8:

case 10:

case 12:

if (1 <= day && day <= 31)

dDay = day;

else

dDay = 1;

break;

case 4:

case 6:

case 9:

case 11:

if (1 <= day && day <= 30)

dDay = day;

else

dDay = 1;

break;

case 2:

if (isLeapYear())

{

if (1 <= day && day <= 29)

dDay = day;

else

dDay = 1;

}

else

{

if (1 <= day && day <= 28)

dDay = day;

else

dDay = 1;

}

int dateType::getDay() const

{

return dDay;

}

int dateType::getMonth() const

{

return dMonth;

}

int dateType::getYear() const

{

return dYear;

}

bool dateType::isLeapYear()

{

if (((dYear % 4 == 0) && (dYear % 100 != 0)) || dYear % 400 == 0)

return true;

else

return false;

}

void dateType::printDate() const

{

cout << dMonth << "-" << dDay << "-" << dYear;

}

//constructor

dateType::dateType(int month, int day, int year)

{

setDate(month, day, year);

}

You have the following statements:

dateType date1(3, 15, 2008);

dateType date2(15, 20, 2008);

dateType date3(2, 30, 2009);

Write a test main() C++ program to print pintDate() and checking whether the written date has the leap year. Rewrite the definitions of the function SetDate and the constructor so that the values of the month, day, and year are checked before storing the date in the member variables. Add a member function, isLeapYear, to check whether a year is a leap year.

Write a test main() C++ Program:

// Name: Your Name

// ID: Your ID

#include <iostream>

#include "dateType.h"

using namespace std;

int main()

{

dateType date1(3, 15, 2008);

dateType date2(15, 20, 2008);

dateType date3(2, 30, 2009);

dateType date4;

int m, d, y;

…

YOUR CODE HERE

…

return 0;

}

papayaprofessor

2. In this section you will be shown several classes. Inside the code for each class will be a question. You should provide your answer to the question inside the chart. Many of the questions will ask you whether a variable has changed or not. In cases that the variable being asked about is a primitive type, you should provide your answer based on the data stored in the primitive type. In cases that the variable being asked about is a reference type, you should provide your answer based on the data stored at the Object linked to by the reference type. For example, in the first snippet, the question asks about the variable x defined in the main method. Since x is a primitive type, you should answer YES if you think the variable x has had its value changed after the method methodOne() returns. All your answers should go in the chart below: (9 points) Part Answer to question x changed (circle one)? YES NO y changed (circle one)? a changed (circle one)? b changed (circle one)? d1 a changed (circle one)? b changed (circle one)? YES e words changed (circle one)? YES NO Values in array of array referred to by y: What is printed to the screen? (a) public class ReferenceTesti public static void methodOne (int x){ x++; public static void main(String[args) { int x = 0; methodOne (x); //IS THE DATA STORED OR REFERRED TO BY X THE SAME? (ANSWER IN CHART)

ALGORITHMS Lecture Notes - Erik Demaine, Insertion Sort, Binary Search Algorithm

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