Skip to main content

Counting


In everyday life, if we have N objects and want to identify them by numbers, we assign the numbers
1,2,3,. .., N to them. Another way to look at this is to say that the set of numbers forms a closed
interval which we can write as either 1 ≤ i ≤ N or [1, N].

Programmers are different. Given N objects, they number them 0,1,2,. .., N−1. This set of numbers
forms a semi-closed (or semi-open interval which we can write as either 0 ≤ i < N or [0, N). The
advantages of semi-closed intervals include:

• They reduce the risk of “off-by-one” or “fencepost” errors.
To see why off-by-one errors are called “fencepost errors”, consider the length of a fence with
N posts spaced 10 feet apart. The length of the fence is 10(N − 1)


• The closed interval [M, N] has N −M +1 elements; the semi-closed interval [M, N) has N −M
elements, which is easier to remember and calculate.
• Semi-closed intervals are easier to join together. Compare
[A, B), [B, C), [C, D),.. .

to

[A, B − 1], [B,C − 1], [C, D − 1],.. .
• The index of the first element of an array A in C++ is 0. The address of the I’th element of the
array is &A + sI where &A is the address of the array and s is the size of one element.
Typical C++ loops do not have the form
for (int i = M; i <= N; ++i) ....
but, instead, have the form
for (int i = M; i < N; ++i) ....
Note that, in the first case, N is the last element processed but, in the second case, N is the first element not processed. In fact, we will see later that there are good reasons for writing the termination
condition as != rather than <=:
for (int i = M; i != N; ++i) ....


Labels:

Popular posts from this blog

C++ Program to find the sum, difference, product and quotient of two integers

#include <iostream.h> #include <conio.h> void main() {   clrscr();   int x = 10;   int y = 2;   int sum, difference, product, quotient;   sum = x + y;   difference = x - y;   product = x * y;   quotient = x / y;   cout << "The sum of " << x << " & " << y << " is " << sum << "." << endl;   cout << "The difference of " << x << " & " << "y <<  is " << difference << "." << endl;   cout << "The product of " << x << " & " << y << " is " << product << "." << endl;   cout << "The quotient of " << x << " & " << y << " is " << quotient << "." << endl;   getch(); }
Read more

Program of virtual piano

//////////////Tested And Created By C++/////////////////////////////// #include<stdio.h> #include<dos.h> #include<conio.h> #include<stdlib.h> #define SHOW 1 #define HIDE 2 union REGS input,output; class piano {  public:int BIGKEY,MIDKEY,back,border;     piano()//init constructor     {         BIGKEY=15;         MIDKEY=1;         back=7;         border=15;     } }color; void drawpiano(int x,int y); int check_xy(int x,int y); void BOX(int c,int r,int c1,int r1,int col); int initmouse(); void setupscreen(); void pointer(int on); void restrictmouse(int x1,int y1,int x2,int y2); void check_keys(int x,int y); void getmouse(int *button,int *x,int *y); float freq[7] = {130.81, 146.83, 164.81, 174.61,196, 220, 246.94 } ; int n=0,a=4,backcolor=2,exitcode=1; void showbar(int t) {  if(t>65) t=65;  if(t<1) t=1;  textcolor(15);  for(int q=0;q<=t;t++)  {     gotoxy(3+q,4);     cprintf("Û");  } } void main() {  int
Read more

Putimage function in c

putimage function outputs a bit image onto the screen. Declaration:- void putimage(int left, int top, void *ptr, int op); putimage puts the bit image previously saved with getimage back onto the screen, with the upper left corner of the image placed at (left, top). ptr points to the area in memory where the source image is stored. The op argument specifies a operator that controls how the color for each destination pixel on screen is computed, based on pixel already on screen and the corresponding source pixel in memory. c smiling face animation This animation using c draws a smiling face which appears at random position on screen. See output below the code, it will help you in understanding the code easily. C programming code #include<graphics.h> #include<conio.h> #include<stdlib.h>   main() { int gd = DETECT, gm, area, temp1, temp2, left = 25, top = 75; void *p;   initgraph(&gd,&gm,"C:\\TC\\BGI");   setcolor(YELLOW);
Read more