recursively add integers from 1^2 to n^2 - java

i'm having some trouble recursively adding integers in java from 1^2 to n^2.
I want to be able to recursively do this in the recurvMath method but all i'm getting is an infinite loop.
import java.util.Scanner;
public class Lab9Math {
int count = 0;
static double squareSum = 0;
public static void main(String[] args){
int n = 0;
Scanner scan = new Scanner(System.in);
System.out.println("Please enter the value you want n to be: ");
n = scan.nextInt();
Lab9Math est = new Lab9Math();
squareSum = est.recurvMath(n);
System.out.println("Sum is: "+squareSum);
}
public int recurvMath(int n){
System.out.println("N:" +n);
if(n == 0){
return 0;
}//end if
if (n == 1){
return 1;
}//end if
if (n > 1){
return (recurvMath((int) ((int) n+Math.pow(n, 2))));
}//end if
return 0;
}//end method
}//end class
I'm not fully grasping the nature of defining this recursively, as i know that i can get to here:
return (int) (Math.pow(n, 2));
but i can't incorporate the calling of the recurvMath method correctly in order for it to work.
Any help would be appreciated. Thanks!

In general, when trying to solve recursive problems, it helps to try to work them out in your head before programming them.
You want to sum all integers from 12 to n2. The first thing we need to do is express this in a way that lends itself to recursion. Well, another way of stating this sum is:
The sum of all integers from 12 to (n-1)2, plus n2
That first step is usually the hardest because it's the most "obvious". For example, we know that "a + b + c" is the same as "a + b", plus "c", but we have to take a leap of faith of sorts and state it that way to get it into a recursive form.
So, now we have to take care of the special base case, 0:
When n is 0, the sum is 0.
So let's let recurvMath(n) be the sum of all integers from 12 to n2. Then, the above directly translates to:
recurvMath(n) = recurvMath(n-1) + n2
recurvMath(0) = 0
And this is pretty easy to implement:
public int recurvMath(int n){
System.out.println("N:" +n);
if(n == 0){
return 0;
} else {
return recurvMath(n-1) + (n * n);
}
}
Note I've chosen to go with n * n instead of Math.pow(). This is because Math.pow() operates on double, not on int.
By the way, you may also want to protect yourself against a user entering negative numbers as input, which could get you stuck. You could use if (n <= 0) instead of if (n == 0), or check for a negative input and throw e.g. IllegalArgumentException, or even use Math.abs() appropriately and give it the ability to work with negative numbers.
Also, for completeness, let's take a look at the problem in your original code. Your problem line is:
recurvMath((int) ((int) n+Math.pow(n, 2)))
Let's trace through this in our head. One of your int casts is unnecessary but ignoring that, when n == 3 this is recurvMath(3 + Math.pow(3, 2)) which is recurvMath(12). Your number gets larger each time. You never hit your base cases of 1 or 0, and so you never terminate. Eventually you either get an integer overflow with incorrect results, or a stack overflow.

instead of saying:
return (recurvMath((int) ((int) n+Math.pow(n, 2))));
i instead said:
return (int) ((Math.pow(n, 2)+recurvMath(n-1)));

Try this
import java.util.Scanner;
public class Lab9Math {
int count = 0;
static double squareSum = 0;
public static void main(String[] args){
int n = 0;
Scanner scan = new Scanner(System.in);
System.out.println("Please enter the value you want n to be: ");
n = scan.nextInt();
Lab9Math est = new Lab9Math();
squareSum = est.recurvMath(n);
System.out.println("Sum is: "+squareSum);
}
public int recurvMath(int n){
System.out.println("N:" +n);
if(n == 1){
return 1;
}//end if
// More simplified solution
return recurvMath(n-1) + (int) Math.pow(n, 2); // Here is made changes
}//end method
}//end class

Related

How to write a java program that computes the value of e^x

I'm trying to figure out how to answer this question for my Java class, using only while loops:
Write an application that computes the value of mathematical constant e^x by using the following formula. Allow the user to enter the number of terms to calculate. e^x = 1 + (x/1!) + (x^2/2!) + (x^3/3!) + ...
I can't figure out how I would do this without also asking the user for a value for x? Below is the code that I created for calculating x with the number of terms and just the number 1 for the exponent of each fraction. Any help is appreciated
import java.util.Scanner;
public class FactorialB {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int counter = 0;
float answer = 0;
System.out.print("Enter number of terms: ");
int n = scanner.nextInt();
while (counter < n) {
double factorial = 1;
int factCounter = counter;
while (factCounter > 1) {
factorial = factCounter * factorial;
factCounter--;
}
answer += 1 / factorial;
counter++;
}
System.out.printf("e = %f%n", answer);
}
}
Firstly the question you seem to be asking:
There is no way to make a program that will give e for a specific number unless you ask the user for that number.
However it might be that they just want you to make a method that provides the solution (if it were called) independently of user input. (because the code to get user input isn't very interesting, what is interesting is how you reach the result).
An alternative way to provide x and n are for instance passing them as commandline arguments. (args[] in your main would be a way to provide them)
I would create a separate method that receives x and n that covers the main calculation:
e^x = 1 + (x/1!) + (x^2/2!) + (x^3/3!) + ...
And separate methods that cover 'calculating a single term (x^1/1!), (x^2/2!), etc' and 'factorialize(n)'
public void calculatePartialE_term(int x, int n) {
if (n == 0) {
return 1; // this will allow you to use a while loop, covers the n = 0 case
} else {
// removed the implementation, but basically do
// x^n/n! here for whatever value of n this term is calculating.
}
}
public int calcualteNFactorial(int n) {
// assert n >= 1
// use a while loop to calculate n factorial
}
the benefit of doing this in a separate methods is that you can prove / verify the working of calculatePartialE_term or calcualteNFactorial independently of one another.
now you can simply write a while loop based on x and n to do something like
public int calculateE_to_x(int x, int n) {
int current = 0;
int sum = 0;
while (current <= n) {
sum += calculatePartialE_term(x, current);
}
}
I wouldn't expect your teacher to expect you to show code that handles user input but even if that is the case it will be easier for them to verify your work if the actual work (of calculating) is done in a separate method.

Count Multiples

I have been assigned to write a java program for class that counts multiples. The program takes three integers as input: low, high, x. The program then outputs the number of multiples of x between low and high exclusively.
If the input is: 1, 10, 2
the output would be: 5
My teacher has the proclivity to assign problems we haven't covered in class and I am unsure where to begin. Im not asking for the full code, just how to set up the problem
I am unsure of how to follow my logic thru the program: what I have so far is this
import java.util.Scanner;
public class LabProgram {
public static void main(String[] args) {
Scanner scnr = new Scanner(System.in);
int low, high, x;
int count = 0;
low = scnr.nextInt();
high = scnr.nextInt();
x = scnr.nextInt();
for(int i = low; i <= high; i++){
if(i % x == 0){
count++;
}
if (i % x != 0){
//System.out.println(count);// someone suggested to move this
}
}
System.out.println(count);
}
}
~~~~~~
If I input 1, 10, 2
My output is 01234
Moved the print of count outside of the loop... man I am tired.
FINAL EDIT: This code works, it accomplishes the goal. Thank you to #charisma and everyone else that helped me understand what was going on here. I am new to java but determined to learn more! Thanks all!!!!!
You can input numbers using scanner class similar to the following code from w3schools:
import java.util.Scanner; // Import the Scanner class
class Main {
public static void main(String[] args) {
Scanner myObj = new Scanner(System.in); // Create a Scanner object
System.out.println("Enter username");
String userName = myObj.nextLine(); // Read user input
System.out.println("Username is: " + userName); // Output user input
}
}
low, high and x can be of data type int.
To check which numbers between low and high are multiples of x, you can use a for loop. You can declare a new variable count that can be incremented using count++ every time the for loop finds a multiple. The % operator could be useful to find multiples.
You can output using System.out.println(" " + );
Edit:
% operator requires 2 operands and gives the remainder. So if i % x == 0, it means i is a multiple of x, and we do count++.
The value of i will run through low to high.
for (i = low; i <= high; i++) {
if (i % x == 0) {
count++;
}
}
Once you get to the basic implementation (as explained by Charisma), you'll notice, that it can take a lot of time if the numbers are huge: you have high - low + 1 iterations of the loop. Therefore you can start optimizing, to get a result in constant time:
the first multiple is qLow * x, where qLow is the ceiling of the rational quotient ((double) low) / x,
the last multiple is qHigh * x, where qHigh is the floor of the rational quotient ((double) high) / x,
Java provides a Math.floor() and Math.ceil(), but you can get the same result using integer division and playing with the signs:
final int qLow = -(-low / x);
final int qHigh = high / x;
Now you just have to count the number of integers between qLow and qHigh inclusive.
return qHigh - qLow + 1;
Attention: if x < 0, then you need to use qLow - qHigh, so it is safer to use:
return x > 0 ? qHigh - qLow + 1 : qLow - qHigh + 1;
The case x == 0 should be dealt with at the beginning.
put count++; after the last print statement

Java 1 student totally lost. Recursion program

Hi very first Java class and it seems to be going a mile a minute. We learn the basics on a topic and we are asked to produce code for more advanced programs than what helped us get introduced to the topic.
Write a recursive program which takes an integer number as Input. The program takes each digit in the number and add them all together, repeating with the new sum until the result is a single digit.
Your Output should look like exactly this :
################### output example 1
Enter a number : 96374
I am calculating.....
Step 1 : 9 + 6 + 3 + 7 + 4 = 29
Step 2 : 2 + 9 = 11
Step 3 : 1 + 1 =2
Finally Single digit in 3 steps !!!!!
Your answer is 2.
I understand the math java uses to produce the output I want. I can do that much after learning the basics on recursion. But with just setting up the layout and format of the code I am lost. I get errors that make sense but have trouble correcting with my inexperience.
package numout;
import java.util.Scanner;
public class NumOut {
public static void main(String[] args) {
System.out.print("Enter number: ");
Scanner scan = new Scanner(System.in);
int n = scan.nextInt();
System.out.println(n);
}
public int sumDigit(int n){
int sum = n % 9;
if(sum == 0){
if(n > 0)
return 9;
}
return sum;
}
}
The output understandably duplicates the code given by the input from the user.
I had trouble calling the second class when I tried to split it up into two. I also know I am not soprln n, or the sum. So I try to make it into one and I can visibly see the problem but am unaware how to find the solution.
Think of recursion as solving a problem by breaking it into similar problems which are smaller. You also need to have a case where the problem is so small that the solution is obvious, or at least easily computed. For example, with your exercise to sum the digits of a number, you need to add the ones digit to the sum of all the other digits. Notice that sum of all the other digits describes a smaller version of the same problem. In this case, the smallest problem will be one with only a single digit.
What this all means, is that you need to write a method sumDigits(int num) that takes the ones digit of num and adds it to the sum of the other digits by recursively calling sumDigits() with a smaller number.
This is how you need to do : basically you are not using any recursion in your code. Recursion is basically function calling itself. Don't be daunted by the language, you will going to enjoy problem solving once you start doing it regularly.
public static void main(String []args){
Scanner scan = new Scanner(System.in);
int n = scan.nextInt();
printSingleDightSum(n);
}
public static void printSingleDightSum(int N) {
int sum = 0;
int num = N;
while(num !=0 ){
int a = num%10;
sum + = a;
num = num/10;
}
if(sum < 10) {
System.out.println('single digit sum is '+sum);
return;
} else {
printSingleDightSum(sum);
}
}
Here is the code, I will add comments and an explanation later but for now here is the code:
package numout;
import java.util.Scanner;
public class NumOut {
public static void main(String[] args) {
System.out.println("################### output example 1");
System.out.print("Enter number: ");
final int n = new Scanner(System.in).nextInt();
System.out.print("\nI am Calculating.....");
sumSums(n, 1);
}
public static int sumSums(int n, int step) {
System.out.print("\n\nStep " + step + " : ");
final int num = sumDigit(n);
System.out.print("= " + num);
if(num > 9) {
sumSums(num, step+1);
}
return num;
}
public static int sumDigit(int n) {
int modulo = n % 10;
if(n == 0) return 0;
final int num = sumDigit(n / 10);
if(n / 10 != 0)
System.out.print("+ " + modulo + " ");
else
System.out.print(modulo + " ");
return modulo + num;
}
}

Converting From Decimal to Binary In Java

So I have code that will convert a decimal number to binary. I use a recursive algorithm for it, however I cannot seem to get it to do what I want. Here is the code:
import java.util.*;
public class binaryAddition {
public static int toBinary(int a){
int bin = 0;
int remainder = 0;
if(a >= 1){
toBinary(a/2);
bin = (a%2);
}
return bin;
}
public static void main(String[] args){
System.out.println(toBinary(3));
System.out.print(toBinary(3));
}
}
So I want to to return the binary solution so that I can save it as a variable in my main method. However, my current output would only give me that last digit of the binary number. I used the number 3 just as a test case and I get 1 as an output for both print and println methods. Why is that, and how can I fix it?
Many Thanks!
For a start, you might want to have toBinary return a String, not an int. Then you must use the result of it when you recurse. So you might write, inside your if,
bin = toBinary(a / 2) + (a % 2);
assuming, of course, that toBinary returns String.
If you don't do this, then you're just throwing away the result of your calculation.
The code is discarding the results of the recursive calls.
Do something with the result of toBinary in the method.
Just Do it Like i have Done .
public static void main(String[] args)
{
int n, count = 0, a;
String x = "";
Scanner s = new Scanner(System.in);
System.out.print("Enter any decimal number:");
n = s.nextInt();
while(n > 0)
{
a = n % 2;
if(a == 1)
{
count++;
}
x = x + "" + a;
n = n / 2;
}
System.out.println("Binary number:"+x);
System.out.println("No. of 1s:"+count);
}

Understanding methods. Java code

Write a method that computes the sum of the digits in an integer. Use
the following method header: public static int sumDigits(long n)
Programming problem 5.2. Page 212.
Please forgive my newness to programming. I'm having a hard time understanding and answering this question. Here's what I have so far. Please assist and if you dont mind, explain what I'm doing wrong.
import java.util.Scanner;
public class PP52v2 {
public static void main(String [] args) {
int sum = sumDigits(n);
System.out.println("The sum is: " + sum);
}//main
public static int sumDigits(long n) {
Scanner input = new Scanner(System.in);
System.out.println("Enter your digits");
n = input.nextLong();
int num = (int)(n);
int sum;
while(num > 0) {
sum += num % 10; //must mod - gives individual numbers
num = num / 10; //must divide - gives new num
}//loop
return sum;
}//sumDigits
}//class
Basically, you should not be handling the user input inside of the method. You should be passing the user input into your method. Other than that, everything looks good. I've made that slight change below:
import java.util.Scanner;
public class PP52v2 {
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
System.out.println("Enter your digits");
long n = input.nextLong();
int sum = sumDigits(n);
System.out.println("The sum is: " + sum);
}// main
public static int sumDigits(long n) {
int num = (int) (n);
int sum = 0;
while (num > 0) {
sum += num % 10; // must mod - gives individual numbers
num = num / 10; // must divide - gives new num
}// loop
return sum;
}// sumDigits
}// class
Do the prompt
System.out.println("Enter your digits");
n = input.nextLong();
in your main(String[] args) method because n is not currently declared in the scope of the main method.
public static int sumDigits(int num) {
int sum = 0;
while(num > 0) {
sum += num % 10; //must mod - gives individual numbers
num = num / 10; //must divide - gives new number
} //End loop
return sum;
}
For one, you should not read in the number within this method, as it accepts the number as a parameter. The method should be invoked after calling long inputNum = input.nextLong(); by using int digitSum = sumDigits((int)inputNum).
When writing a method, you have input, output, and side effects. The goal is to choose the right combination of the three so that the method, and program as a whole, words as expected.
It seems like your method is supposed to take a number as input and return each digit added together into one final sum.
Write A Test
Usually when you program, you come up with some code that uses your imaginary function. This is called a test. For a test, this could work:
System.out.println("123 should be 6: " + sumDigits(123));
Choose A Signature
You've already managed to right the correct signature. Nice!
Implement Method
Here's where you're a bit confused. Read through what every line of code does, and see if it is accomplishing your goal.
// set up a scanner for reading from the command line
// and print a message that you expect digits
Scanner input = new Scanner(System.in);
System.out.println("Enter your digits");
// read the next long number from the input stream
n = input.nextLong();
Why is this part of your method? You already have the number passed in as the argument n.
// cast the number to an integer
int num = (int)(n);
Again, not sure what this is accomplishing, besides the possibility of a bug for large numbers.
// initialize the sum variable to 0.
int sum;
Would be clearer to explicitly set the sum to 0. int sum = 0;
// add the last digit and truncate the number in a loop
while(num > 0) {
sum += num % 10; //must mod - gives individual numbers
num = num / 10; //must divide - gives new num
}
// actually return the calculated sum
return sum;
This seems like the only part of the method you need. Hopefully this helps!
Since the input number can be either positive or negative, you need to convert it to its absolute value to get the sum of digits. Then for each iteration, you add the remainder to the total sum until the quotient is 0.
public static int sumDigits(long n) {
int sum = 0;
long quotient = Math.abs(n);
while(quotient > 0) {
sum += quotient % 10;
quotient = (long) quotient / 10;
}
return sum;
}
Your code works fine for me.
i just changed int sum = sumDigits(n) to int sum = sumDigits(0) since n wasn't declared.
To have it done correctly, you just would have to put your scanner into the main method and pass the result of it (the long value) to your method sumDigits(long n).

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