Using only 4 'if' statements - Find Largest and Smallest of 4 integers

Question

I have been going through some basic exercises from a recommended beginner's book: C Programming: A Modern Approach (2nd Edition)

The question states: Use as few if statements as possible to determine the largest and smallest of four numbers entered by the user. Four if statements are sufficient. -- Since this question was asked before loops, arrays and functions were covered in the book, I am assuming that these should not be used.

Also, I know there was a similar question to this one, however none meet the requirements of what I am trying to achieve.

1. Using only 4 if statements
2. No for-loops.

The first thing that came to my mind was using the logical or operator however as shown below, eight if statements were used. Also this method is very long and not efficient:

    int a, b, c, d;

printf("Enter 4 intgeres to find largest and smallest: ");
scanf_s("%d %d %d %d", &a, &b, &c, &d);

if (a > b && a > c && a > d)
    printf("Largest: %d\n", a);
if (b > a && b > c && b > d)
    printf("Largest: %d\n", b);
if (c > a && c > b && c > d)
    printf("Largest: %d\n", c);
if (d > a && d > a && d > c)
    printf("Largest: %d\n", d);

if (a < b && a < c && a < d)
    printf("Smallest: %d\n", a);
if (b < a && b < c && b < d)
    printf("Smallest: %d\n", b);
if (c < a && c < b && c < d)
    printf("Smallest: %d\n", c);
if (d < a && d < a && d < c)
    printf("Smallest: %d\n", d);

return 0;

Next, I proceeded to the following code which would be a better solution:

    int a, b, c, d;

printf("Enter 4 intgeres to find largest and smallest: ");
scanf_s("%d %d %d %d", &a, &b, &c, &d);

int max = a, min = a;

if (b > max) 
    max = b;
else if (b < min) 
    min = b;
if (c > max) 
    max = c;
else if (c < min) 
    min = c;
if (d > max) 
    max = d;
else if (d < min) 
    min = d;

printf("max: %d min : %d\n", max, min);

return 0;

However, still not meeting the requirement of using 4 if statements. I was wondering if I could shorten my code even further. Please excuse the basic nature of this question. Any suggestions would be appreciated.

Answer 1

We can use divide n conquer approach to solve this problem.

Imagine our input = [a, b, c, d]

We want to find answer from [a,b] and [c,d]

Then merge the final solution to find the answer.

if(a > b) swap(&a,&b); // solve [a,b]
if(c > d) swap(&c,&d); // solve [c,d]
if(a > c) swap(&a,&c); // find minimum from [a,b] and [c,d]
if(d > b) swap(&b,&d); // find maximum from [a,b] and [c,d]

// a will store the minimum value.
// b will store the maximum value.

Bonus (How to Swap Number in C Language)

void swap(int *a,int *b) {
    int c = *a;
    *a = *b;
    *b = c;
}

Answer 2

Following should work.

It computes max1 = max(a, b) and max2 = max(c, d), as well as min1 = min(a, b) and min2 = min(c, d), using the first 2 ifs.

Then the maximum is equal to max(max(a, b), max(c, d)) = max(max1, max2). (The 3rd if.)

And the minimum is equal to min(min(a, b), min(c, d)) = min(min1, min2). (The 4th if.)

int a, b, c, d;

// ...

int min, max, max1, max2, min1, min2;

if (a > b) // 1
{
    max1 = a;
    min1 = b;
}
else
{
    max1 = b;
    min1 = a;
}

if (c > d) // 2
{
    max2 = c;
    min2 = d;
}
else
{
    max2 = d;
    min2 = c;
}

if (max1 > max2) // 3
    max = max1;
else
    max = max2;

if (min1 < min2) // 4
    min = min1;
else
    min = min2;

Bonus

Zero ifs.

int a, b, c, d;

// ...

int min = a, max = a;
b < min && (min = b);
c < min && (min = c);
d < min && (min = d);
b > max && (max = b);
c > max && (max = c);
d > max && (max = d);

Answer 3

#include <stdio.h>

int main ()
{
    int num1, num2, num3, num4;
  
     printf("enter the numbers: ");
     scanf("%d %d %d %d", &num1, &num2, &num3, &num4);

     int large1 = num1, low1 = num2, low = num3, large = num4;
     if (num1 <= num2) {
         large1 = num2;
         low1 = num1;
     }
     if (num3 >= num4) {
         large = num3;
         low = num4;
     }
     if (large < large) {
         large = large1;
     }
     if (low > low1) {
         low = low1;
     }
     printf("%d\n", large);
     printf("%d\n", low);
     return 0;
}

Answer 4

#include <stdio.h>

int max_of_four(int a,int b, int c, int d)
{
    int max=0;
    max = (a > b ? (a > c ? (a > d ?   a :  d) :  (c > d ? c : d) ) : (b > c ? (b > d ? b : d>c? d : c ) : c>d? c : d)) ;

   return max;
}

int main() {
    int a, b, c, d;
    scanf("%d %d %d %d", &a, &b, &c, &d);
    int ans = max_of_four(a, b, c, d);
    printf("%d", ans);

    return 0;
}

Answer 5

Here is an alternative solution with a single if statement:

#include <stdio.h>

int main() {
    int a, b, c, d;
  
    printf("enter the numbers: ");
    if (scanf("%d%d%d%d", &a, &b, &c, &d) == 4) {
        int lo1 = a * (a <= b) + (a > b) * b;
        int hi1 = a * (a >= b) + (a < b) * b;
        int lo2 = c * (c <= d) + (c > d) * d;
        int hi2 = c * (c >= d) + (c < d) * d;
        int lo = lo1 * (lo1 <= lo2) + (lo1 > lo2) * lo2;
        int hi = hi1 * (hi1 >= hi2) + (hi1 < hi2) * hi2;
        printf("%d %d\n", hi, lo);
        return 0;
    } else {
        return 1;
    }
}

Answer 6

its a very creative question. I have solved your problem using only two if statements.

int a = 22, b = 25, c = 100, d = 4;
        int max = 0, min = 0;
        if ((a > b ? (a > c ? (a > d ? max = a : max = d) : max = c) : (b > c ? (b > d ? max = b : max = d) : max = c)) == 1)
        {
              //Control never goes inside this loop
        }
        else if ((a < b ? (a < c ? (a < d ? min= a : min= d) : min= c) : (b < c ? (b < d ? min = b : min = d) : min = c)) == 1)
        {
             //Control never goes inside this loop
        }
        printf("Maximum Value is:%d and Minimum Value is: %d", max, min);//at this statement max and min will have appropriate values