Write an algorithm to find the greatest among two different numbers entered by the user.

Exercise · Q8

Q. Write an algorithm to find the greatest among two different numbers entered by the user.

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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. …

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Compare the two numbers with a single condition:

GREATEST_OF_TWO
Step 1: INPUT num1, num2      (two different numbers)
Step 2: IF num1 > num2 THEN
            PRINT num1, "is the greatest"
        ELSE
            PRINT num2, "is the greatest"
Step 3: END
``` …

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One comparison decides it: if num1 > num2 the first is the greatest, otherwise the second — a pure selection (if–else) algorithm.

The idea (selection). Finding the larger of two values needs no loop, just a decision: compare once and branch. Because the question guarantees the numbers are different, exactly one of num1 > num2 / num2 > num1 is true, and a plain if–else covers everything.

Algorithm

GREATEST_OF_TWO_ALGO
Step 1: INPUT num1
Step 2: INPUT num2          (num2 different from num1)
Step 3: IF num1 > num2 THEN
            PRINT num1, "is the greatest"
        ELSE
            PRINT num2, "is the greatest"
        END IF
Step 4: END

Flowchart in words: Start (oval) → Input num1, num2 (parallelogram) → Decision "num1 > num2?" (diamond) → Yes-arrow → Output num1 (parallelogram) → Stop; No-arrow → Output num2 (parallelogram) → Stop.

Python verification

num1 = float(input("Enter first number: "))
num2 = float(input("Enter second number: "))
if num1 > num2:
    print(num1, "is the greatest")
else: …

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Q.Write an algorithm to find the greatest among two different numbers entered by the user.

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