Write a Program That Finds the Maximum Product of Three Numbers in a List of Integers.

One of the classical programs to build programming logic is, write a program to find the largest of three numbers. I am sure many of you have already done this exercise in a variety of languages including C, C++, C#, JavaScript, Perl, Ruby, PHP, etc. This time we will do it in Java. We will first learn the logic by understanding the flowchart of the largest of three numbers and then we will implement a solution using the ternary operator in Java. I love this program for its sheer simplicity and how it can help beginners to build logic. As always, you are not allowed to use any library function which can solve this problem directly, your main task is to build logic using primitive language tools e.g. operators.

In Java, this problem is also used to teach how a ternary operator works, as one of the popular versions of this requires you to find the largest of three numbers using a ternary operator.

This problem is in a similar category as to how to determine if the number is prime. This Java program finds the largest of three numbers and then prints it. If the entered numbers are unequal then one version of this program returns Integer.MIN_VALUE, while others return the number itself.

By the way, the method used here is not general and doesn't scale well for many numbers. For example, If you want to find out the largest of a list of numbers say 10 integers then using the above approach is not easy, instead you can use array data structure, and keep track of the largest number while comparing with other numbers.

We will also see how we can use the ternary operator in Java to find the biggest of three integers. I have made both method static because they are actually utility method and only operates on their arguments, and I can call them from the main method directly, without creating an object of this class.

Btw, it's essentials for every programmer to know about basic data structures like an array, linked list, binary tree, hash table, and others. It helps you to write better code and also crack interviews, if you want to brush up your algorithms skills then you can also join a comprehensive Data Structure and Algorithms courses to fill the gaps in your understanding.

Logic to find Greatest of Three Integers

Algorithm or logic is independent of programming language. More or less they are same in every language. For example, if you build logic without using library method e.g. only based upon standard operators and data structures e.g. array, you can use them in different language.

For example, first logic can be used in JavaScript, C, C++ or C#. Second logic uses a special operator, known as a ternary operator, as it has three arguments, that's why it can only be applied to languages which support ternary operator e.g. Java. Logic to find the biggest of three number is as follows :

1. Check if the first number is greater than the second and third, if Yes, then first number is largest.
2. Check if the second number is greater than second and third, if Yes, the second number is the largest.
3. Otherwise, the third number is the largest.

This is the most simple logic of finding maximum of three numbers, it can't be simpler than this. By the way, there is some opportunity to improve my logic of finding biggest of three, as you may notice, I am comparing the same numbers more than one time. I leave that as exercise for you, but will give you some hint in the flowchart, which we will see in next section.

Largest of Three Numbers FlowChart

This is the flowchart of finding the largest of three numbers in Java, it first reads three numbers A, B, and C from the console, using utilities like Scanner. Then it first compares A against B, if A > B then it goes to compare A and C. If A > C, the A is the largest number, else C is the maximum number.

On the other hand, if A < B in the first comparison then the second comparison happens between B and C if B > C then B is largest otherwise C is the largest number.

This logic is shown below flowchart, I am sure it's much easier to understand a flowchart than its description :)

The complexity of Our Solution

If you look at the flow chart, you will find that we at least need to do two comparisons to find the maximum of three numbers. To understand this, you can see how many diamond boxes we are using in each path, there are only two.

So to find the maximum of three numbers, we have done 2 comparisons, which means to find the maximum of n numbers, we need to do the n-1 comparison. That's why the time complexity of this solution is O(n).

Java Program to Find Largest of Three Numbers

Here is our complete Java solution to this problem. As I said before, we have two solutions, one which finds the largest of three numbers using the ternary operator and the other which uses if-else-if loop. First solution is very simple as it compares numbers more than required, in the worst case it does 8 comparisons.

The second solution uses the logic from the flowchart and only does two comparisons to find the largest of three. This example is also user-driven, we read input from user, and then feed them into our method to find the biggest of three numbers. You are free to improve the logic, but don't forget to explain why it's better, this is where you score.

            import            java.util.Scanner;            /** * Java program to find largest of three Integer numbers.  * You can not use any library method to  * solve this problem. You need to build logic by yourself.  * Input : 3, 5, 7 * Output : 7 * *              @author              Javin Paul */            public            class            LargestOfThree{            public            static            void            main(String            args[]) {            Scanner            cmd            =            new            Scanner(System            .in);            System            .out.println("Please enter three different numbers                        to find largest of them");            int            first            =            cmd.nextInt();            int            second            =            cmd.nextInt();            int            third            =            cmd.nextInt();            int            largest            =            largestOfThree(first, second, third);            System            .out.printf("Largest of three numbers,                      between %d, %d and %d is %d %n",                 first, second, third, largest);            int            greatest            =            greatestOfThreeUsingTernaryOperator(first,                                second, third);            System            .out.printf("Greatest of three numbers in Java                            using ternary operator is %d %n", greatest);            //close the scanner to prevent resource leak            cmd.close();      }            /**      * Find largest of three numbers in Java. All three numbers must be      * distinct.      *      *              @param              first      *              @param              second      *              @param              third      *              @return              largest of three numbers, or Integer.MIN_VALUE       * if numbers are not      * distinct.      */            public            static            int            largestOfThree(int            first,            int            second,            int            third) {            if            (first            >            second            &&            first            >            third) {            return            first;         }            else            if            (second            >            first            &&            second            >            third) {            return            second;         }            else            if            (third            >            first            &&            third            >            second) {            return            third;         }            return            Integer                          .MIN_VALUE;     }            /**      * function to find largest of three numbers in Java using       * ternary operator      *              @param              one      *              @param              two      *              @param              three      *              @return              biggest of three numbers      */            public            static            int            greatestOfThreeUsingTernaryOperator(int            one,            int            two,            int            three) {            return                          (one                        >                          two)                        ?                          (one            >                          three                        ?                          one                        :                          three)                                      :                          (two                        >                          three                        ?                          two                        :                          three);            }  }            Output            :            Please            enter three different numbers to find largest of them            11            21            31            Largest            of three numbers, between            11,            21            and            31            is            31            Greatest            of three numbers in            Java            using ternary operator is            31            Please            enter three different numbers to find largest of them            4            5            4            Largest            of three numbers, between            4,            5            and            4            is            5            Greatest            of three numbers in            Java            using ternary operator is            5            Please            enter three different numbers to find largest of them            23            23            23            Largest            of three numbers, between            23,            23            and            23            is            -            2147483648            Greatest            of three numbers in            Java            using ternary operator is            23          

If you look at the last case, it seems this program has some bugs, it doesn't return the correct value if all three numbers are equal, at least the first method. Can you modify this program to return the number itself if all three integers are same? for example in this case it should return 23. For your help, I have implemented that logic in the second version of that function, which finds largest of three numbers using ternary operator.

That's all about how to find the maximum of three numbers in Java. We have also learned about use of ternary operators to solve this problem. If you are absolute beginner and face problem understanding logic, I suggest to take a look at the flowchart to find largest of three numbers. It's much easier to understand a flowchart than all description. It's said for nothing that, a picture is worth more than thousand words :). If you love to learn by solving coding problems, here are some of them to try your hands.

Coding Problems to learn Programming
Write a program to find Greatest Common Divisor of two numbers (solution)
Write a program to check if number is power of two (solution)
Write a program to swap two numbers without using third variable (answer)
How to find middle element of linked list in one pass? (solution)
How to find loop in linked list? (answer)

Write a Program That Finds the Maximum Product of Three Numbers in a List of Integers.

Source: https://javarevisited.blogspot.com/2014/07/how-to-find-largest-of-three-integers-in-Java-program.html

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