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omeli [17]
2 years ago
15

Prove that any amount of postage greater than or equal to 64 cents can be obtained using only 5-cent and 17-cent stamps?

Computers and Technology
1 answer:
elixir [45]2 years ago
6 0
Let P(n) be "a postage of n cents can be formed using 5-cent and 17-cent stamps if n is greater than 63".Basis step: P(64) is true since 64 cents postage can be formed with one 5-cent and one 17-cent stamp.Inductive step: Assume that P(n) is true, that is, postage of n cents can be formed using 5-cent and 17-cent stamps. We will show how to form postage of n + 1 cents. By the inductive hypothesis postage of n cents can be formed using 5-cent and 17-cent stamps. If this included a 17-cent stamp, replace this 17-cent stamp with two 5-cent stamps to obtain n + 1 cents postage. Otherwise, only 5-cent stamps were used and n  65. Hence there are at least three 5-cent stamps forming n cents. Remove three of these 5-cent stamps and replace them with two 17-cent stamps to obtain n + 1 cents postage.Hence P(n + 1) is true.
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g 18.6 [Contest 6 - 07/10] Reverse an array Reversing an array is a common task. One approach copies to a second array in revers
Blababa [14]

Answer:

I am writing C++ program. Let me know if you want the program in some other programming language.  

#include <iostream> //to use input output functions

using namespace std; //to identify objects like cin cout

void reverse(int array[], int size){ //method to reverse an array  

int i, j, temp; //declare variables  

for (i = 0; i < size / 2; i++) { /* the loop swaps the first and last elements, then swap the second and second-to-last elements and so on until the middle of the array is reached */  

temp = array[i];  

array[i] = array[size - i - 1];  

array[size - i - 1] = temp; }  

cout<<"Reversed array: "; //prints the resultant reversed array after swapping process  

for (j = 0; j < size; j++) { //loop to print the reversed array elements  

cout<<array[j]<<" "; } }    

int main() { //start of main() function body  

cout<<"Enter the length of array: "; //prompts user to enter the length of the array

       int n; //stores the value of size of array

       cin>>n; //reads the input size of array

       int A[n]; //declare array A of size n

       cout<<"Enter the elements: "; //prompts user to enter array elements

       for(int i=0;i<n;i++){ //loop for reading the elements of array

           cin >> A[i];        }

         reverse(A,n); } //calls reverse function to reverse the elements of the input array A by passing array A and its length n to function reverse

Explanation:  

The reverse function takes an array and its length as parameter. In the body of reverse function three integer type variables i,j and temp are declared.

for (i = 0; i < size / 2; i++) The for loop has a variable to iterate through the array. The for loop checks if the value of i is less than the array length. Lets say we have an array of elements 1, 2, 3, 4. As i=0 and size/2 = 4/2= 2. So the condition checked in for loop is true as 0<2 which means the body of for loop will be executed.

In the body of the loop there are three swap statements.

temp = array[i] This statement stores the element of array at i-th index to temp variable.

array[i] = array[size - i - 1] statement stores the element of array at size-i-1 to array index i.  

array[size - i - 1] = temp statement stores the the value in temp variable to the array index size-i-1

In simple words first, the first and last elements of array are swapped, then the second and second last elements are swapped. This process keeps repeating and for loop keeps executing these swap statements until the middle of the array is reached. In this program no extra array is used for reversing procedure but just a variable temp is used to hold the array elements temporarily.

array[4] = { 1 , 2 , 3 , 4}  

At first iteration  

i < size/2 is true as 0<2  

So the program control moves in the body of the loop where three swap statement works as following:  

temp = array[i]  

temp = array[0]  

As element at 0-th index which is the first element of array is 1 so

temp= 1  

array[i] = array[size - i - 1];  

array[0] = array[4-0-1]  

           = array[3]  

As the element at 3rd index of array is 4 which is the last element of the array so

array[0] = 4

This means that 4 becomes the first element of array now.

array[size - i - 1] = temp  

As the value in temp was set to 1 so  

array[4-0-1] = 1  

array[3] = 1  

This means 1 is assigned to the 3rd index of array. Which means 1 becomes the last element of the array now.

This is how the first and last elements of array are swapped.  

2nd iteration: value of i is incremented to 1 and now i = 1  

Again for loop condition is checked which evaluates to true as 1<2

temp = array[i]  

temp = array[1]  

As element at 1st index which is the second element of array is 2 so

temp= 2  

array[i] = array[size - i - 1];  

array[1] = array[4-1-1]  

           = array[2]  

As the element at second index of array is 3 which is the last element of the array so

array[1] = 3  

This means that 3 becomes the second element of array now.

array[size - i - 1] = temp  

As the value in temp was set to 2 so  

array[4-1-1] = 2  

This means 2 is assigned to the 2nd index of array. Which means 2 becomes the second last element of the array now.

This is how the second and second to last elements of array are swapped.  

3rd iteration: value of i=2 The for loop body will not execute now as the for loop condition i<size-2 evaluates to false because 2=2. So the loop stops and next for (j = 0; j < size; j++) loop iterates through array[] which has now been reversed and print the elements of this reversed array.

Next the main() method passes length of the array and the array elements to the   reverse function and prints these elements in reverse.  

The output is:

4  3 2  1  

The program and output according to the example 2,5,9,7 given in the question is attached as a screenshot.

3 0
2 years ago
How would GIS, GPS, or remote sensing technology be used to evaluate the destruction caused by a tornado in Oklahoma?
emmainna [20.7K]

Answer:

They can be used to compare a certain region before and after disaster.

Explanation:

4 0
2 years ago
Which of these tools can best be used as a self assessment for career planning purposes? a personality test an asset analysis a
Ivahew [28]

Answer:

a goal development checklist

Explanation:

8 0
2 years ago
Ajay wants to read a brief overview about early settlers in the United States. Which type of online text source should he most l
Tanzania [10]
Well, integrity is a must if you are reading anything. So it would be any website that has either a .edu or a .gov at the end of a URL. 

I never suggest Wikipedia for brief, since 100's of people will edit one topic at a time, the answer to what he is looking for is buried in 18 pages about one settler in the United States!
5 0
2 years ago
Read 2 more answers
Writing in Java, write a program that prompts the user to input an integer and then outputs both the individual digits of the nu
larisa [96]

Answer:

//Here is code in java.

import java.util.*;

class Main

{

public static void main (String[] args) throws java.lang.Exception

{

   try{

       int in;

     //scanner class object to read the input

    Scanner scr=new Scanner(System.in);

     // variable to keep running total

    int total=0;

    System.out.println("please enter an Integer:");

     // read the input first time

    in=scr.nextInt();

    System.out.print("individual digits of "+in+" is ");

    if(in<0)

    {

        in=-(in);

    }

   

 

     //call the function to print the digits of number

   print_dig(in);

   System.out.println();

    //calculate the sum of all digits

   do{

       int r=in%10;

       total=total+r;

       in=in/10;

   }while(in>0);

    //print the sum

   System.out.println("total of digits is: "+total);

     

   }catch(Exception ex){

       return;}

}

 //recursive function to print the digits of number

public static void print_dig(int num)

{  

    if(num==0)

    return;

    else

    {

    print_dig(num/10);

    System.out.print(num%10+" ");

    }

}

}

Explanation:

Read a number with the help of object of scanner class.if the input is negative

then make it positive number before calling the function print_dig().call

the recursive method print_dig() with parameter "num".It will extract the digits

of the number and print then in the order. Then in the main method, calculate

sum of all the digits of number.

Output:

please enter an Integer:                                                                                                  

3456                                                                                                                      

individual digits of 3456 is 3 4 5 6                                                                                      

total of digits is: 18

please enter an Integer:                                                                                                  

-2345                                                                                                                      

individual digits of -2345 is 2 3 4 5                                                                                      

total of digits is: 14

6 0
2 years ago
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