Find maximum and minimum value of a triplet without using a conditional statement

Given three integers, find the maximum and minimum number between them without using conditional statements or ternary operator.

Approach 1: Using short-circuiting in Boolean expressions

The idea is to take advantage of short-circuiting in Boolean expressions. We know that in Boolean AND operations such as x && y, y is only evaluated if x is true. If x is false, then y is not evaluated because the whole expression would be false, which can be deduced without even evaluating y. This is called short-circuiting in Boolean expressions.

The idea is to apply this principle to the following code. Initially, max is a. If max < b is true, then that means b is greater than a, so the second subexpression max = b is evaluated, and max is set to b. If, however, max < b is false, then the second subexpression is not evaluated, and max will remain a (greater than b). Similarly, the second expression is evaluated.

We can implement the minimum function as well, in a similar fashion, as demonstrated below in C++:

#include <iostream>

using namespace std;

int maximum(int a, int b, int c)

{

// initialize `max` with `a`

int max = a;

// set `max` to `b` if and only if `max` is less than `b`

(max < b) && (max = b); // these are not conditional statements

// set `max` to `c` if and only if `max` is less than `c`

(max < c) && (max = c); // these are just boolean expressions

return max;

}

int minimum(int a, int b, int c)

{

// initialize `min` with `a`

int min = a;

// set `min` to `b` if and only if `min` is more than `b`

(min > b) && (min = b);

// set `min` to `c` if and only if `min` is more than `c`

(min > c) && (min = c);

return min;

}

int main()

{

cout << maximum(7, 9, 4) << endl;

cout << minimum(6, 3, 9) << endl;

return 0;

}

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Approach 2: Using array index

#include <iostream>

using namespace std;

int maximum(int a, int b, int c)

{

// `first` will contain the first two elements

int first[] = { a, b };

// `second` will contain the maximum of the first two elements at

// the 0th index and the third element at index 1

int second[] = { first[a < b], c };

// finally, return the maximum element

return second[second[0] < c];

}

int minimum(int a, int b, int c)

{

// `first` will contain the first two elements

int first[] = { a, b };

// `second` will contain the minimum of the first two elements at the

// 0th index and the third element at index 1

int second[] = { first[a > b], c };

// finally, return the minimum element

return second[second[0] > c];

}

int main()

{

cout << maximum(6, 3, 9) << endl;

cout << minimum(6, 3, 9) << endl;

return 0;

}

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We can simplify the above approach by breaking the problem into finding the maximum/minimum of two numbers. The following C++ program demonstrates it:

#include <iostream>

using namespace std;

int maximum(int a, int b)

{

int lookup[] = {a, b};

return lookup[a < b];

}

int maximum (int a, int b, int c) {

return maximum(a, maximum(b, c));

}

int main()

{

cout << maximum(6, 3, 9) << endl;

return 0;

}

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We can implement the minimum function, in a similar fashion, as demonstrated below in C++:

#include <iostream>

using namespace std;

int minimum(int a, int b)

{

int lookup[] = {a, b};

return lookup[a > b];

}

int minimum(int a, int b, int c) {

return minimum(a, minimum(b, c));

}

int main()

{

cout << minimum(6, 3, 9) << endl;

return 0;

}

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Approach 3: Using repeated subtraction

#include <iostream>

using namespace std;

int minimum (int a, int b, int c)

{

int min = 0;

while (a && b && c) {

a--, b--, c--, min++;

}

return min;

}

int maximum (int a, int b, int c)

{

int max = 0;

while (a > 0 || b > 0 || c > 0) {

a--, b--, c--, max++;

}

return max;

}

int main()

{

cout << maximum(6, 3, 9) << endl;

cout << minimum(6, 3, 9) << endl;

return 0;

}

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References: https://stackoverflow.com/questions/7074010/find-maximum-of-three-number-in-c-without-using-conditional-statement-and-ternar

Find maximum and minimum value of a triplet without using a conditional statement

Approach 1: Using short-circuiting in Boolean expressions

Approach 2: Using array index

Approach 3: Using repeated subtraction

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