Develop Reference

Flipping a coin and stopping when it lands heads 4 times in a row

The assignment is to flip a coin until four heads in a row are seen and display all the results leading up to that. I keep getting the last error message I put in just in case it fell through. I have no idea what I messed up and was wondering if someone was able to help.
class Main {
public static void main(String[] args) {
int h = 2;
int t = 1;
int count = 0;
int result;
while (count<=4)
{
result = (int)Math.random()*2;
if (result == 2)
{
count++;
System.out.print("H ");
}
else if (result == 1)
{
count=0;
System.out.print("T ");
}
else
System.out.println("error");
}
}
}

(int)Math.random() * 2
is the same as
((int)Math.random()) * 2
Given that Math.random() returns a number at least zero but less than one, your expression is always going to be zero.
Put in parentheses:
(int) (Math.random() * 2)
But then, also look at the values of result in your conditionals: you will never generate 2.

You need to add 1 to have possible values of one or two:
result = (int) (Math.random() * 2 + 1);

You can use the Randomclass and boolean
Random random = new Random();
int count = 0;
while (count < 4) {
if (random.nextBoolean()) {
System.out.print("H");
count++;
} else {
count = 0;
System.out.print("T");
}
}

As the result of Math.random() is between 0 and 1 type casting it to int will remove the digits after decimal point and you'll always have zero as answer.
Below code will help you to generate a random number between min and max.
// define the range
int max = 2;
int min = 1;
int range = max - min + 1;
int rand = (int)(Math.random() * range) + min;
For an explanation of how this works you can put the min possible value of 0 and max possible of 0.99 and multiply both by any range, let's say 20 the answer will still be in between 1 to 20.8 which gets turned to 20 as it's not rounding off but directly type casting. Hence, this can give you a random number for any range.

How to reverse the order of an int without turning it into a string

I have been tasked with the assignment of creating a method that will take the 3 digit int input by the user and output its reverse (123 - 321). I am not allowed to convert the int to a string or I will lose points, I also am not allowed to print anywhere other than main.
public class Lab01
{
public int sumTheDigits(int num)
{
int sum = 0;
while(num > 0)
{
sum = sum + num % 10;
num = num/10;
}
return sum;
}
public int reverseTheOrder(int reverse)
{
return reverse;
}
public static void main(String[] args)
{
Scanner input = new Scanner(System.in);
Lab01 lab = new Lab01();
System.out.println("Enter a three digit number: ");
int theNum = input.nextInt();
int theSum = lab.sumTheDigits(theNum);
int theReverse = lab.reverseTheOrder(theSum);
System.out.println("The sum of the digits of " + theNum + " is " + theSum);
}

You need to use the following.
% the remainder operator
/ the division operator
* multiplication.
+ addition
Say you have a number 987
n = 987
r = n % 10 = 7 remainder when dividing by 10
n = n/10 = 98 integer division
Now repeat with n until n = 0, keeping track of r.
Once you understand this you can experiment (perhaps on paper first) to see how
to put them back in reverse order (using the last two operators). But remember that numbers ending in 0 like 980 will become 89 since leading 0's are dropped.

You can use below method to calculate reverse of a number.
public int reverseTheOrder(int reverse){
int result = 0;
while(reverse != 0){
int rem = reverse%10;
result = (result *10) + rem;
reverse /= 10;
}
return result;
}

Java Split Number into Digit's Algorithm

package test;
import java.util.Scanner;
public class SplitNumber
{
public static void main(String[] args)
{
int num, temp, factor = 1;
Scanner sc = new Scanner(System.in);
System.out.println("Enter a number: ");
num = sc.nextInt();
temp = num;
while (temp != 0) {
temp = temp / 10;
factor = factor * 10;
}
System.out.print("Each digits of given number are: ");
while (factor > 1) {
factor = factor / 10;
System.out.print((num / factor) + " ");
num = num % factor;
}
}
}
I can't understand this int factor's job. Can someone help me to understand this codes algorithm?

In programming languages, if you hold double value in the int,it rounds the number to lower one thus if you do 15/10 it will return 1 as int and if you do 5/10 it will return 0. With this knowledge you can understand.
For example,let the number be 953,
while (temp != 0) {
temp = temp / 10;
factor = factor * 10;
}
1.Iteration temp = 95 , factor = 10
2.Iteration temp = 9 , factor = 100
3.Iteration temp = 0 , factor = 1000
end of while loop because temp is 0.
while (factor > 1) {
factor = factor / 10;
System.out.print((num / factor) + " ");
num = num % factor;
}
1.Iteration num = 953 factor = 100 , 953/100 = 9 (you get first digit)
2.Iteration num = 953%100 = 53 , factor = 10 , 53/10 = 5 (you get second digit)
3.Iteration num = 53%10 = 3 , factor = 1 , 3/1 = 3 (you get last digit)
End of while loop.
Actually it is basic math. When you want to extract nth digit of number, you just have to divide it by 10^n.

The modulus operator to extract the rightmost digit or digits from a number. For example, x % 10 yields the rightmost digit of x (in base 10). Similarly x % 100 yields the last two digits.
Here more info

If you would not care about flipping the order of digits, you could simply write
int num = sc.nextInt();
do {
System.out.println(num % 10);
num = num / 10;
} while(num != 0);
The modulo operation num % 10 calculates the remainder of dividing num by 10, effectively gets the digit at the lowest position ("ones"). 0 % 10 is 0 ... 9 % 10 is 9, 10 % 10 is 0 again, and so on. Then the division by 10 makes the old "tens" the new "ones", and the entire thing is repeated until 0 remains.
The hassle in your code is about emitting the digits in the "correct" order, highest position first, ones last. So it first checks how many digits are in your number, factor grows to the same size in the process. temp=temp/10; has the same role as num=num/10; in the short snippet (cutting a digit from the number in each iteration), and factor=factor*10 "adds" a digit to factor at the same time. [I just stop here as there is an accepted answer already explaining this]

Represent an Integer as a sum of Consecutive positive integers

I am writing code for counting the number of ways an integer can be represented as a sum of the consecutive integers. For Example
15=(7+8),(1+2+3+4+5),(4+5+6). So the number of ways equals 3 for 15.
Now the input size can be <=10^12. My program is working fine till 10^7(i think so, but not sure as i didnt check it on any online judge. Feel free to check the code for that)
but as soon as the i give it 10^8 or higher integer as input. it throws many runtime exceptions(it doesnt show what runtime error). Thanks in advance.
import java.io.*;
//sum needs to contain atleast 2 elements
public class IntegerRepresentedAsSumOfConsecutivePositiveIntegers
{
public static long count = 0;
public static void main(String[] args) throws IOException
{
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
long num = Long.parseLong(br.readLine()); //Enter a number( <=10^12)
driver(num);
System.out.println("count = " + count);
}
public static void driver(long num)
{
long limit = num / 2;
for(long i = 1 ; i <= limit ; i++)
{
func(i,num);
}
}
public static void func(long i,long num)
{
if(i < num)
{
func(i + 1,num - i);
}
else if(i > num)
{
return;
}
else
{
count++;
}
}
}

Use some math: if arithmetic progression with difference 1 starts with a0 and contains n items, then its sum is
S = (2 * a0 + (n-1))/2 * n = a0 * n + n * (n-1) / 2
note that the second summand rises as quadratic function. So instead of checking all a0 in range S/2, we can check all n is smaller range
nmax = Ceil((-1 + Sqrt(1 + 8 * S)) / 2)
(I used some higher approximation).
Just test whether next expression gives integer positive result
a0 = (S - n * (n - 1) / 2) / n

Recursive function isn't suitable when you have big input size like your case.
The maximum depth of the java call stack is about 8900 calls and sometimes only after 7700 calls stack overflow occurs so it really depends on your program input size.
Try this algorithm I think it worked for your problem:
it will work fine until 10^9 after that it will take much more time to finish running the program.
long sum = 0;
int count = 0;
long size;
Scanner in = new Scanner(System.in);
System.out.print("Enter a number <=10^12: ");
long n = in.nextLong();
if(n % 2 != 0){
size = n / 2 + 1;
}
else{
size = n / 2;
}
for(int i = 1; i <= size; i++){
for(int j = i; j <= size; j++){
sum = sum + j;
if(sum == n){
sum = 0;
count++;
break;
}
else if(sum > n){
sum = 0;
break;
}
}
}
System.out.println(count);
Output:
Enter a number <=10^12: 15
3
Enter a number <=10^12: 1000000000
9
BUILD SUCCESSFUL (total time: 10 seconds)

There's a really excellent proof that the answer can be determined by solving for the unique odd factors (Reference). Essentially, for every odd factor of a target value, there exists either an odd series of numbers of that factor multiplied by its average to produce the target value, or an odd average equal to that factor that can be multiplied by double an even-sized series to reach the target value.
public static int countUniqueOddFactors(long n) {
if (n==1) return 1;
Map<Long, Integer> countFactors=new HashMap<>();
while ((n&1)==0) n>>>=1; // Eliminate even factors
long divisor=3;
long max=(long) Math.sqrt(n);
while (divisor <= max) {
if (n % divisor==0) {
if (countFactors.containsKey(divisor)) {
countFactors.put(divisor, countFactors.get(divisor)+1);
} else {
countFactors.put(divisor, 1);
}
n /= divisor;
} else {
divisor+=2;
}
}
int factors=1;
for (Integer factorCt : countFactors.values()) {
factors*=(factorCt+1);
}
return factors;
}

As #MBo noted, if a number S can be partitioned into n consecutive parts, then S - T(n) must be divisible by n, where T(n) is the n'th triangular number, and so you can count the number of partitions in O(sqrt(S)) time.
// number of integer partitions into (at least 2) consecutive parts
static int numberOfTrapezoidalPartitions(final long sum) {
assert sum > 0: sum;
int n = 2;
int numberOfPartitions = 0;
long triangularNumber = n * (n + 1) / 2;
while (sum - triangularNumber >= 0) {
long difference = sum - triangularNumber;
if (difference == 0 || difference % n == 0)
numberOfPartitions++;
n++;
triangularNumber += n;
}
return numberOfPartitions;
}
A bit more math yields an even simpler way. Wikipedia says:
The politeness of a positive number is defined as the number of ways it can be expressed as the sum of consecutive integers. For every x, the politeness of x equals the number of odd divisors of x that are greater than one.
Also see: OEIS A069283
So a simple solution with lots of room for optimization is:
// number of odd divisors greater than one
static int politeness(long x) {
assert x > 0: x;
int p = 0;
for (int d = 3; d <= x; d += 2)
if (x % d == 0)
p++;
return p;
}

The method returns true if the integer is divisible by 3 and returns false if the integer is not divisible by 3

This is what I have so far; I have to use this main method.
public class HW4 {
public static boolean isDivisibleByThree(String n) {
int sum = 0;
int value;
for (int k = 0; k < n.length(); k++) {
char ch = n.charAt(k);
value = Character.getNumericValue(ch);
sum = sum*value;
}
return sum*3 == 0;
}
}
It always comes out true and I'm really stuck in this part. So if you can, can you help me out?

A sum is a cumulative addition (not multiplication).
Change this line:
sum = sum * value;
To
sum = sum + value;
Or the more brief version:
sum += value;

Much easier solution: use the mod-function:
int number = int.Parse(input);
bool result = (number % 3 == 0);

Two things:
sum = sum * value? This should probably be sum = sum + value, or short sum += value
sum * 3 == 0 should probably be sum % 3 == 0
If you are required to not use the % operator, you could alternatively do:
double check = (double)sum / 3.0;
return check == (int)check;
The problem with negative numbers is that the - gets parsed too, you could sove it by dropping it:
if (n[0] == '-') {
n = n.substring(1);
}
This drops the sign if it is negative and does nothing otherwise.

Unless I'm missing something, you would first use Integer.parseInt(String) to parse the int from the String. Then you can divide that value by 3 using integer division. Finally, test if that number multiplied by 3 is the original value.
int value = Integer.parseInt(n);
int third = value / 3;
return (value == third * 3);