Write an algorithm that accepts four numbers as input and find the largest and smallest of them.

Exercise · Q10

Q. Write an algorithm that accepts four numbers as input and find the largest and smallest of them.

Bihar BsebTextbookSubjective· 3mImportance★★★★★est

78% · 28/36 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Concept understanding — Maximum Element Selection

Maximum Element Selection — The Intuition

Imagine you have a handful of numbers written on slips of paper. You want the biggest one. How do you find it? You look at the first number, call it the "current max." Then you go through the rest one by one: if you see a number bigger than your current max, you replace it. At the end, whatever you're holding is the largest number.

That's the core idea. Maximum element selection is the process of identifying the largest element in a collection — an array, a list, a set — by comparing elements pairwise. It's not a fancy algorithm; it's the most natural thing you'd do with a deck of cards if someone asked "which card has the highest value?"

The Precise Statement

Given a non-empty collection of $n$ elements, each drawn from a set that has a total order (meaning any two elements can be compared, and one is always "greater" or they are equal), the maximum element is the element $M$ such that for every other element $x$ in the collection, $M \geq x$ .

The standard procedure to find it:

Let $M$ be the first element.
For each remaining element $x$ $x$ :
- If $x > M$ , set $M = x$ .
After all elements are processed, $M$ is the maximum.

This takes exactly $n-1$ comparisons in the worst case — you cannot do better because every element except the eventual maximum must lose at least one comparison.

Important

The maximum element is not guaranteed to be unique. If there are ties, any one of the tied largest values qualifies as a maximum. The algorithm above returns the first one encountered.

Why This Matters

Maximum element selection is the simplest building block of many sorting and selection algorithms. Quickselect, heap construction, and tournament methods all rely on this basic operation. It's also the reason you can find the largest number in a list in linear time — no faster method exists because you must at least look at every element once. …

Start your 14-day free trial to unlock the full solution →

Take the first number as both the running largest and smallest, then compare the other three against each:

LARGEST_SMALLEST_OF_FOUR
    INPUT a, b, c, d
    SET large = a, small = a
    IF b > large THEN large = b
    IF c > large THEN large = c
    IF d > large THEN large = d
    IF b < small THEN small = b
    IF c < small THEN small = c
    IF d < small THEN small = d
    PRINT "Largest =", large, "Smallest =", small
END
``` …

Start your 14-day free trial to unlock the full solution →

Assume the first number is both the largest and the smallest, then let each remaining number challenge those titles — six comparisons find both answers.

The idea (running maximum/minimum). The standard technique for extremes is: seed the candidate with the first value, then compare every other value against it and replace when beaten. Doing this simultaneously for large and small classifies all four inputs in one pass.

Algorithm

LARGEST_SMALLEST_OF_FOUR
Step 1: INPUT a, b, c, d
Step 2: SET large = a
Step 3: SET small = a
Step 4: IF b > large THEN large = b
Step 5: IF c > large THEN large = c
Step 6: IF d > large THEN large = d
Step 7: IF b < small THEN small = b
Step 8: IF c < small THEN small = c
Step 9: IF d < small THEN small = d
Step 10: PRINT "Largest =", large
Step 11: PRINT "Smallest =", small
END

Python verification

a = float(input("Enter first number: "))
b = float(input("Enter second number: "))
c = float(input("Enter third number: "))
d = float(input("Enter fourth number: "))

large = small = a
if b > large: large = b
if c > large: large = c
if d > large: large = d
if b < small: small = b
if c < small: small = c
if d < small: small = d

print("Largest =", large)
print("Smallest =", small)

Dry run for inputs 12, 5, 29, 17:

Start your 14-day free trial to unlock the full solution →

←Previous questionQ9 — Write an algorithm that performs the following: Ask a user to enter a …→Next questionQ11 — Write an algorithm to display the total water bill charges of the mont…

Q.Write an algorithm that accepts four numbers as input and find the largest and smallest of them.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days