Modifying Summation using Recursion - java

How do I modify the summation method using recursive definition to get the sum of 1 to N via - (1 to N/2) + ((N/2+1) to N)?
I'm confused a bit here, I've typed out something along the lines of this, but it's not recursion:
public static int Sum(int n){
int sum1 = 0;
int sum2 = 0;
int totalSum = 0;
for(int i = 1; i <= n/2; i++){
sum1 += i;
}
for(int i = n/2 + 1; i <= n; i++){
sum2 += i;
}
totalSum = sum1 + sum2;
return totalSum;
}

First off, your implementation is not recursive.
Your question states the right algorithm: to sum the values between 1 and n, you can sum them between 1 and n/2, then between n/2 + 1 and n. This means we need to create a helper function sum(int a, int b) whose goal will be to return the sum of all the values between a and b.
The base case is when a == b: in this case, the helper should just return a.
In the recursive step, we do the previous algorithm: sum from a to (a+b)/2 and sum from (a+b)/2 + 1 to b.
This would be an implementation:
public static int sum(int a, int b) {
if (a == b) {
return a;
}
int middle = (a + b) / 2;
return sum(a, middle) + sum(middle + 1, b);
}
with this, the initial task becomes:
public static int sum(int n) {
return sum(1, n);
}
Some samples:
public static void main(String[] args) {
System.out.println(sum(4)); // prints 10
System.out.println(sum(5)); // prints 15
System.out.println(sum(6)); // prints 21
}

Related

Use 3 methods(Addition, Average, numberEvenOdd) in an array

I have an array named tab with several numbers
int[] tab = {1,3,4,2};
I have to create 3 methods:
1) the first addition() method
2) the second average() method
3) the third numberEvenOdd() method
My goal : I have to calculate the average of the odd numbers in the array by using my 3 methods.
Here is my addition() method
public static int addition(int[] tab){
int sum = 0;
for(int i=0;i<tab.length;i++){
sum += tab[i];
}
return sum;
}
Then, my average() method
public static double averages(int[] tab){
return (double) addition(tab) / tab.length;
}
And my numberOddEven() method
public static int numberOddAdd(int[] tab, boolean value){
int parity = 0;
if(! value){
parity = 1;
}
int n = 0;
for(int i=0; i<tab.length;i++){
if(tab[i] % 2 == parity){
n += tab[i];
}
}
return n;
}
In my print, I have a problem in the syntax ?
I have tried this
System.out.println(averages(numberOddEven(tableau1, false));
My error message is -> incompatible types: int cannot be converted to int ?

Depth of an array

If we are given an array arr1 consisting of n integers, we can calculate the depth of it in the following way as in image.
The first line of input contains 3 integers n, a, b where n is the size of array.
The second line of input contains array elements. Now if the depth of array = a/b we need to print "yes" else "no".
I have tried to implement the following code:
public static void solve(int n, int a,int b, int[] arr) {
String result = "";
double depth = 0;
for (int i = 0; i < n - 1; i++) {
depth = (double)((double)(depth + arr[i]) + (double)(1 / arr[i + 1]));
}
double d = (double) a / b;
if (depth == d) {
result = "YES";
} else {
result = "NO";
}
System.out.println(result);
}

Reduce sum of digits recursively down to one digit number

How do I make a function return the sum of all digits until it becomes a 1 digit number, using recursion? I was able to make a function that gets the sum of all digits, but cant seem to find a way to recursively sum the digits of the sum itself:
class sum_of_digits
{
static int sum_of_digit(int n)
{
if (n == 0)
return 0;
return (n % 10 + sum_of_digit(n / 10));
}
public static void main(String args[])
{
int num = 12345;
int result = sum_of_digit(num);
System.out.println("Sum of digits in " +
num + " is " + result);
}
}
This code prints the sum of '12345', which is 15. But I need to change it so it prints the sum of 1 + 5, which is 6.
do you think it is possible to make it work without an additional
method?
Why can't we just let the recursion do the work for us and simply say:
static int sum_of_digit(int n)
{
if (n < 10)
return n;
return sum_of_digit(n % 10 + sum_of_digit(n / 10));
}
Things will become a lot easier if you define an additional recursive "layer" in conjunction with sum_of_digit. This new function can call sum_of_digit until it has a single digit as a result. Here is what I mean:
static int sum_to_one_digit(int n) {
if(n/10 == 0) return n;
return sum_to_one_digit(sum_of_digit(n));
}
The code from main will be:
public static void main(String args[])
{
int num = 12345;
int result = sum_to_one_digit(num);
System.out.println("Sum of digits in " +
num + " is " + result);
}
You could add a clause at the end to check whether the sum is smaller than 10, if it isn't then recursively call it again with the newly calculated sum, ie.
static int sum_of_digit(int n)
{
if (n == 0)
return 0;
int temp = (n % 10 + sum_of_digit(n / 10));
if (temp < 10)
return temp;
return sum_of_digit(temp);
}
There are several ways to do it, one would be like this if global variables are allowed :
public class Sum_of_digits{
static int sum = 0;
public static void main(String args[]){
int n = 12345;
System.out.println(sum_of_digit(n));
sum = 0;
}
static int sum_of_digit(int n){
if(n==0){
if(sum/10 == 0){
return sum;
}else{
n=sum;
sum=0;
}
}
sum = sum+(n%10);
n=n/10;
return sum_of_digit(n);
}
}
and if Global variable are not allowed then passing sum as a parameter will help :
public class Sum_of_digits{
public static void main(String args[]){
int n = 12345;
int sum = 0;
System.out.println(sum_of_digit(n,sum));
}
static int sum_of_digit(int n,int sum){
if(n==0){
if(sum/10 == 0){
return sum;
}else{
n=sum;
sum=0;
}
}
sum = sum+(n%10);
n=n/10;
return sum_of_digit(n,sum);
}
}
Here we are just shifting the focus from n to sum to evaluate the condition when the loop/recursion will terminate.

difficulty with fibonacci function

I'm supposed to change this recursive function, into an iterative function...
int rFib(int n)
{ //assumes n >= 0
if(n <= 1)
return n;
else
return (rFib(n-1) + rFib(n-2));
}
But I'm drawing a blank on the mathematical view of this... I would appreciate any assistance. I was able to get the other 3 functions, but I just can't seem to figure out the math of this one.
public static int fib(int n)
{
int theFib = 1;
while(n > 1)
{
theFib = n - 1;
n = n + n - 2;
}
System.out.println(theFib);
return theFib;
}
The next number in the Fibonacci sequence is the sum of the last two numbers, so you'll need to remember the last two numbers.
In pseudo code, since you should do some of the homework yourself:
n1 = 0
n2 = 1
loop
n = n1 + n2
n1 = n2
n2 = n
end loop
I'll leave it to you to limit the looping.
You can find an example here.
The code in question:
public class FibonacciIterative {
public static int fib(int n) {
int prev1=0, prev2=1;
for(int i=0; i<n; i++) {
int savePrev1 = prev1;
prev1 = prev2;
prev2 = savePrev1 + prev2;
}
return prev1;
}
}
It does not really matter which direction (up or down) you count. The challenge is to deal with the limits properly.
Using dynamic programming technique:
static int fib(int n) {
int[] fibs = new int[n + 1];
for (int i = 0; i <= n; i++) {
if (i <= 1) {
fibs[i] = i;
} else {
fibs[i] = fibs[i - 1] + fibs[i - 2];
}
}
return fibs[n];
}

LCM (lowest common multiple) in Java

I need help with this loop. One of my course assignments is to make a LCM program.
Sample output:
(8,12) LCM is 24
(4,3) LCM is 12
(5,10,20) LCM is 20
(18,24,52) LCM is 936
(12,10,26) LCM is 780
(99,63,24) LCM is 5544
(62,16,24) LCM is 1488
I have this so far for 2 numbers but I'm not sure how to do 3 numbers. We're supposed to use methods on other classes so this is what I have for the LCM class.
public class LCM {
private int n, x, s = 1, t = 1;
public LCM()
{
n = 0;
x = 0;
s = 1;
t = 1;
}
public int lcmFind(int i, int y) {
for (n = 1;; n++) {
s = i * n;
for (x = 1; t < s; x++) {
t = y * x;
}
if (s == t)
break;
}
return (s);
}
}
If you want to get LCM of 3+ numbers you can use your method lcmFind in following way:
int a = 2;
int b = 3;
int c = 5;
LCM l = new LCM();
int lcm = l.lcmFind(l.lcmFind(a, b), c);
Reccomendations:
Make n,x, s and t variables local in lcmFind. Because you need them ONLY in lcmFind method and you need to reset their values in every invocation of lcmFind.
Make your lcmFind method static. You don't need to instantiate new object in order to calc lcm. This way you can use it like LCM.lcmFind(3,4), or even better rename method and use something like LCM.find(3,4).
EDIT
If you need to make method that takes variable number of argument you should check varargs. So you'll get something like:
public int lcmFind(int.. args) {
// args is actually array of ints.
// calculate lcm of all values in array.
// usage: lcmFind(1,4) or lcmFind(1,5,6,3)
}
You can use your first version of lcmFind that takes 2 arguments and calculate lcm of many values using it.
EDIT 2
If you need only 2 and 3-args version of lcmFind than you can just add 3-arg version:
public int lcmFind(int a, int b, int c) {
return lcmFind(lcmFind(a, b), c);
}
I found this link and I guess this is most simple and clean solution:
/**
* Calculate Lowest Common Multiplier
*/
public static int LCM(int a, int b) {
return (a * b) / GCF(a, b);
}
/**
* Calculate Greatest Common Factor
*/
public static int GCF(int a, int b) {
if (b == 0) {
return a;
} else {
return (GCF(b, a % b));
}
}
try
public int lcm(int... a) {
for (int m = 1;; m++) {
int n = a.length;
for (int i : a) {
if (m % i != 0) {
break;
}
if (--n == 0) {
return m;
}
}
}
}
public static int gcd(int a, int b){
return (b == 0) ? a : gcd(b, a % b);
}
public static int gcd(int... args){
int r = args[0];
int i = 0;
while(i < args.length - 1)
r = gcd(r,args[++i]);
return r;
}
public static int lcm(int a, int b){
return a * b / gcd(a,b);
}
public static int lcm(int... args){
int r = args[0];
int i = 0;
while(i < args.length - 1)
r = lcm(r,args[++i]);
return r;
}
static int getLCM(int a,int b)
{
int x;
int y;
if(a<b)
{
x=a;
y=b;
}
else
{
x=b;
y=a;
}
int i=1;
while(true)
{
int x1=x*i;
int y1=y*i;
for(int j=1;j<=i;j++)
{
if(x1==y*j)
{
return x1;
}
}
i++;
}
}
I think you have the answer already, since it's an old post. still posting my answer. Below is the code to find the LCM for an array:
import java.util.Arrays;
import java.util.Scanner;
public class ArrayEqualAmz {
static int lcm =1;
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int [] arr = new int[n];
for(int i=0; i<n; i++){
arr[i] = sc.nextInt();
}
System.out.println("lcm = "+lcm(arr));
}
// find the factor
public static int divisor(int x[]){
Arrays.sort(x);
int num=0;
for(int i=x.length-1; i>=0; i--){
if(x[i] != 1 )
num=x[i];
}
for(int j=2; j<=num; j++){
if(num%j==0){
return j;}
}
return num;
}
//finding the lcm
public static int lcm(int arr[]){
while(true){
int j = divisor(arr);
if(j==0){break;}
lcm = lcm*j;
for(int i=0; i<arr.length; i++){
if(arr[i]%j==0){
arr[i] = arr[i]/j;}
System.out.print(arr[i]+",");
}
System.out.println( " factor= "+lcm);
return lcm(arr);
}
return lcm;
}
}
Try this
int n1 = 72, n2 = 120, lcm;
// maximum number between n1 and n2 is stored in lcm
lcm = (n1 > n2) ? n1 : n2;
// Always true
while(true)
{
if( lcm % n1 == 0 && lcm % n2 == 0 )
{
System.out.printf("The LCM of %d and %d is %d.", n1, n2, lcm);
break;
}
++lcm;
}
You can re use the same function written for lcm of two numbers. Just pass one of the arguments as follows:
The function code can be like this:
public static int lcm(int num1,int num2) {
boolean flag = false;
int lcm = 0;
for(int i= 1;!flag; i++){
flag = (num1 < num2)?(num2*i)%num1==0:(num1*i)%num2==0;
lcm = num1<num2?num2*i:num1*i;
}
return lcm;
}
Call the function like this:
public static void main(String[] args) {
System.out.println("lcm "+lcm(lcm(20,80),40));
}

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