I was trying to find out the frequency of execution of some statements in the following code.
I wanted to check how many times each for loop was executed for a given input array.
For this purpose,I added three variables icnt,jcnt and kcnt.
public class FreqCounter{
public static void count1(int[] a){
int N = a.length;
int count = 0;
int icnt = 0;
int jcnt = 0;
int kcnt = 0;
for(int i=0;i<N;i++){
icnt++;
for(int j=i+1;j<N;j++){
jcnt++;
for(int k=j+1; k<N;k++){
kcnt++;
}
}
}
System.out.printf("i loop=%d times\n",icnt);
System.out.printf("j loop=%d times\n",jcnt);
System.out.printf("k loop=%d times\n",kcnt);
}
public static void main(String[] args) {
int N = 100;
int[] a = new int[N];
count1(a);
}
}
I got the following output
i loop=100 times
j loop=4950 times
k loop=161700 times
I tried to analyze this as follows
The outer for loop (i=0 to < N)
This executes N times ,so for N=100 ,the count will be 100
Inner for loop(j=i+1 to < N)
This is equivalent to finding combinations of N elements ,taken 2 at a time
which means C(N,2) = N! /((N-2)! * 2!) = (N *(N-1))/2 = ((N^2)/2)-(N/2)
For N=100 , this will be (100*100/2)-50 = 4950
Innermost loop (k=j+1 to < N)
Equivalent to finding combinations of N elements ,taken 3 at a time
ie, C(N,3) = N!/((N-3)! * 3!) = N*(N-1)*(N-2)/3! = (N^3/6)-(N^2/2)+N/3
For N=100, this will be 100^3/6 - 100^2/2 + 100/3 = 161700
I am getting the correct values,but wanted to know if the analysis(combinations stuff) is proper.(I have only recently learned the permutation/combinations lessons).If someone can add more to this analysis, it would be helpful.
Your combinatorics is perfectly fine, you have n distinct elements, and you need the number of possibilities to chose 3 elements, order does not matter, no repeats. This is indeed C(N,3).
(Disclaimer, I was a combinatorics TA during the last months)
Related
I'm trying to refresh my pseudo-code understanding and wanted to see what the correct way of writing out a Fibonacci number # n would be.
Given the code:
public class FibAtN{
public static void main(String args[]){
int j = 0;
int k = j;
int l = 1;
int n =; /*input*/
for(int i=0;i<n;i++){
j=k;
k=l;
l=j+k;
}
System.out.println(j);
}
}
Would the correct use of Pseudo-code be?
PROGRAM FibonnacciAtN
INITIALIZE four integers (say: j,k,l,n)
SET j equal zero, k equal j, l equal 1
SET n equal to INPUT
FOR (integer count is less than n, INCREMENT count every loop) DO
SET j=k, k=l, l=j+k
PRINT integer j
Thanks!
I am very new to Java and I was trying to solve this problem on Hackerrank:
Here's the task:
https://www.hackerrank.com/challenges/cut-the-sticks
You are given N sticks, where the length of each stick is a positive
integer. A cut operation is performed on the sticks such that all of
them are reduced by the length of the smallest stick.
Suppose we have six sticks of the following lengths:
5 4 4 2 2 8
Then, in one cut operation we make a cut of length 2 from each of the six
sticks. For the next cut operation four sticks are left (of non-zero length), > whose lengths are the following:
3 2 2 6
The above step is repeated until no sticks are left.
Given the length of N sticks, print the number of sticks that are left before > each subsequent cut operations.
Note: For each cut operation, you have to recalcuate the length of smallest
sticks (excluding zero-length sticks).
Here is my attempt at it, but it doesnt seem to be working. The output gets stuck in while loop (4 gets printed out infinitely)
import java.io.*;
import java.util.*;
public class Solution {
private static int findMin (int[] A)
{
int min = A[0];
for (int i =0; i<A.length; i++)
{
if (A[i] < min)
{
min = A[i];
}
}
return min;
}
private static int countNonZeros (int[] A)
{
int zeros = 0;
for (int i =0; i<A.length; i++)
{
if (A[i] == 0)
{
zeros++;
}
}
int nonZeros = A.length - zeros;
return nonZeros;
}
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int n = scanner.nextInt();
int[] A = new int[n];
for (int i=0; i<n; i++)
{
A[i] = scanner.nextInt();
}
int nums = countNonZeros(A);
while (nums > 0)
{
int mins = findMin(A);
for (int j = 0; j<A.length; j++)
{
A[j]=A[j]-mins;
}
nums = countNonZeros(A);
System.out.println(nums);
}
}
}
Any help is appreciated
(PS I know I can just look the solution up somewhere, but I want to know why my code isn't working)
The problem that you have is that your findMin is not excluding zero-length elements, so once you have a zero that will be the min, and as a result an iteration of the while loop will be the same as the previous iteration, having subtracted 0 from each of the elements of A.
I want to find all possible binary permutations with a given number of ones in Java:
x is the desired number of ones in each sequence
n is the desired length of each sequence
For an example:
x=2, n=4
Output: 1100, 0011, 1010, 1001, 0101, 0110
I'm searching for an elegant and fast way to do this. Can you help me?
I've tested eboix solution in Print list of binary permutations but it is unfortunately too slow because the algorithm in this example is searching for all 2^n binary permutations.
I want to find sequences with a length of 50 or 100.
First of all, you're missing 0110 as an output case.
It's fairly intuitive that there are n choose x possibilities. You're finding all valid arrangements of x identical items among n total slots. So you can find the total number of sequences in O(1).
As a hint, try simply finding all permutations of the bitstring consisting of x ones followed n - x zeros.
To specifically address the problem, try creating a recursive algorithm that decides at every ith iteration to either include 1 or 0. If 1 is included, you need to decrement the count of 1's available for the rest of the string.
Actually, there may be an elegant way, but no fast way to do this. The number of string permutations is given by the binomial coefficient (see https://en.wikipedia.org/wiki/Binomial_coefficient). For example, x=10, n= 50 gives over 10 million different strings.
Here is just a basic version that will generate your desired output. Please work on it to make it more accurate/efficient -
This will not generate all the combinations, but you will get the idea of how to do it. Off course, for all the possible combinations generated by this, you will have to generate all the other possible combinations.
public class Test {
static int iter = 0;
public static void main(String args[]){
int n = 50;
int x = 5;
byte[] perms = new byte[n];
for(int i=0; i<x; i++){
perms[i] = 1;
}
print(perms);
for(int j=x-1; j>=0; j--){
for(int i=1; i<(n/2-j); i++){
iter++;
swap(perms, j, i);
}
}
}
public static void swap(byte[] perms, int pos, int by){
byte val = perms[pos+by];
perms[pos+by] = perms[pos];
perms[pos] = val;
print(perms);
val = perms[pos+by];
perms[pos+by] = perms[pos];
perms[pos] = val;
}
public static void print(byte[] perms){
System.out.println("iter = "+iter);
for(int i=0; i<perms.length; i++){
System.out.print(perms[i]);
}
System.out.println();
for(int i=perms.length-1; i>=0; i--){
System.out.print(perms[i]);
}
System.out.println();
}
}
Another inspiration for you. A dirty version which works. It allocates extra array space (you should adjust size) and uses String Set at the end to remove duplicates.
public static void main(String[] args) {
int x = 2;
int n = 4;
Set<BigInteger> result = new LinkedHashSet<>();
for (int j = x; j > 0; j--) {
Set<BigInteger> a = new LinkedHashSet<>();
for (int i = 0; i < n - j + 1; i++) {
if (j == x) {
a.add(BigInteger.ZERO.flipBit(i));
} else {
for (BigInteger num : result) {
if (num != null && !num.testBit(i) && (i >= (n - j) || num.getLowestSetBit() >= i-1))
a.add(num.setBit(i));
}
}
}
result = a;
}
String zeros = new String(new char[n]).replace("\0", "0");
for (BigInteger i : result) {
String binary = i.toString(2);
System.out.println(zeros.substring(0, n - binary.length()) + binary);
}
}
EDIT: changed the primitives version to use BigInteger instead to support larger n,x values.
This question already has an answer here:
How to iterate through array combinations with constant sum efficiently?
(1 answer)
Closed 9 years ago.
I have 12 products at a blend plant (call them a - l) and need to generate varying percentages of them, the total obviously adding up to 100%.
Something simple such as the code below will work, however it is highly inefficient. Is there a more efficient algorithm?
*Edit: As mentioned below there are just too many possibilities compute, efficiently or not. I will change this to only having a maximum of 5 or the 12 products in a blend and then running it against the number of ways that 5 products can be chosen from the 12 products.
There is Python code that some of you have pointed to that seems to work out the possibilities from the combinations. However my Python is minimal (ie 0%), would one of you be able to explain this in Java terms? I can get the combinations in Java (http://www.cs.colostate.edu/~cs161/Fall12/lecture-codes/Subsets.java)
public class Main {
public static void main(String[] args) throws FileNotFoundException, UnsupportedEncodingException {
for(int a=0;a<=100;a++){
for(int b=0;b<=100;b++){
for(int c=0;c<=100;c++){
for(int d=0;d<=100;d++){
for(int e=0;e<=100;e++){
for(int f=0;f<=100;f++){
for(int g=0;g<=100;g++){
for(int h=0;h<=100;h++){
for(int i=0;i<=100;i++){
for(int j=0;j<=100;j++){
for(int k=0;k<=100;k++){
for(int l=0;l<=100;l++){
if(a+b+c+d+e+f+g+h+i+j+k+l==100)
{
System.out.println(a+" "+b+" "+c+" "+d+" "+e+" "+f+" "+g+" "+h+" "+i+" "+j+" "+k+" "+l);
}}}}}}}}}}}}}
}
}
Why make it so difficult. Think simple way.
To explain the scenario simpler, consider 5 numbers to be generated randomly. Pseudo-code should be something like below.
Generate 5 random number, R1, R2 ... R5
total = sum of those 5 random number.
For all item to produce
produce1 = R1/total; // produce[i] = R[i]/total;
Please, don't use nested for loops that deep! Use recursion instead:
public static void main(String[] args) {
int N = 12;
int goal = 100;
generate(N, 0, goal, new int[N]);
}
public static void generate(int i, int sum, int goal, int[] result) {
if (i == 1) {
// one number to go, so make it fit
result[0] = goal - sum;
System.out.println(Arrays.toString(result));
} else {
// try all possible values for this step
for (int j = 0; j < goal - sum; j++) {
// set next number of the result
result[i-1] = j;
// go to next step
generate(i-1, sum + j , goal, result);
}
}
}
Note that I only tested this for N = 3 and goal = 5. It absolutely makes no sense to try generating all these possibilities (and would take forever to compute).
Let's take your comment that you can only have 5 elements in a combination, and the other 7 are 0%. Try this:
for (i = 0; i < (1<<12); ++i) {
if (count_number_of_1s(i) != 5) { continue; }
for (j = 0; j < 100000000; ++j) {
int [] perc = new int[12];
int val = j;
int sum = 0;
int cnt = 0;
for (k = 0; k < 12; ++k) {
if (i & (1 << k)) {
cnt++;
if (cnt == 5) {
perc[k] = 100 - sum;
}
else {
perc[k] = val % 100;
val /= 100;
}
sum += perc[k];
if (sum > 100) { break; }
}
else { perc[k] = 0; }
}
if (sum == 100) {
System.out.println(perc[0] + ...);
}
}
}
The outer loop iterates over all possible combinations of using 12 items. You can do this by looping over all numbers from 1:2^12, and the 1s in the binary representation of that number are the elements you're using. The count_number_of_1s is a function that loops over all the bits in the parameter and returns the number of 1s. If this is not 5, then just skip this iteration because you said you only want at most 5 mixed. (There are 792 such cases).
The j loop is looping over all the combinations of 4 (not 5) items from 0:100. There are 100^4 such cases.
The inner loop is looping over all 12 variables, and for those that have a 1 in their bit-position in i, then it means you're using that one. You compute the percentage by taking the next two decimal digits from j. For the 5th item (cnt==5), you don't take digits, you compute it by subtracting from 100.
This will take a LONG time (minutes), but it won't be nearly as bad as 12 nested loops.
for(int a=0;a<=100;a++){
for(int b=0;b<=50;b++){
for(int c=0;c<=34;c++){
for(int d=0;d<=25;d++){
for(int e=0;e<=20;e++){
for(int f=0;f<=17;f++){
for(int g=0;g<=15;g++){
for(int h=0;h<=13;h++){
for(int i=0;i<=12;i++){
for(int j=0;j<=10;j++){
for(int k=0;k<=10;k++){
for(int l=0;l<=9;l++){
if(a+b+c+d+e+f+g+h+i+j+k+l==100)
{
// run 12 for loops for arranging the
// 12 obtained numbers at all 12 places
}}}}}}}}}}}}}
In Original approach(permutation based), the iterations were 102^12 = 1.268e24. Even though the 102th iteration was false, it did check the loop terminating condition for 102th time.
So you had 102^12 condition checks in "for" loops, in addition to "if" condition checks 101^12 times, so in total, 2.4e24 condition checks.
In my solution(combination based),No of for loop checks reduces to 6.243e15 for outer 12 loops, &
if condition checks = 6.243e15.
Now, the no of for loops(ie inner 12 for loops) for every true "if" condition, is 12^12 = 8.9e12.
Let there be x number of true if conditions. so total condition checks
=no of inner for loops*x
= 8.9e12 * x + 6.243e15
I'm not able to find the value of x. however, I believe it wouldnt be large enough to make total conditon checks greater than 2.4e24
I'm trying to find prime numbers with a specific condition in Java.
The challenge is to show all the prime numbers (under 100.000) which contain a '3' four times.
I already have a code which shows all the prime numbers under 100.000, but I can't seem to figure out how to count the ones that contain the number '3' four times.
I can however count all the prime numbers.
Can someone help me with this?
Here's the code I have, where am I going to put the numbers into strings?
package Proeftentamen;
import java.util.regex.*;
/**
*
* #author Stefan
*/
public class Vraag_6 {
/// priemgetallen waar 4x een 3 in voor komt???? wtf...
public static void main(String[] args) {
boolean[] lijst = new boolean[1000000]; // hoeveelheid getallen
vularray(lijst);
lijst = zeef(lijst);
drukaf(lijst);
}
public static void vularray(boolean[] lijst) {
for (int i = 2; i < lijst.length; i++) {
lijst[i] = true;
}
}
public static boolean[] zeef(boolean[] lijst) {
for (int i = 2; i < lijst.length / 2; i++) {
if (lijst[i]) {
for (int j = 2 * i; j < lijst.length; j += i) {
lijst[j] = false;
}
}
}
return lijst;
}
public static void drukaf(boolean[] lijst) {
int count = 0;
for (int i = 2; i < lijst.length; i++) {
if (lijst[i] == true) {
System.out.println(i + " " + lijst[i]);
count++;
}
}
System.out.println("Aantal priemgetallen: " + count);
}
}
This question really sounds like a homework, so you should write down what you have come up with and what you tried so far.
There are a lot of ways to count numbers. Just to give you a clue, you can use the reminder operation (in Java - %):
56 % 10 = 6
25 % 5 = 0
So, when you divide by 10 and use a reminder operation you can get the last digit of your number. Now use a loop and counter and you'll be fine.
Another option (very ugly, so don't really use it :) ) - to turn your number into a String and iterate (loop) over its characters.
Hope this helps and good luck!
This code generate 50 permutation of numbers that has four '3' in it's digits
so check each number that is prime or not
public void generateNumbers() {
StringBuilder s = new StringBuilder();
s.append("3333");
for (int i = 0; i < 5; i++) {
for (int j = 0; j <= 9; j++) {
if (j%3==0) continue;
s.insert(i,String.valueOf(j));
int number=Integer.parseInt(s.toString());
System.out.println(number);
s.delete(i,i+1);
}
}
}
Iterate across each prime number.
For each prime number, convert it to a string using the Integer.toString(int) static method.
With this string, iterate over every character (use a for loop and the non-static method String.charAt(int index)) and count the number of times that method returns '3'. (The character '3', not the String "3").
Unless you have some other purpose for an array of prime-number Strings, don't bother to store them anywhere outside the loop.
Please refer below code to validate all such prime numbers.
void getPrimes(int num ,int frequency,char digit) {
int count = 0;
String number=Integer.toString(num);
for (int i = 0; i < number.length(); i++) {
if (count < frequency) {
if (number.charAt(i) == digit)
count++;
}
if (count == frequency)
{
System.out.println(number);
return ;
}
}
}
Using the primes function from an exercise on the Sieve of Eratosthenes, as well as the digits and filter functions from the Standard Prelude, this Scheme expression finds the seven solutions:
(filter
(lambda (n)
(= (length
(filter
(lambda (d) (= d 3))
(digits n)))
4))
(primes 100000))
The outer filter runs over all the primes less than 100000 and applies the test of the outer lambda to each. The inner filter computes the digits of each prime number and keeps only the 3s, then the length function counts them and the equality predicate keeps only those that have 4 3s. You can run the program and see the solution at http://codepad.org/e98fow2u.
you only have at most five digits, four of which must be 3. So what can you say about the remaining digit?
It's not hard to just write out the resulting numbers by hand, and then test each one for primality. Since there are no more than 50 numbers to test, even the simplest trial division by odds will do.
But if you want to generate the numbers programmatically, just do it with 5 loops: add 10,000 to 03333 9 times; add 1,000 to 30333 9 times; add 100 to 33033 9 times; etc. In C++:
int results[50];
int n_res = 0;
int a[5] = {13333, 31333, 33133, 33313, 33331};
for( int i=0, d=10000; i<5; ++i, d/=10)
for( int j=1; j<9; ++j, a[i]+=d )
if( is_prime(a[i]) )
results[n_res++] = a[i];