A herbal quantity is claimed to be high if it’s only divisible on its own and 1. Briefly, a chief quantity has best two elements which are 1 and the quantity itself. The numbers that aren’t high are referred to as composite numbers.
A major quantity may also be written as a manufactured from best two numbers. As an example, imagine 3. Now, 3 may also be written within the type of the product of 2 numbers in just one means i.e., 1 * 3. While, 8 which is a composite quantity may also be written as 1 * 8 and a couple of * 4.
The next diagrammatic representation presentations the high numbers between 1 and 100. Follow this desk to search out some attention-grabbing information in regards to the high numbers which might be mentioned within the subsequent phase.
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C Program for High Numbers The use of For Loop
Set of rules to In finding High Quantity Program in C
STEP 1: Take num as enter.
STEP 2: Initialize a variable temp to 0.
STEP 3: Iterate a “for” loop from 2 to num/2.
STEP 4: If num is divisible by way of loop iterator, then increment temp.
STEP 5: If the temp is the same as 0,
Go back “Num IS PRIME”.
Else,
Go back “Num IS NOT PRIME”.
Pseudocode to In finding High Quantity The use of For Loop
Get started
Enter num
Initialize variable temp = 0
FOR loop = 2 to num/2
IF num is divisible by way of loop
Increment temp
END IF
END FOR
IF temp is the same as 0
RETURN “Num IS PRIME”
END IF
ELSE
RETURN “Num IS NOT PRIME”
END ELSE
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Enforcing C program for top numbers The use of For Loop
#come with <stdio.h>
int major()
{
int i, num, temp = 0;
// learn enter from consumer.
printf("Input any numb to Test for High: ");
scanf("%d", &num);
// iterate as much as n/2.
for (i = 2; i <= num / 2; i++)
{
// test if num is divisible by way of any quantity.
if (num % i == 0)
{
temp++;
destroy;
}
}
// test for the price of temp and num.
if (temp == 0 && num != 1)
{
printf("%d is a High quantity", num);
}
else
{
printf("%d isn't a High quantity", num);
}
go back 0;
}
Within the above program, a “for” loop is iterating from 2 to n/2. The place “n” is the enter quantity. We’re checking for each quantity until n/2 if it divides the num. If any a couple of of n is located, replace the price of temp and go back “Now not high” else “High”.
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Time Complexity: O(n)
Because the loop is iterating from 2 to n/2, the time complexity for the worst case might be O(n), the place n is the enter component.
Area Complexity: O(1)
This system isn’t the use of any additional auxiliary house, best consistent house is getting used. So, the distance complexity is O(1).
Reason why for Iterating the Loop Until n/2
It’s essential to ask why we’re iterating the loop until n/2 as a substitute of n. What’s the cause of leaving the opposite part? Allow us to perceive this with the assistance of examples. Imagine the criteria of the integer 12. The criteria are 1, 2, 3, 4, 6, 12. You’ll apply right here that when 12/2 i.e. 6, there is just one issue left that’s the quantity itself (12 on this case). That is true for all integers.
Now imagine a chief integer 17. The criteria of 17 are 1. After 17/2, i.e. 8.5 there is just one issue i.e. 17. So, to search out if a host is key or now not, discovering just one issue is sufficient. That one issue may also be discovered within the first part, as you’ll be able to understand that there’s just one think about the second one part and that i.e. the quantity itself.
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C Program for High Numbers The use of Whilst Loop
Set of rules to In finding High Quantity Program in C
STEP 1: Take num as enter.
STEP 2: Initialize a variable temp to 0.
STEP 3: Initialize the iterator variable loop to two.
STEP 4: Iterate a “whilst” with the situation, loop <= num/2.
STEP 5: If num is divisible by way of loop iterator, then increment temp.
STEP 6: If the temp is the same as 0,
Go back “Num IS PRIME”.
Else,
Go back “Num IS NOT PRIME”.
Pseudocode to In finding High Quantity The use of Whilst Loop
Get started
Enter num
Initialize variable temp = 0
Initialize loop = 2
WHILE loop <= num/2
IF num is divisible by way of loop
Increment temp
END IF
END WHILE
IF temp is the same as 0
RETURN “Num IS PRIME”
END IF
ELSE
RETURN “Num IS NOT PRIME”
END ELSE
FinishEnforcing C Program for High Numbers The use of Whilst Loop
#come with <stdio.h>
int major()
{
int num, temp = 0;
// learn enter from the consumer.
printf("Input any quantity to Test for High: ");
scanf("%d", &num);
// initialization
int i = 2;
// loop situation
whilst (i <= num / 2)
{
// test if num is divisible by way of any quantity.
if (num % i == 0)
{
temp++;
destroy;
}
// incrementation
i++;
}
// test for the price of temp and num.
if (temp == 0 && num != 1)
{
printf("%d is a High Quantity", num);
}
else
{
printf("%d is Now not a High Quantity", num);
}
go back 0;
}
Within the following program, we’ve got carried out a “whilst” loop as a substitute of a “for” loop. The good judgment is equal to the former program.
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Time Complexity: O(n)
The loop in this system runs from 2 to n/2, due to this fact, the time complexity for the worst case might be O(n). Right here, n is the enter component.
Area Complexity: O(1)
On this program, best consistent house is getting used for some variables. Subsequently, the distance complexity is O(1).
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C Program for High Numbers The use of Purposes
Set of rules to In finding High Quantity
STEP 1: Outline a serve as that accepts an integer num.
STEP 2: Initialize a variable temp to 0.
STEP 3: Iterate a “for” loop from 2 to num/2.
STEP 4: If num is divisible by way of loop iterator, then increment temp.
STEP 5: Go back num.
STEP 6: In the primary serve as: If the temp is the same as 0,
Go back “Num IS PRIME”.
Else,
Go back “Num IS NOT PRIME”.
Pseudocode to In finding High Quantity The use of Purposes
Get started
FUNCTION find_Prime (num)
Initialize variable temp = 0
FOR loop = 2 to num/2
IF num is divisible by way of loop
Increment temp
END IF
END FOR
IF temp is the same as 0
RETURN “Num IS PRIME”
END IF
ELSE
RETURN “Num IS NOT PRIME”
END ELSE
END FUNCTION
END Enforcing C Program for High Numbers The use of Purposes
#come with <stdio.h>
// serve as to test if
// the num is key or now not.
int find_Prime(int num)
{
int i, temp = 0;
// iterate as much as num/2.
for (i = 2; i <= num / 2; i++)
{
// if num has elements,
// replace temp.
if (num % i == 0)
{
temp++;
}
}
go back temp;
}
int major()
{
int num, temp = 0;
printf("Input any quantity to Test for High: ");
scanf("%d", &num);
// serve as name
temp = find_Prime(num);
if (temp == 0 && num != 1)
{
printf("n %d is a High Quantity", num);
}
else
{
printf("n %d is Now not a High Quantity", num);
}
go back 0;
}
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Time Complexity: O(n)
The serve as has just one “for” loop that runs from 2 to n/2. Subsequently, within the worst case, the time complexity might be O(n).
Area Complexity: O(1)
No more room is getting used right here. The serve as makes use of best consistent house to retailer the variables. So, the distance complexity might be O(1).
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C Program for High Numbers The use of Recursion
Set of rules to In finding High Quantity
STEP 1: Outline a recursive serve as that accepts an integer num.
STEP 2: Initialize a variable ”i” to two.
STEP 3: If num is the same as 0 or 1, then RETURN false.
STEP 4: If num is the same as “i”, then RETURN true.
STEP 4: If num is divisible by way of “i”, then RETURN false.
STEP 5: Increment “i”.
STEP 6: Recursively name the serve as and move num as an issue.
Pseudocode to In finding High Quantity The use of Recursion
Get started
FUNCTION find_Prime (num)
Initialize variable i = 2
IF num is the same as i
RETURN true
END IF
IF num is divisible by way of i
RETURN false
END IF
Recursively name find_Prime
END FUNCTION
END Enforcing C program for High Numbers The use of Recursion
#come with <stdio.h>
#come with <stdbool.h>
// recursive serve as to test if a host
// is key or now not.
bool find_Prime(int num)
{
static int i = 2;
// Base Case
if (num == 0 || num == 1)
{
go back false;
}
// Recursive Case
if (num == i)
go back true;
// test if num is divisible by way of any quantity
if (num % i == 0)
{
go back false;
}
i++;
// recursive serve as name.
go back find_Prime(num);
}
int major()
{
// check case 1
int num = 20;
if (find_Prime(num))
{
printf("%d is a High numbern", num);
}
else
{
printf("%d isn't a High quantity n", num);
}
// check case 2
num = 2;
if (find_Prime(num))
{
printf("%d is a High numbern", num);
}
else
{
printf("%d isn't a High quantity n", num);
}
go back 0;
}
This can be a recursive solution to to find the high numbers. Right here, a recursive serve as find_Prime is made that merely assessments if the num is divisible by way of any quantity. Whether it is, then it returns false else the recursive name is made. This procedure repeats till any a couple of of num is located.
Time Complexity: O(n)
The serve as is looking itself recursively n instances till both an element is located or one of the crucial prerequisites is glad. Subsequently, the time complexity is O(n).
Area Complexity: O(n)
The n calls made by way of the recursive serve as might be saved within the stack which can eat house within the reminiscence. Subsequently, the distance complexity of the recursive way might be O(n).
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C Program for High Numbers: Optimized Manner
Set of rules to In finding High Quantity
STEP 1: Take num as enter.
STEP 2: Initialize a variable temp to at least one.
STEP 3: Iterate a “for” loop from 2 to sqrt(num).
STEP 4: If num is divisible by way of loop iterator, then replace temp price to 0.
STEP 5: If the temp is the same as 1,
Go back “Num IS PRIME”.
Else,
Go back “Num IS NOT PRIME”.
Pseudocode to In finding High Quantity
Get started
Enter num
Initialize variable temp = 1
FOR loop = 2 to sqrt(n)
IF num is divisible by way of loop
replace temp = 0
END IF
END FOR
IF temp is the same as 1
RETURN “Num IS PRIME”
END IF
ELSE
RETURN “Num IS NOT PRIME”
END ELSE
Finish Enforcing C Program for High Numbers: Optimized Manner
#come with <stdio.h>
#come with <math.h>
int major()
{
int num, i, temp = 1;
// learn the enter from the consumer.
printf("Input a host: ");
scanf("%d", &num);
// initialize i as 2.
// iterate upto sqrt of num.
for (i = 2; i <= sqrt(num); i++)
{
// test if num is divisible by way of any quantity.
if (num % i == 0)
{
// replace temp.
temp = 0;
destroy;
}
}
// 1 is divisible by way of each
// quantity and isn't high.
if (num <= 1)
temp = 0;
if (temp == 1)
{
printf("%d is a High Quantity", num);
}
else
{
printf("%d isn't a High Quantity", num);
}
go back 0;
}
Within the above program, we’ve got used an optimized option to test if a host is key or now not. Right here, as a substitute of iterating the loop as much as the quantity itself, we’re iterating it as much as its sq. root (√n). It is because the smallest issue of a host (more than 1) can’t be more than the sq. root of the quantity. As an example, for 64 the smallest issue is two which isn’t more than √64.
Time Complexity: O(n1/2)
It is because the “for” loop is iterating from 2 to the sq. root of (√n), the place n is the enter component.
Area Complexity: O(1)
No more room is being utilized in this system. Just a consistent auxiliary house is used to retailer variables and iteration is completed in position.
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C Program for High Numbers Inside a Vary
Set of rules to In finding High Quantity
STEP 1: Take the variability values left and appropriate as enter.
STEP 2: Initialize a loop iterator num to left.
STEP 3: Iterate a “for” loop from left to appropriate.
STEP 4: Iterate a “for” loop from 2 to num/2.
STEP 5: Initialize a variable temp to 0.
STEP 6: If num is divisible by way of loop iterator, then increment temp.
STEP 5: If the temp is the same as 0,
Go back “Num IS PRIME”.
Else,
Go back “Num IS NOT PRIME”.
Pseudocode to In finding High Quantity Inside a Vary
Get started
Enter left, appropriate
FOR num = left to appropriate
FOR loop = 2 to num/2
Initialize variable temp = 0
IF num is divisible by way of loop
Increment temp
END IF
END FOR
IF temp is the same as 0
RETURN “Num IS PRIME”
END IF
ELSE
RETURN “Num IS NOT PRIME”
END ELSE
FinishEnforcing C Program for High Numbers Inside a Vary
#come with <stdio.h>
int major()
{
int i, num, temp, sum = 0, left, appropriate;
// learn the values of the variability shape the consumer.
printf("Input the left & appropriate Values: ");
scanf("%d %d", &left, &appropriate);
// iterate “for” loop inside the given vary.
for (num = left; num <= appropriate; num++)
{
temp = 0;
// for loop to test for the high numbers.
for (i = 2; i <= num / 2; i++)
{
// test if num is divisible by way of any quantity.
if (num % i == 0)
{
temp++;
destroy;
}
}
// test for the values of temp and num.
if (temp == 0 && num != 1)
{
sum = sum + num;
}
}
printf("Sum of High nums between %d and %d = %d", left, appropriate, sum);
go back 0;
}
Within the above program, we’re printing the sum of the high numbers within the given vary. The beginning and finishing issues are being learn by way of the consumer. We’ve got iterated a nested for loop. The outer loop is operating from the left until appropriate and the interior loop is operating as much as n/2 for every iteration of the outer loop.
Time Complexity: O((right-left)*num)
(Right here, “num” is the enter quantity, “left” and “appropriate” are the beginning and finishing level of the given vary). We’ve got used a nested “for” loop the place the outer loop is iterating from “left” to “appropriate”, the interior loop is iterating from 2 as much as n/2. So, the outer loop runs (right-left) instances, and the interior loop iterates “num” instances,
Area Complexity: O(1)
No more room is getting used right here. The serve as makes use of best consistent house to retailer the variables. So, the distance complexity might be O(1).
C Program for High Numbers The use of Sieve of Eratosthenes
Set of rules to In finding High Quantity
STEP 1: Take a herbal quantity num as an enter.
STEP 2: Create a boolean array isPrime[] and initialize all its parts to at least one (assuming first of all all parts are high).
STEP 3: If a component okay is the same as 1 (or true), mark all its multiples more than k2 to 0.
STEP 4: Repeat STEP 2 for all unmarked (equivalent to at least one or true) parts till the sq. root of the num is reached.
STEP 5: Iterate over the boolean array isPrime[], If the isPrime[i] is the same as 1,
Go back “Num IS PRIME”.
Else,
Go back “Num IS NOT PRIME”.
Pseudocode to In finding High Quantity The use of Sieve of Eratosthenes
Get started
Enter num
Create a boolean array isPrime[]
Initialize all parts of isPrime[] to at least one
FOR okay = 2 to k2 <= num
IF isPrime[k] is the same as 1
FOR i = k2 to i <= num
isPrime[i] = 0
END FOR
END IF
END FOR
FOR loop = 2 to num
IF isPrime[loop] is the same as 1
PRINT "isPrime[loop] IS PRIME"
END IF
END FOR
FinishEnforcing C Program for High Numbers The use of Sieve of Eratosthenes
#come with <stdio.h>
#come with <stdbool.h>
#come with <string.h>
// serve as to search out the entire
// high numbers from 1 to num.
void find_Prime(int num)
{
// initialize all parts of
// the array isPrime as true i.e., 1.
// A component of the array will
// be up to date to false, if it isn't high.
bool isPrime[num + 1];
memset(isPrime, true, sizeof(isPrime));
for (int okay = 2; okay * okay <= num; okay++)
{
// if isPrime[k] isn't up to date,
// then this can be a High.
if (isPrime[k] == true)
{
// replace the entire multiples of
// okay as false, ranging from
// its sq. upto num
for (int i = okay * okay; i <= num; i += okay)
isPrime[i] = false;
}
}
// print the High numbers.
for (int okay = 2; okay <= num; okay++)
if (isPrime[k])
printf("%d, ", okay);
}
int major()
{
int num = 30;
printf("Following are the High numbers smaller ");
printf("%d, than or equivalent to ", num);
printf("n");
// serve as name
find_Prime(num);
go back 0;
}
The above way is primarily based upon the sieve of Eratosthenes. We’ve got outlined an array of the boolean sort whose all parts are first of all true. True approach we’ve got meant that first of all, the entire parts are high. If a host is up to date as false, then it is going to now not be a chief quantity. We’ve got iterated a loop ranging from 2 that may mark the entire multiples of two which might be more than or equivalent to its sq. as much as num as false. We will be able to repeat this procedure as much as √num. After this, the weather that stay unmarked (or true) will all be the high numbers.
Time Complexity: O(n*log(log(n)))
The time complexity of marking all non-prime numbers is thought to be consistent. Now to search out the time complexity to run the loop till okay, the equation turns into,
Via fixing this equation the use of formulae of Harmonic Development and Taylor collection enlargement, Euler’s Formulation adopted by way of summation and simplification, the general end result may also be deduced which is the same as n * log(log(n)).
Area Complexity: O(n)
Area is ate up by way of the boolean array isPrime which is asserted to be of a measurement equivalent to num. Subsequently, the time complexity is O(n), the place n is the enter component.
That was once all about C program for High numbers.
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Ultimate Ideas!
To wrap up, on this article, you might have realized in regards to the a couple of techniques to put in writing a C program for top numbers. You began with a snappy advent to high numbers in addition to some attention-grabbing information about high numbers.
Whilst exploring the area of programming, delving into algorithmic demanding situations comparable to making a C program to test whether or not a host is key may also be each intriguing and enlightening. Then again, if you are aiming to develop your horizons and grasp a collection of applied sciences that may get ready you for a flexible profession in instrument building, making an allowance for a java complete stack developer path could be your subsequent strategic transfer.
Transferring forward, within the C program for High numbers article you noticed other ways to test for a chief quantity the use of for loops, whilst loops, purposes, recursion, optimized way, and so forth. You realized the best way to print high numbers inside of a variety and probably the most common strategies referred to as Sieves of Erastosthenes. You noticed the set of rules, pseudocode, C program, time, and house complexities for every of the strategies that we’ve got mentioned.
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