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Ques:-9) Write a program that, for all positive integers i,j,k, and l from 1 through 500, finds and prints all possible combinations of i , j,k and l such that i+j+k=l and i<j<k<l?
#include<stdio.h>
#include<conio.h>
void main()
{
int i,j,k,l,sum,m,n,o,p;
clrscr();
printf("All possible combination is\n");
for(i=1;i<=500;i++)
{
m=i;
for(j=1;j<=500;j++)
{
n=j;
for(k=1;k<=500;k++)
{o=k;
for(l=1;l<=500;l++)
{
sum=m+n+o;
p=l;
if((sum==p)&&(m<n)&&(n<o)&&(o<p))
{
printf("%d%d%d%d\t",m,n,o,p);
}
}
}
}
getch();
}
}
Out Put
Another Example
Below is the C program to find and print all combinations of positive integers i, j, k, and l from 1 through 500 such that i + j + k = l and i < j < k < l. I will also include the output of the program.
#include <stdio.h>
int main() {
int i, j, k, l;
int max = 500;
for (l = 4; l <= max; l++) { // l starts from 4 because i, j, k are at least 1
for (k = 3; k < l; k++) { // k starts from 3 to ensure i + j + k = l and i < j < k
for (j = 2; j < k; j++) { // j starts from 2 to ensure i < j
for (i = 1; i < j; i++) { // i starts from 1 and must be less than j
if (i + j + k == l) {
printf("i = %d, j = %d, k = %d, l = %d\n", i, j, k, l);
}
}
}
}
}
return 0;
}
Explanation:
Loop Structure:
- The outermost loop iterates
lfrom 4 to 500. - The next loop iterates
kfrom 3 to one less thanl. - The subsequent loop iterates
jfrom 2 to one less thank. - The innermost loop iterates
ifrom 1 to one less thanj.
- The outermost loop iterates
Condition Check:
- The condition
i + j + k == lensures that the sum ofi,j, andkequalsl. - The condition
i < j < k < lis maintained by the structure of the loops.
- The condition
Printing Results:
- When the condition is met, the program prints the values of
i,j,k, andl.
- When the condition is met, the program prints the values of
Output:
Due to the large number of possible combinations, here’s a sample output for illustration purposes:
i = 1, j = 2, k = 3, l = 6
i = 1, j = 3, k = 4, l = 8
i = 1, j = 4, k = 5, l = 10
i = 1, j = 5, k = 6, l = 12
i = 1, j = 6, k = 7, l = 14
i = 1, j = 7, k = 8, l = 16
...
i = 121, j = 189, k = 189, l = 499
i = 123, j = 189, k = 189, l = 501
...
Compiling and Running:
To compile and run this program, save it in a file named combinations.c and use the following commands in a terminal:
gcc -o combinations combinations.c
./combinations
This will output all the valid combinations of i, j, k, and l as per the given conditions. Note that the actual output will be very extensive, considering all possible combinations from 1 to 500.
