Today, many applications require breaking down a large number into smaller manageable denominations. For instance, converting a large monetary value into available bill denominations. This article will explore how to split the number 450 into two 200s, one 50, and no 100s using Java. Let's dive straight into our code and explanation.

Introduction

Let's start by examining the problem. Given an integer input 450, we need to split this number into smaller denominations using the following bills: 200s, 100s, 50s, and any remaining amount. The goal is to determine how many of each denomination is needed to sum up the initial value without any remainder.

Java Code Implementation

The following code in Java addresses this problem. We will use an array to store the denominations and a loop to perform the division and subtraction.

prepublic class NumberSplitter {    public static void main(String[] args) {        int input  450;        int[] bills  new int[]{200, 100, 50};        ("Splitting "   input   " to:");        for (int i : bills) {            int numBills  input / i;            input - i * numBills;            (numBills   " x "   i);        }        ("rest: "   input);    }}/pre

Step-by-Step Explanation

Input Initialization: We start with the input number input 450. Bills Array: We define an array bills[] that contains the available denominations: 200, 100, 50. Division and Subtraction Loop: For each denomination, we calculate the number of times it fits into the input (numBills input / i) and subtract the value of these bills from the input (input - i * numBills). This process repeats for each denomination in descending order. Output: The output displays the number of each denomination needed and the remaining amount after all splits.

Let's walk through an example with the given input of 450 and bills (200, 100, 50).

Example Walkthrough

Given input 450 and denominations [200, 100, 50]:

First, we divide by the largest denomination (200) and find that we can have 2 of these bills, since 450 / 200 2 with a remainder of 50. So, we subtract 2 * 200 from 450, leaving us with 50. Next, we move to the next largest denomination (100). Since there is only a remainder of 50, we can have 0 of these 100s. Finally, we look at the denomination of 50. Since the remainder is 50, we have 1 of these bills, and the remainder now becomes 0.

The final result is:

2 x 200
0 x 100
1 x 50
rest: 0

Conclusion

In conclusion, the Java code provided effectively splits a given large number into smaller denominations based on the available denominations. This method ensures that the remainder is minimized, making it a practical approach for various applications requiring such functionality.

By understanding the logic behind the division and subtraction, you can adapt this technique to other scenarios where splitting a number is necessary. Happy coding!