This function returns the max char subset sequence. Example input and output are below. Can someone help with time complexity
function shortenString(str) {
let result = str.charAt(0);
for (let i = 1; i< str.length; i++) {
const c = str.charAt(i);
let j = i - 1;
while (j >= 0) {
const charA = result.charAt(j);
const charB = str.charAt(i);
console.log(`comparing ${charA} to ${charB}`);
if (result.charAt(j) < str.charAt(i)) {
result = result.substring(0, j);
}
j--;
}
result = result + str.charAt(i);
}
return result;
}
We can use the Big O notation to calculate its complexity here
If we look at the code we have to main loops - for and while
The for loop will do n iterations.
Meanwhile the while loop will do n(n+1)/2 iterations - which represent the sum of a series of n numbers. Its complexity is give by O(n^2);
Therefor the complexity of the code if n*n^2 = O(n^3)
Related
We are trying to use these in us-west2 - https://github.com/GoogleCloudPlatform/bigquery-utils/tree/master/udfs/community.
this first query processes just fine, in US
this second query wont run
Our dataset models is in us West 2. It seems all queries from the 2nd query editor are then processed in us-west 2 where, it seems bqutil does not exist? How can we find the function bqutil.fn.levenshtein when processing in us-west2 (where our datasets all exist)?
To use the levenshtein UDF in your BigQuery table, you need to create a UDF in the location where your dataset resides.
You can refer to the below UDF and the screenshot where the data resides in us-west2 location.
UDF :
CREATE OR REPLACE FUNCTION
`stackdemo.fn_LevenshteinDistance`(in_a STRING, in_b STRING) RETURNS INT64 LANGUAGE js AS R"""
var a = in_a.toLowerCase();
var b = in_b.toLowerCase();
if(a.length == 0) return b.length;
if(b.length == 0) return a.length;
var matrix = [];
// increment along the first column of each row
var i;
for(i = 0; i <= b.length; i++){
matrix[i] = [i];
}
// increment each column in the first row
var j;
for(j = 0; j <= a.length; j++){
matrix[0][j] = j;
}
// Fill in the rest of the matrix
for(i = 1; i <= b.length; i++){
for(j = 1; j <= a.length; j++){
if(b.charAt(i-1) == a.charAt(j-1)){
matrix[i][j] = matrix[i-1][j-1];
} else {
matrix[i][j] =
Math.min(matrix[i-1][j-1] + 1, // substitution
Math.min(matrix[i][j-1] + 1, // insertion
matrix[i-1][j] + 1)); // deletion
}
}
}
return matrix[b.length][a.length];
""";
Query :
SELECT
source,
target,
`stackdemo.fn_LevenshteinDistance`(source, target) distance,
FROM UNNEST([
STRUCT('analyze' AS source, 'analyse' AS target),
STRUCT('opossum', 'possum'),
STRUCT('potatoe', 'potatoe'),
STRUCT('while', 'whilst'),
STRUCT('aluminum', 'alumininium'),
STRUCT('Connecticut', 'CT')
]);
Output :
Here's a sample solution for Sliding Window Maximum problem in Java.
Given an array nums, there is a sliding window of size k which is
moving from the very left of the array to the very right. You can only
see the k numbers in the window. Each time the sliding window moves
right by one position.
I want to get the time and space complexity of this function. Here's what I think would be the answer:
Time: O((n-k)(k * logk)) == O(nklogk)
Space (auxiliary): O(n) for return int[] and O(k) for pq. Total of O(n).
Is this correct?
private static int[] maxSlidingWindow(int[] a, int k) {
if(a == null || a.length == 0) return new int[] {};
PriorityQueue<Integer> pq = new PriorityQueue<Integer>(k, new Comparator<Integer>() {
// max heap
public int compare(Integer o1, Integer o2) {
return o2 - o1;
}
});
int[] result = new int[a.length - k + 1];
int count = 0;
// time: n - k times
for (int i = 0; i < a.length - k + 1; i++) {
for (int j = i; j < i + k; j++) {
// time k*logk (the part I'm not sure about)
pq.offer(a[j]);
}
// logk
result[count] = pq.poll();
count = count + 1;
pq.clear();
}
return result;
}
You're right in most of the part except -
for (int j = i; j < i + k; j++) {
// time k*logk (the part I'm not sure about)
pq.offer(a[j]);
}
Here total number of executions is log1 + log2 + log3 + log4 + ... + logk. The summation of this series -
log1 + log2 + log3 + log4 + ... + logk = log(k!)
And second thought is, you can do it better than your linearithmic time solution using double-ended queue property which will be O(n). Here is my solution -
public int[] maxSlidingWindow(int[] nums, int k) {
if (nums == null || k <= 0) {
return new int[0];
}
int n = nums.length;
int[] result = new int[n - k + 1];
int indx = 0;
Deque<Integer> q = new ArrayDeque<>();
for (int i = 0; i < n; i++) {
// remove numbers out of range k
while (!q.isEmpty() && q.peek() < i - k + 1) {
q.poll();
}
// remove smaller numbers in k range as they are useless
while (!q.isEmpty() && nums[q.peekLast()] < nums[i]) {
q.pollLast();
}
q.offer(i);
if (i >= k - 1) {
result[indx++] = nums[q.peek()];
}
}
return result;
}
HTH.
Can you please share your thoughts on what will be time complexity for this
for(int i = 0; i <= n/2; i++) {
for(int j = n - i; j > n/2; j--) {
}
}
You just have to compute the number of times you execute your operation :
Hence, the complexity is O(n²).
I got a question to answer with the best complexity we can think about.
We got one sorted array (int) and X value. All we need to do is to find how many places in the array equals the X value.
This is my solution to this situation, as i don't know much about complexity.
All i know is that better methods are without for loops :X
class Question
{
public static int mount (int [] a, int x)
{
int first=0, last=a.length-1, count=0, pointer=0;
boolean found=false, finish=false;
if (x < a[0] || x > a[a.length-1])
return 0;
while (! found) **//Searching any place in the array that equals to x value;**
{
if ( a[(first+last)/2] > x)
last = (first+last)/2;
else if ( a[(first+last)/2] < x)
first = (first+last)/2;
else
{
pointer = (first+last)/2;
count = 1;
found = true; break;
}
if (Math.abs(last-first) == 1)
{
if (a[first] == x)
{
pointer = first;
count = 1;
found = true;
}
else if (a[last] == x)
{
pointer = last;
count = 1;
found = true;
}
else
return 0;
}
if (first == last)
{
if (a[first] == x)
{
pointer = first;
count = 1;
found = true;
}
else
return 0;
}
}
int backPointer=pointer, forwardPointer=pointer;
boolean stop1=false, stop2= false;
while (!finish) **//Counting the number of places the X value is near our pointer.**
{
if (backPointer-1 >= 0)
if (a[backPointer-1] == x)
{
count++;
backPointer--;
}
else
stop1 = true;
if (forwardPointer+1 <= a.length-1)
if (a[forwardPointer+1] == x)
{
count++;
forwardPointer++;
}
else
stop2 = true;
if (stop1 && stop2)
finish=true;
}
return count;
}
public static void main (String [] args)
{
int [] a = {-25,0,5,11,11,99};
System.out.println(mount(a, 11));
}
}
The print command count it right and prints "2".
I just want to know if anyone can think about better complexity for this method.
Moreover, how can i know what is the time/space-complexity of the method?
All i know about time/space-complexity is that for loop is O(n). I don't know how to calculate my method complexity.
Thank a lot!
Editing:
This is the second while loop after changing:
while (!stop1 || !stop2) //Counting the number of places the X value is near our pointer.
{
if (!stop1)
{
if ( a[last] == x )
{
stop1 = true;
count += (last-pointer);
}
else if ( a[(last+forwardPointer)/2] == x )
{
if (last-forwardPointer == 1)
{
stop1 = true;
count += (forwardPointer-pointer);
}
else
forwardPointer = (last + forwardPointer) / 2;
}
else
last = ((last + forwardPointer) / 2) - 1;
}
if (!stop2)
{
if (a[first] == x)
{
stop2 = true;
count += (pointer - first);
}
else if ( a[(first+backPointer)/2] == x )
{
if (backPointer - first == 1)
{
stop2 = true;
count += (pointer-backPointer);
}
else
backPointer = (first + backPointer) / 2;
}
else
first = ((first + backPointer) / 2) + 1;
}
}
What do you think about the changing? I think it would change the time complexity to O(long(n)).
First let's examine your code:
The code could be heavily refactored and cleaned (which would also result in more efficient implementation, yet without improving time or space complexity), but the algorithm itself is pretty good.
What it does is use standard binary search to find an item with the required value, then scans to the back and to the front to find all other occurrences of the value.
In terms of time complexity, the algorithm is O(N). The worst case is when the entire array is the same value and you end up iterating all of it in the 2nd phase (the binary search will only take 1 iteration). Space complexity is O(1). The memory usage (space) is unaffected by growth in input size.
You could improve the worst case time complexity if you keep using binary search on the 2 sub-arrays (back & front) and increase the "match range" logarithmically this way. The time complexity will become O(log(N)). Space complexity will remain O(1) for the same reason as before.
However, the average complexity for a real-world scenario (where the array contains various values) would be very close and might even lean towards your own version.
I need to perform an accumulative sum in an array in Java according to iteration number, like this.
for (int it = 1; it < 3; it++) {
for(int i = 0; i < simSource.length; i++) {
for (int j = 0; j < resulting.length; j++) {
results [i][j] = resulting[i][j] + (simSource[i] * 0.5)/3;
}
}
newResults = results;
}
Thus, in each iteration, the values in the array results[i][j] increase, and these values, are stored in an array. This process is repeated until the max amount of iterations - in the first "for".
My question/trouble is: How to store in the array the final values after each iteration?
Thank you very much.