C Programming

• Syntax errors -- Errors in spelling and grammar.
  • You can use the compiler or interpreter to uncover syntax errors.
  • You must have a good working knowledge of error messages to discover the cause of the error.
• Logical errors -- Errors that indicate the logic used when coding the program failed to solve the problem.
  • You do not get error messages with logic errors.
  • Your only clue to the existence of logic errors is the production of wrong solutions.

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The MERGESORT algorithm performs atmost a single call to any pair of indices

of the array that is being sorted. In otherwords, the subproblems do not

overlap and therefore memoization will not improve the running time.

otherwise........take the look at following:

It does not have the Overlapping Subproblems property.

(Not re-visiting subproblems.)

Needs lot of space to store solutions of subproblems.

Overlapping sub-problems property is as follows:

We accidentally recalculate the same problem twice or more.

60=6*10, 126=6*21, so their gcd is 6.

I hope ot is not too late for your homework.

In C, decimal values are called "floating point" because the number of digits after the decimal point can vary. There are two types used for floating point operations: float and double.

Although the decimal point can shift anywhere within the number, C only allows a certain number of consecutive digits worth of precision. The float type only allows 7 consecutive digits, and the double type allows 15. Any digits before and after those consecutive digits are generally displayed as zero (0).

Here's an example program that uses the float type with arithmetic operators:

#include

void main()

{

float myfloat=0.0, counter;

printf("* perform addition on the float:\n");

for (counter=5; counter<10; counter++) {

myfloat+=(counter/10);

printf("myfloat is: %0.7f\n", myfloat);

}

printf("* perform subtraction on the float:\n");

for (counter=0; counter<5; counter++) {

myfloat-=(counter/10);

printf("myfloat is: %0.7f\n", myfloat);

}

printf("* perform multiplication on the float:\n");

for (counter=5; counter<10; counter++) {

myfloat*=(counter/10);

printf("myfloat is: %0.7f\n", myfloat);

}

printf("* perform division on the float:\n");

for (counter=2; counter<8; counter++) {

myfloat/=(counter/10);

printf("myfloat is: %0.7f\n", myfloat);

}

}

The %0.7f inside the printf() format string tells the compiler you want to display a minimal number of integer places, and no more than 7 decimal places. Play around with this value and see what happens.

If you compile and run this program, you may notice something odd. The last (right-most) decimal place has an errant number popping in. This is a result of the low precision of the float type. The following output is an example:

* perform addition on the float:

myfloat is: 0.5000000

myfloat is: 1.1000000

myfloat is: 1.8000001

myfloat is: 2.6000001

myfloat is: 3.5000002

* perform subtraction on the float:

myfloat is: 3.5000002

myfloat is: 3.4000003

myfloat is: 3.2000003

myfloat is: 2.9000003

myfloat is: 2.5000002

* perform multiplication on the float:

myfloat is: 1.2500001

myfloat is: 0.7500001

myfloat is: 0.5250000

myfloat is: 0.4200000

myfloat is: 0.3780000

* perform division on the float:

myfloat is: 1.8900001

myfloat is: 6.3000002

myfloat is: 15.7500000

myfloat is: 31.5000000

myfloat is: 52.5000000

myfloat is: 75.0000000

However, if you're displaying only a couple of decimal points, the discrepancy is generally unseen.