Determine whether there exists a graph with a sequence of degrees of vertices (s = s1, s2...sn).
What is the best and most optimized algorithm for solving this problem.
Input:
the first line contains `t<100` - amount of sequnces.
the second line contains value `n <= 1000000`(length of a sequence).
the third line contains contains `n` non-negative integer numbers. And so on.
Output:
if the graph can exist print "yes" otherwise print "no".
For example:
Input:
3
5
1 2 3 2 1
4
3 3 2 2
3
1 3 2
Output:
No
Yes
Yes
The maximum execution time should be 0.4 second.
Here is my code (If the number of odd vertices is even, then the graph exists):
import java.util.Scanner;
public class Main {
public static final Scanner in = new Scanner(System.in);
public static void isGraph (int []a, int n) {
int k=0;
for(int i=0; i< n; i++) {
if(a[i] %2 != 0) {
k++;
}
}
if(k%2 == 0)
System.out.println("Yes");
else
System.out.println("No");
}
public static void main(String[] args) throws Exception{
double t1 = System.nanoTime();
int n;
int []a;
int t = Integer.parseInt(in.nextLine());
while(t-- > 0) {
n = in.nextInt();
a = new int[n];
for(int i=0; i<n; i++)
a[i] = in.nextInt();
isGraph(a,n);
}
System.out.println(System.nanoTime() - t1);
}
}
But the execution time of this program is more than 0.4 second. I get run time exceeded. How I can optimize code and speed up runtime. May be there is another algorithm to solve this task, please help me.
I think I have a faster way for you. Please verify this. If you are concerned about the final outcome of even/odd, then there seems to be no reason to keep track of the k counter. You can keep a dynamic value of whether the running sequence is even or odd:
public static void isGraph (int []a, int n) {
int k = 0;
for(int i=0; i< n; i++) {
k += a[i] & 1;
}
if(k%2 == 0)
System.out.println("Yes");
else
System.out.println("No");
}
This might help your reading: I have no experience with it however, I got it from a competition website:
Slow way to read:
/** Read count integers using Scanner */
static int scanInteger(int count) {
Scanner scanner = new Scanner(input);
int last = 0;
while (count-- > 0) {
last = scanner.nextInt();
}
return last;
}
Faster way:
static int readIntegers(int count)
throws IOException {
BufferedReader reader = new BufferedReader(
new InputStreamReader(input) );
StringTokenizer tokenizer = new StringTokenizer("");
int last = 0;
while (count-- > 0) {
if (! tokenizer.hasMoreTokens() ) {
tokenizer = new StringTokenizer(reader.readLine());
}
last = Integer.parseInt(tokenizer.nextToken());
}
return last;
}
EDIT: to show how to avoid two phases where Phase 1 is the read loop, and Phase 2 is the algorithm:
public static void main(String[] args) throws Exception{
double t1 = System.nanoTime();
int n;
// int []a; // Not necessary
int t = Integer.parseInt(in.nextLine());
while(t-- > 0) {
n = in.nextInt();
// a = new int[n]; // Not necessary
int k = 0;
int a;
for(int i=0; i<n; i++) {
a = in.nextInt();
k += a & 1;
}
// isGraph(a,n); // Not necessary
if(k % 2 == 0)
System.out.println("Yes");
else
System.out.println("No");
}
System.out.println(System.nanoTime() - t1);
}
May be there is another algorithm to solve this task
That's not the problem (IMO).
Hint 1: since you know the length of the sequence beforehand, you can create the array and parse the sequence faster than this:
a = Arrays.stream(s.split(" ")).mapToInt(Integer::parseInt).toArray();
(Java 8+ streams are elegant, but they are not the fastest way.)
Hint 2: using Scanner is probably faster than reading strings and parsing them.
Hint 3: you could probably avoid creating an array entirely. (It would be poor coding practice IMO ... but if performance is critical ...)
Related
Conditions of the 6-digit code:
None of the digits are 0
Each digit of the combination is different
The 6-digit number is divisible by each one of the digits
Input:
Two integers, L and H
L is the limit on the smallest number on the range
H is the limit on the largest number on the range
Output:
C, which defines the number of possible combinations where L<=c<=H
I thought I could use arrays as the condition check, then realized I couldn't use it to find the number of possible combinations. Tried using loops, but couldn't figure it out, all I got for the pseudocode is the input, then a condition if L is less or equal to H. Then I sort of ran to a brick wall.
Here's the code.
''''''''
public static void main(String[] args) {
Scanner FF = new Scanner(System.in);
List<Integer> result = new ArrayList<>();
int l = FF.nextInt();
int h = FF.nextInt();
for (int i = l; i <= h; i++) {
result.add(i);
}
for (int i=l; i<=h; i++){
if (result.get(i) == result.get(i)){
result.remove(i);
}
int temp = result.get(i);
while (result.get(i)>0){
int k = result.get(i)%10;
if (temp % k != 0){
result.remove(i);
}
}
if (String.valueOf(result.get(i)).contains("0")){
result.remove(i);
}
}
System.out.println(result);
}
}
You can create a stream of integers, here 111111 to 1000000 and then filter out everything what doesnot meet your conditions.
public class SixDigitCode {
public static void main(String[] args) {
IntStream.iterate(111111, i -> i < 1000000, i -> i + 1)
.filter(containsZero.negate())
.filter(digitDifferent)
.filter(divideByDigits)
.forEach(System.out::println);
}
static IntPredicate containsZero = i -> Integer.toString(i).contains("0");
static IntPredicate digitDifferent = i -> Integer.toString(i).chars().boxed().collect(Collectors.toSet()).size() == 6;
static IntPredicate divideByDigits = i -> Integer.toString(i).chars().boxed()
.filter( x -> i%Character.getNumericValue(x) ==0)
.count() ==6;
}
There are multiple ways to solve this problem.
Let's start with an easy, but inefficient one:
boolean isOk(int number){
String numberStr = Integer.toString(number);
if(numberStr.contains("0"))
return false;
for(int i = 0; i < numberStr.length(); i++){
for(int j = i + 1; j < numberStr.length(); j++){
if(numberStr.charAt(i) == numberStr.charAt(j))
return false;
}
}
return true;
}
...
int count = 0;
for(int i = L; i <= H; i++){
if(isOk(i))
count ++;
}
Note: this code is by no means optimal, but I think it is a straight forward easy to understand solution.
However, I cannot test it right now, so it may contain minor issues.
The longest increasing subsequence is the well known problem and I have a solution with the patience algorithm.
Problem is, my solution gives me the "Best longest increasing sequence" instead of the First longest increasing sequence that appears.
The difference is that some of the members of the sequence are larger numbers in the first(but the sequence length is exactly the same).
Getting the first sequence is turning out to be quite harder than expected, because having the best sequence doesn't easily translate into having the first sequence.
I've thought of doing my algorithm then finding the first sequence of length N, but not sure how to.
So, how would you find the First longest increasing subsequence from a sequence of random integers?
My code snippet:
public static void main (String[] args) throws java.lang.Exception {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
int inputInt;
int[] intArr;
try {
String input = br.readLine().trim();
inputInt = Integer.parseInt(input);
String inputArr = br.readLine().trim();
intArr = Arrays.stream(inputArr.split(" ")).mapToInt(Integer::parseInt).toArray();
} catch (NumberFormatException e) {
System.out.println("Could not parse integers.");
return;
}
if(inputInt != intArr.length) {
System.out.println("Invalid number of arguments.");
return;
}
ArrayList<ArrayList<Integer>> sequences = new ArrayList<ArrayList<Integer>>();
int sequenceCount = 1;
sequences.add(new ArrayList<Integer>());
sequences.get(0).add(0);
for(int i = 1; i < intArr.length; i++) {
for(int j = 0; j < sequenceCount; j++) {
if(intArr[i] <= intArr[sequences.get(j).get(sequences.get(j).size() - 1)]) {
sequences.get(j).remove(sequences.get(j).size() - 1);
sequences.get(j).add(i);
break;
} else if (j + 1 == sequenceCount) {
sequences.add(new ArrayList<Integer>(sequences.get(j)));
sequences.get(j + 1).add(i);
sequenceCount++;
break; //increasing sequenceCount causes infinite loop
} else if(intArr[i] < intArr[sequences.get(j + 1).get(sequences.get(j + 1).size() - 1)]) {
sequences.set(j+ 1, new ArrayList<Integer>(sequences.get(j)));
sequences.get(j+ 1).add(i);
break;
}
}
}
int bestSequenceLength = sequenceCount;
ArrayList<Integer> bestIndexes = new ArrayList<Integer>(sequences.get(bestSequenceLength - 1));
//build bestSequence, then after it I'm supposed to find the first one instead
int[] bestSequence = Arrays.stream(bestIndexes.toArray()).mapToInt(x -> intArr[(int) x]).toArray();
StringBuilder output = new StringBuilder("");
for(Integer x : bestSequence) {
output.append(x + " ");
}
System.out.println(output.toString().trim());
}
I'm storing indexes instead in preparation for having to access the original array again. Since it's easier to go from indexes to values than vice versa.
Example:
3 6 1 2 8
My code returns: 1 2 8
First sequence is: 3 6 8
Another Example:
1 5 2 3
My code correctly returns: 1 2 3
Basically, my code works as long as the first longest sequence is the same as the best longest sequence. But when you have a bunch of longest sequences of the same length, it grabs the best one not the first one.
Code is self-explanatory. (Have added comments, let me know if you need something extra).
public class Solution {
public static void main(String[] args) {
int[] arr = {3,6,1,2,8};
System.out.println(solve(arr).toString());
}
private static List<Integer> solve(int[] arr){
int[][] data = new int[arr.length][2];
int max_length = 0;
// first location for previous element index (for backtracing to print list) and second for longest series length for the element
for(int i=0;i<arr.length;++i){
data[i][0] = -1; //none should point to anything at first
data[i][1] = 1;
for(int j=i-1;j>=0;--j){
if(arr[i] > arr[j]){
if(data[i][1] <= data[j][1] + 1){ // <= instead of < because we are aiming for the first longest sequence
data[i][1] = data[j][1] + 1;
data[i][0] = j;
}
}
}
max_length = Math.max(max_length,data[i][1]);
}
List<Integer> ans = new ArrayList<>();
for(int i=0;i<arr.length;++i){
if(data[i][1] == max_length){
int curr = i;
while(curr != -1){
ans.add(arr[curr]);
curr = data[curr][0];
}
break;
}
}
Collections.reverse(ans);// since there were added in reverse order in the above while loop
return ans;
}
}
Output:
[3, 6, 8]
An input n of the order 10^18 and output should be the sum of all the numbers whose set bits is only 2. For e.g. n = 5 setbit is 101--> 2 set bits. For n = 1234567865432784,How can I optimize the below code?
class TestClass
{
public static void main(String args[])
{
long N,s=0L;
Scanner sc = new Scanner(System.in);
N=sc.nextLong();
for(long j = 1; j<=N; j++)
{
long b = j;
int count = 0;
while(b!=0)
{
b = b & (b-1);
count++;
}
if(count == 2)
{
s+=j;
count = 0;
}
else
{
count = 0;
continue;
}
}
System.out.println(s%1000000007);
s=0L;
}
}
Java has a function
if (Integer.bitCount(i) == 2) { ...
However consider a bit: that are a lot of numbers to inspect.
What about generating all numbers that have just two bits set?
Setting the ith and jth bit of n:
int n = (1 << i) | (1 << j); // i != j
Now consider 31² steps, not yet 1000 with N steps.
As this is homework my advise:
Try to turn the problem around, do the least work, take a step back, find the intelligent approach, search the math core. And enjoy.
Next time, do not spoil yourself of success moments.
As you probably had enough time to think about Joop Eggen's suggestion,
here is how i would do it (which is what Joop described i think):
import java.util.Scanner;
public class Program {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
long n = sc.nextLong();
long sum = 0;
for (int firstBitIndex = 0; firstBitIndex < 64; firstBitIndex++) {
long firstBit = 1L << firstBitIndex;
if (firstBit >= n)
break;
for (int secondBitIndex = firstBitIndex + 1; secondBitIndex < 64; secondBitIndex++) {
long value = firstBit | (1L << secondBitIndex);
if (value > n)
break;
sum += value;
}
}
System.out.println(sum % 1000000007);
sc.close();
}
}
Java provides the class BigInteger, which includes a method nextProbablePrime(). This means you could do something like this:
BigInteger n = new BigInteger(stringInputN);
BigInteger test = BigInteger.valueOf(2);
BigInteger total = BigInteger.valueOf(0);
while (test.compareTo(n) < 0){
total = total.add(test);
test = test.nextProbablePrime();
}
System.out.println(total);
This this has an extremely low probability of getting the wrong answer (but nonzero), so you might want to run it twice just to doublecheck. It should be faster than manually iterating it by hand though.
As the title reads, I have been thinking about creating multiple nested loops that aim to achieve one purpose. Move two generated random numbers between 0-9 through each possible possition of an array.
For example, App generates first number (fNum) 1 and second number (sNum) 6. It then moves these numbers in the array which containts ABC. However firstNum and secondNum will need to also try all the possible combinations, so each one will need to be different with each loop.
-1ABC6
-A1BC6
-AB1C6
-ABC16
-ABC61
-AB6C1
-A6BC1
-6ABC1
-A6B1C
-A61BC
-A16BC
-A1B6C
-A1BC6
and so on...
I beleive the best way will be to create a method for generating a counter, which increments the numbers which I can call.
private int getNextNumber(int num) {
if (num == 0) {
return num;
} else {
num++;
}
if (num < 10) {
return num;
} else {
return -1;
}
}
Then I will need multiple nested loops... I have decided to go for several loops which will go infinitly.
while (j < maxlen) {
//J = 0 and maxlen = length of text so in this case 3 as it is ABC
//Add two numbers and check against answer
while (fNum != -1 || sNum != -1) {
//incrememnt numbers
fNum = getNextNumber(fNum);
System.out.println(fNum);
sNum = getNextNumber(sNum);
System.out.println(fNum);
}
String textIni = "ABC";
int lenOfText = textIni.length();
char[] split = textIni.toCharArray();
for (int i = 0; i < lenOfText; i++) {
//here it will look at the length of the Text and
//try the possible positions it could be at....
//maybe wiser to do a longer loop but I am not too sure
}
}
Since you don't need to store all possible combinations, we will save some memory using only O(n) storage with an iterative solution. I propose you a basic implementation but don't expect to use it on large arrays since it has a O(n³) complexity.
public static void generateCombinationsIterative(List<Integer> original, int fnum, int snum) {
int size = original.size();
for (int i=0 ; i<=size ; i++) {
List<Integer> tmp = new ArrayList<>(original);
tmp.add(i,fnum);
for (int j=0 ; j<=size + 1 ; j++) {
tmp.add(j,snum);
System.out.print(tmp + (i == size && j == size + 1 ? "" : ", "));
tmp.remove(j);
}
}
}
For your culture, here is an example of a recursive solution, which takes a lot of memory so don't use it if you don't need to generate the lists of results. Nevertheless, this is a more general solution that can deal with any number of elements to insert.
public static List<List<Integer>> generateCombinations(List<Integer> original, Deque<Integer> toAdd) {
if (toAdd.isEmpty()) {
List<List<Integer>> res = new ArrayList<>();
res.add(original);
return res;
}
int element = toAdd.pop();
List<List<Integer>> res = new LinkedList<>();
for (int i=0 ; i<=original.size() ; i++)
// you must make a copy of toAdd, otherwise each recursive call will perform
// a pop() on it and the result will be wrong
res.addAll(generateCombinations(insertAt(original,element,i),new LinkedList<>(toAdd)));
return res;
}
// a helper function for a clear code
public static List<Integer> insertAt(List<Integer> input, int element, int index) {
List<Integer> result = new ArrayList<>(input);
result.add(index,element);
return result;
}
Note that I did not use any array in order to benefit from dynamic data structures, however you can call the methods like this :
int[] arr = { 1,2,3 };
int fnum = 4, snum = 5;
generateCombinationsIterative(Arrays.asList(arr),fnum,snum);
generateCombinations(Arrays.asList(arr),new LinkedList<>(Arrays.asList(fnum,snum));
Note that both methods generate the combinations in the same order.
I am working on a school assignment and I have the following question:
I am given a number of sticks (with distinct or similar length), and am tasked to find out the minimum number of sticks required to form a longer stick of given length.
For instance,
Given 6 sticks of length 1,1,1,1,1,3 to form a longer stick of length 5, the output would be 3.
NOTE: Sticks cannot be reused.
However, if it is impossible to form the given length, output -1.
For instance,
Given 3 sticks of length 1,2,6, to form a longer stick of length 5, output would be -1.
I have the following code, which have passed all public test cases. However, I failed the private test cases which I cannot figure out my mistake.
Here's my code:
import java.util.*;
class Result {
static int min = 100000;
public static int solve(int pos, int currSum, int len, int numStk) {
// implementation
for (int i=1; i<=Stick.data.length - pos; i++){
if (currSum > len){
continue;
}
else if (currSum < len){
if (pos+i >= Stick.data.length){
break;
}
else{
solve(pos+i,currSum+Stick.data[pos+i], len, numStk+1);
}
}
else if (currSum == len){
if (numStk < min){
min = numStk;
}
}
}
return min;
}
}
class Stick {
static int[] data;
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int sticks = sc.nextInt();
data = new int[sticks];
int len = sc.nextInt();
for (int i=0; i<sticks; i++){
data[i] = sc.nextInt();
}
for (int i=0; i<sticks; i++){
Result.solve(i,0,len,1);
}
if (Result.min == 100000){
System.out.println(-1);
} else {
System.out.println(Result.min-1);
}
}
}
Things I notice about your code:
Bug: In main,
Result.solve(i,0,len,1);
assumes that stick i is taken (hence numsticks = 1 in the arguments list), but currSum is given as 0. Shouldn't that be data[i]?
Better code quality: The checks for currSum > len and currSum == len can be done outside the for loop, which is more efficient.