This question has to do with this challenge on HackerRank. It seems to be failing some cases, but I'm not clear what's wrong with the algorithm (many people seem to have problem with timeouts, that's not an issue here, everything runs plenty fast, and all the cases that are visible to me pass, so I don't have a specific case that's failing).
The essential outline of how the algorithm works is as follows:
First be sure that Alice isn't already winning over the existing highest score (degenerate case), if she is just tell the world she's #1 from start to finish. Otherwise, at least one score on the leaderboard beats Alice's first try.
Start by walking down the scores list from the highest until we find a place where Alice fits in and record the scores that beat Alice's initial score along the way.
If we reach the end of the scores list before finding a place for Alice's bottom score, pretend there is a score at the bottom of the list which matches Alice's first score (this is just convenient for the main loop and reduces the problem to one where Alice's first score is on the list somewhere)
At this point we have a (sorted) array of scores with their associated ranks, rankAry[r - 1] is the minimum score needed for Alice to attain rank r as of the end of the if clause following the first while loop.
From there, the main algorithm takes over where we walk through Alice's scores and note her rank as we go by comparing against the benchmarks from the scores array that we setup as rankAry earlier. curRank is our candidate rank at each stage which we've definitely achieved by the time this loop starts (by construction).
If we're at rank 1 we will be forever more, so just populate the current rank as 1 and move on.
If we're currently tied with or beating the current benchmark and that's not the end of the line, keep peeking at the next one and if we're also beating that next one, decrease the current benchmark location and iterate
Once this terminates, we've found the one we're going to supplant and we cannot supplant anything further, so assign this rank to this score and repeat until done
As far as I can tell this handles all cases correctly, even if Alice has repeated values or increases between the benchmarks from scores, we should stay at the same rank until we hit the new benchmarks, but the site feedback indicates there must be a bug somewhere.
All the other approaches I've been able to find seem to be some variation on doing a binary search to find the score each time, but I prefer not having to constantly search each time and just use the auxiliary space, so I'm a little stumped on what could be off.
static int[] climbingLeaderboard(int[] scores, int[] alice) {
int[] res = new int[alice.Length];
if (scores.Length == 0 || alice[0] >= scores[0]) { //degenerate cases
for (int i = 0; i < alice.Length; ++i) {
res[i] = 1;
}
return res;
}
int[] rankAry = new int[scores.Length + 1];
rankAry[0] = scores[0]; //top score rank
int curPos = 1; //start at the front and move down
int curRank = 1; //initialize
//initialize from the front. This way we can figure out ranks as we go
while (curPos < scores.Length && scores[curPos] > alice[0]) {
if (scores[curPos] < scores[curPos-1]) {
rankAry[curRank] = scores[curPos]; //update the rank break point
curRank++; //moved down in rank
}
curPos++; //move down the array
}
if (curPos == scores.Length) { //smallest score still bigger than Alice's first
rankAry[curRank] = alice[0]; //pretend there was a virtual value at the end
curRank++; //give rank Alice will have for first score when we get there
}
for (int i = 0; i < alice.Length; ++i) {
if (curRank == 1) { //if we're at the top, we're going to stay there
res[i] = 1;
continue;
}
//Non-degenerate cases
while (alice[i] >= rankAry[curRank - 1]) {
if (curRank == 1 || alice[i] < rankAry[curRank - 2]) {
break;
}
curRank--;
}
res[i] = curRank;
}
return res;
}
You have a couple of bugs in your algorithm.
Wrong mapping
Your rankAry must map a rank (your index) to a score. However, with this line rankAry[0] = scores[0];, the highest score is mapped to 0, but the highest possible rank is 1 and not 0. So, change that to:
rankAry[1] = scores[0];
Wrong initial rank
For some reason, your curRank is set to 1 as below:
int curRank = 1; //initialize
However, it's wrong since your alice[0] is less than scores[0] because of the following block running at the beginning of your method:
if (scores.Length == 0 || alice[0] >= scores[0]) { //degenerate cases
for (int i = 0; i < alice.Length; ++i) {
res[i] = 1;
}
return res;
}
So, at best your curRank is 2. Hence, change it to:
int curRank = 2;
Then, you can also remove curRank++ as your curRank has a correct initial value from:
if (curPos == scores.Length) { //smallest score still bigger than Alice's first
rankAry[curRank] = alice[0]; //pretend there was a virtual value at the end
curRank++; // it's not longer needed so remove it
}
Improve "Non-degenerate cases" handling
Your break condition should consider rankAry at curRank - 1 and not curRank - 2 as it's enough to check the adjacent rank value. Also, a value at curRank - 2 will produce wrong results for some input but I won't explain for which cases specifically - I'll leave it up to you to find out.
Fixed Code
So, I fixed your method according to my comment above and it passed it all the tests. Here it is.
static int[] climbingLeaderboard(int[] scores, int[] alice) {
int[] res = new int[alice.Length];
if (scores.Length == 0 || alice[0] >= scores[0]) { //degenerate cases
for (int i = 0; i < alice.Length; ++i) {
res[i] = 1;
}
return res;
}
int[] rankAry = new int[scores.Length + 1];
rankAry[1] = scores[0]; //top score rank
int curPos = 1; //start at the front and move down
int curRank = 2; //initialize
//initialize from the front. This way we can figure out ranks as we go
while (curPos < scores.Length && scores[curPos] > alice[0]) {
if (scores[curPos] < scores[curPos-1]) {
rankAry[curRank] = scores[curPos]; //update the rank break point
curRank++; //moved down in rank
}
curPos++; //move down the array
}
if (curPos == scores.Length) { //smallest score still bigger than Alice's first
rankAry[curRank] = alice[0]; //pretend there was a virtual value at the end
}
for (int i = 0; i < alice.Length; ++i) {
if (curRank == 1) { //if we're at the top, we're going to stay there
res[i] = 1;
continue;
}
//Non-degenerate cases
while (alice[i] >= rankAry[curRank - 1]) {
if (curRank == 1 || alice[i] < rankAry[curRank - 1]) {
break;
}
curRank--;
}
res[i] = curRank;
}
return res;
}
Related
I've been going though www.testdome.com to test my skills and opened a list of public questions. One of the practice questions was:
Implement function CountNumbers that accepts a sorted array of
integers and counts the number of array elements that are less than
the parameter lessThan.
For example, SortedSearch.CountNumbers(new int[] { 1, 3, 5, 7 }, 4)
should return 2 because there are two array elements less than 4.
And my answer was:
using System;
public class SortedSearch
{
public static int CountNumbers(int[] sortedArray, int lessThan)
{
int count = 0;
int l = sortedArray.Length;
for (int i = 0; i < l; i++) {
if (sortedArray [i] < lessThan)
count++;
}
return count;
}
public static void Main(string[] args)
{
Console.WriteLine(SortedSearch.CountNumbers(new int[] { 1, 3, 5, 7 }, 4));
}
}
It seems that I've failed on two counts:
Performance test when sortedArray contains lessThan: Time limit exceeded
and
Performance test when sortedArray doesn't contain lessThan: Time limit exceeded
To be honest I'm not sure what to optimize there? Maybe I'm using a wrong method and there is a similar way to speed up the calculation?
If someone could point out my mistake or explain what I'm going wrong, I'd really appreciate it!
Because the array is sorted, you can stop counting as soon as you reach or exceed the lessThan parameter.
else break would probably do it.
Does it have to be really a loop? You could do Lambda exp for that
public static int CountNumbers(int[] sortedArray, int lessThan)
{
return sortedArray.ToList().Where(x=>x < lessThan).Count();
}
Harold's answer and approach is spot on.
Find below another code sample in case you're practicing for technical interviews. It handles cases when the array is null or empty, when lessThan is presented in the array (including duplicates), etc.
private static int CountNumbers(int[] sortedArray, int lessThan)
{
if (sortedArray == null)
{
throw new ArgumentNullException("Sorted array cannot be null.");
}
if (sortedArray.Length == 0)
{
throw new ArgumentException("Sorted array cannot be empty.");
}
int start = 0;
int end = sortedArray.Length;
int middle = int.MinValue;
while (start < end)
{
middle = (start + end) / 2;
if (sortedArray[middle] == lessThan)
{
break; // Found the "lessThan" number in the array, we can stop and move left
}
else if (sortedArray[middle] < lessThan)
{
start = middle + 1;
}
else
{
end = middle - 1;
}
}
// Adjust the middle pointer based on the "current" and "lessThan" numbers in the sorted array
while (middle >= 0 && sortedArray[middle] >= lessThan)
{
middle--;
}
// +1 because middle is calculated through 0-based (e.g. start)
return middle + 1;
}
So I am trying to figure out why filling sudoku board in order of how I generate fields is many times faster then filling it which shuffled order, and I can't come to any reasonable conclusions.
Speed of filling and checking should be about the same no matter if fields are shuffled or not, only noticeable difference is the fact that filling boxes in a shuffled order causes the main loop to easily go for 60.000.000+ iterations not sure how many on average as I am not patient enough to check. And filling them in order of how they were generated gets finished in usually < 1.000 iterations rarely going over it and basically never going over 5.000.
I do understand that code doesn't follow C# standards too strictly but it's a project I am supposed to make and it's not my main language there are probably some possible optimizations but it's not what I am interested in all i want to know why shuffling the order of fill the boxes causes the process to take this much longer.
Edit: forgot to attach order of creating/filling boxes order of filling/creating boxes:
Edit2: more concise rephrased question:
The question is why generating an valid fully filled sudoku board in order from image creates a lot less invalid boards from which there is required backtracking, as compared to generating a board in a random order of choosing fields?
example of random order
Here is the code used for the project https://github.com/Piterm21/sudoku
And here are all the parts used in generation.
filledBox class:
public class filledBox
{
public int textBoxIndex;
public int value;
public int nextIndexToTry;
public int[] values;
public int lineIndex;
public int columnIndex;
public int groupIndex;
}
Here is a main loop:
filledBox[] boxes = this.shuffleBoxesCreateCheckingLists();
long iter = 0;
int nextIndexToFill = 0;
while (nextIndexToFill != 81) {
for (; boxes[nextIndexToFill].nextIndexToTry < 9; boxes[nextIndexToFill].nextIndexToTry++) {
// check if is valid
if (!createsError(boxes[nextIndexToFill])) {
boxes[nextIndexToFill].value = boxes[nextIndexToFill].values[boxes[nextIndexToFill].nextIndexToTry];
nextIndexToFill++;
break;
}
if (boxes[nextIndexToFill].nextIndexToTry == 8) {
boxes[nextIndexToFill].nextIndexToTry = 0;
boxes[nextIndexToFill].value = 0;
nextIndexToFill--;
boxes[nextIndexToFill].nextIndexToTry++;
while (boxes[nextIndexToFill].nextIndexToTry == 9) {
boxes[nextIndexToFill].nextIndexToTry = 0;
boxes[nextIndexToFill].value = 0;
nextIndexToFill--;
boxes[nextIndexToFill].nextIndexToTry++;
}
break;
}
}
iter++;
}
System.Diagnostics.Debug.WriteLine(iter);
Generation of boxes with setting of lists used for checking for errors:
List<filledBox>[] generationLines;
List<filledBox>[] generationColumns;
List<filledBox>[] generationGroups;
public filledBox[] shuffleBoxesCreateCheckingLists()
{
filledBox[] boxes = new filledBox[81];
for (int i = 0; i < 81; i++) {
boxes[i] = new filledBox();
boxes[i].values = new int[9]{ 1, 2, 3, 4, 5, 6, 7, 8, 9 };
boxes[i].values = shuffle(boxes[i].values, true);
}
generationLines = new List<filledBox>[9];
generationColumns = new List<filledBox>[9];
generationGroups = new List<filledBox>[9];
for (int i = 0; i < 9; i++) {
generationLines[i] = new List<filledBox>();
generationColumns[i] = new List<filledBox>();
generationGroups[i] = new List<filledBox>();
}
int boxIndex = 0;
for (int y = 0; y < 3; y++) {
for (int x = 0; x < 3; x++) {
for (int innerY = 0; innerY < 3; innerY++) {
for (int innerX = 0; innerX < 3; innerX++) {
int subPanelIndex = x + y * 3;
int lineIndex = innerY + y * 3;
int columnIndex = innerX + x * 3;
boxes[boxIndex].textBoxIndex = boxIndex;
boxes[boxIndex].groupIndex = subPanelIndex;
boxes[boxIndex].columnIndex = columnIndex;
boxes[boxIndex].lineIndex = lineIndex;
boxes[boxIndex].nextIndexToTry = 0;
boxes[boxIndex].value = 0;
generationLines[lineIndex].Add(boxes[boxIndex]);
generationColumns[columnIndex].Add(boxes[boxIndex]);
generationGroups[subPanelIndex].Add(boxes[boxIndex]);
boxIndex++;
}
}
}
}
#if !fast
boxes = shuffle(boxes);
#endif
return boxes;
}
Shuffling code:
public T[] shuffle<T> (T[] array)
{
int i = array.Length;
while (i > 1) {
i--;
int j = rnd.Next(0, i - 1);
T temp = array[i];
array[i] = array[j];
array[j] = temp;
}
return array;
}
And code responsible for checking for errors:
public bool hasError (List<filledBox> list, filledBox box)
{
bool result = false;
foreach (filledBox filledBoxToCheck in list) {
if (filledBoxToCheck.value == box.values[box.nextIndexToTry]) {
if (box.lineIndex != filledBoxToCheck.lineIndex ||
box.columnIndex != filledBoxToCheck.columnIndex) {
result = true;
break;
}
}
}
return result;
}
public bool createsError (filledBox box)
{
bool result = false;
if (hasError(generationGroups[box.groupIndex], box)) {
result = true;
} else if (hasError(generationLines[box.lineIndex], box)) {
result = true;
} else if (hasError(generationColumns[box.columnIndex], box)) {
result = true;
}
return result;
}
The reason the shuffled order of visiting boxes is worse is that, for the first few boxes, you've increased the odds of filling them in independently. I'm calling a 3x3 region a box. You could visit each little square randomly, but I'll confine my analysis to fillng in one 3x3 box at a time. It should illustrate the problem.
Lets assume, whether you used the in-order or random method, you filled in the top left box first.
VISITING BOXES IN ORDER:
Now consider filling in the box next to it, that is, the top middle box. Just look at filling in the top row of that box, there are 6x5x4 = 120 ways to fill it in.
VISITING BOXES RANDOMLY:
Now consider instead choosing any box to fill in next. If you happen to choose a box that is not in the top row or left column, filling it in is unaffected by the way the first box was filled. The top row of that box can be filled in 9x8x7 = 504 ways.
Taking this further, if you fill in the boxes sequentially, say, across the top, the third box (the top right one), begins with only 3x2x1 = 6 ways to fill in the top row of it. Whereas, if you select the next box randomly, you might, at worst, select a box that is not in the same row or column of either of the first 2 boxes, which means that the top row of that box has yet again 9x8x7 = 504 ways of being filled in.
If you tried randomly selecting the order for each little square to be filled in, the first few might all be in different rows and columns. At worst, none of the first 9 squares will align meaning there will be 9^9 = 387,420,489 options. But filling them in across the top row, the choices are guaranteed to be 9! = 362,880.
This illustrates one of the strategies for how to approach backtracking. Ideally, you first solve parts of the problem that most tightly constrain the rest of the problem. For some problems sequential is better, and for some random is better.
The setup is that, given a list of N objects like
class Mine
{
public int Distance { get; set; } // from river
public int Gold { get; set; } // in tons
}
where the cost of moving the gold from one mine to the other is
// helper function for cost of a move
Func<Tuple<Mine,Mine>, int> MoveCost = (tuple) =>
Math.Abs(tuple.Item1.Distance - tuple.Item2.Distance) * tuple.Item1.Gold;
I want to consolidate the gold into K mines.
I've written an algorithm, thought it over many times, and don't understand why it isn't working. Hopefully my comments help out. Any idea where I'm going wrong?
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
class Mine
{
public int Distance { get; set; } // from river
public int Gold { get; set; } // in tons
}
class Solution
{
static void Main(String[] args)
{
// helper function for reading lines
Func<string, int[]> LineToIntArray = (line) => Array.ConvertAll(line.Split(' '), Int32.Parse);
int[] line1 = LineToIntArray(Console.ReadLine());
int N = line1[0], // # of mines
K = line1[1]; // # of pickup locations
// Populate mine info
List<Mine> mines = new List<Mine>();
for(int i = 0; i < N; ++i)
{
int[] line = LineToIntArray(Console.ReadLine());
mines.Add(new Mine() { Distance = line[0], Gold = line[1] });
}
// helper function for cost of a move
Func<Tuple<Mine,Mine>, int> MoveCost = (tuple) =>
Math.Abs(tuple.Item1.Distance - tuple.Item2.Distance) * tuple.Item1.Gold;
// all move combinations
var moves = from m1 in mines
from m2 in mines
where !m1.Equals(m2)
select Tuple.Create(m1,m2);
// moves in ascending order of cost
var ordered = from m in moves
orderby MoveCost(m)
select m;
int sum = 0; // running total of move costs
var spots = Enumerable.Repeat(1, N).ToArray(); // spots[i] = 1 if hasn't been consildated into other mine, 0 otherwise
var iter = ordered.GetEnumerator();
while(iter.MoveNext() && spots.Sum() != K)
{
var move = iter.Current; // move with next smallest cost
int i = mines.IndexOf(move.Item1), // index of source mine in move
j = mines.IndexOf(move.Item2); // index of destination mine in move
if((spots[i] & spots[j]) == 1) // if the source and destination mines are both unconsolidated
{
sum += MoveCost(move); // add this consolidation to the total cost
spots[i] = 0; // "remove" mine i from the list of unconsolidated mines
}
}
Console.WriteLine(sum);
}
}
An example of a test case I'm failing is
3 1
11 3
12 2
13 1
My output is
3
and the correct output is
4
The other answer does point out a flaw in the implementation, but it fails to mention that in your code, you aren't actually changing the Gold values in the remaining Mine objects. So even if you did re-sort the data, it wouldn't help.
Furthermore, at each iteration all you really care about is the minimum value. Sorting the entire list of data is overkill. You can just scan it once to find the minimum-valued item.
You also don't really need the separate array of flags. Just maintain your move objects in a list, and after choosing a move, remove the move objects that include the Mine you would otherwise have flagged as no longer valid.
Here is a version of your algorithm that incorporates the above feedback:
static void Main(String[] args)
{
string input =
#"3 1
11 3
12 2
13 1";
StringReader reader = new StringReader(input);
// helper function for reading lines
Func<string, int[]> LineToIntArray = (line) => Array.ConvertAll(line.Split(' '), Int32.Parse);
int[] line1 = LineToIntArray(reader.ReadLine());
int N = line1[0], // # of mines
K = line1[1]; // # of pickup locations
// Populate mine info
List<Mine> mines = new List<Mine>();
for (int i = 0; i < N; ++i)
{
int[] line = LineToIntArray(reader.ReadLine());
mines.Add(new Mine() { Distance = line[0], Gold = line[1] });
}
// helper function for cost of a move
Func<Tuple<Mine, Mine>, int> MoveCost = (tuple) =>
Math.Abs(tuple.Item1.Distance - tuple.Item2.Distance) * tuple.Item1.Gold;
// all move combinations
var moves = (from m1 in mines
from m2 in mines
where !m1.Equals(m2)
select Tuple.Create(m1, m2)).ToList();
int sum = 0, // running total of move costs
unconsolidatedCount = N;
while (moves.Count > 0 && unconsolidatedCount != K)
{
var move = moves.Aggregate((a, m) => MoveCost(a) < MoveCost(m) ? a : m);
sum += MoveCost(move); // add this consolidation to the total cost
move.Item2.Gold += move.Item1.Gold;
moves.RemoveAll(m => m.Item1 == move.Item1 || m.Item2 == move.Item1);
unconsolidatedCount--;
}
Console.WriteLine("Moves: " + sum);
}
Without more detail in your question, I can't guarantee that this actually meets the specification. But it does produce the value 4 for the sum. :)
When you consolidate mine i into mine j, the amount of gold in the mine j is increased. This makes consolidations from mine j to other mines more expensive potentially making the ordering of the mines by the move cost invalid. To fix this, you could re-sort the list of mines at the beginning of each iteration of your while-loop.
Hi there I'm trying to write a method that reads every number in a list and detects where it spikes and drops. This is what I have so far:
I basically figure if I loop through the list, loop through it again to get the next number in the list, then detecting if it's more or less. If it's more it'll save to one list, vice versa.
What I want this method to do is determine where there's a spike of 100 or more, save the point that it does this (which is 'counter') and also save the points where the numbers drop.
This so far notices only a drop and it will save every number in the list until it spikes again and once it has spiked it shows no numbers, until it drops again and so on.
I've put 'check' and 'check2' to try and counteract it saving every number after it notices a drop and only save it once but no luck.
Any ideas?
public void intervalDetection()
{
//Counter is the point in the list
int counter = 0;
int spike = 0;
int drop = 0;
//Loop through power list
for (int i = 0; i < powerList.Count(); i++)
{
counter++;
int firstNumber = powerList[i];
//Loop again to get the number after??
for (int j = 1; j < 2; j++)
{
//Detect Spike
spike = firstNumber + 100;
drop = firstNumber - 100;
if (powerList[j] > spike)
{
if (check2 == false)
{
intervalStartList.Add(counter);
check2 = true;
check = false;
}
}
//Detect Drop
else if (powerList[j] < drop)
{
if (check == false)
{
intervalEndList.Add(counter);
check = true;
check2 = false;
}
}
}
Create integer "average"
Loop through List/Array and add each value to average
Divide average by the count of the List/Array
Loop through List/Array and check deviation to the average integer
derp
Code example:
public class DSDetector {
public static List<int>[] getDropsnSpikes(List<int> values, int deviation) {
List<int> drops = new List<int>();
List<int> spikes = new List<int>();
int average = 0;
foreach (int val in values) {
average += val;
}
average = average/values.Count;
foreach (int val in values) {
if (val < average - deviation) {
drops.add(val);
}
if (val > average + deviation) {
spikes.add(val);
}
}
//derp.
return new List<int>{drops, spikes};
}
}
not tested but I think it works. Just try it.
What exactly do you mean saying "peaks" and "drops"?
Let's say you have following list of integers
112, 111, 113, 250, 112, 111, 1, 113
In this case value 250 is peak and 1 drop relative to average value and you can get it using Kai_Jan_57 answer.
But also 250 is peak to previous value 113 and 112 is drop for 250.
If you want to find local peaks and drops you can check each value relative to previous and next: find average as avg=(val[i-1]+val[i+1])/2 and check if val[i]>avg + 100 (peak) or val[i]
I am currently developing a game in Unity and I decided to use a depth-first search to generate a maze. This involves recursion, the dreaded beast, and I keep getting a stack overflow error even though I seem to have set up the recursion correctly. I've been looking through it for a while, but I can't seem to find the error.
Here is the code:
private void MazeDigger(int[,] maze, int r, int c){
int[] directions = new int[] {1, 2, 3, 4};
Shuffle(directions);
for(int i = 0; i < directions.Length; i++){
switch(directions[i]){
case 1:
if(r-2 <= 0)
{
continue;
}
if(maze[r-2, c] != 0)
{
maze[r-2, c] = 2;
maze[r-1, c] = 2;
MazeDigger(maze, r-2, c);
}
break;
case 2:
if(c+2 >= MazeWidth - 1)
{
continue;
}
if(maze[r, c+2] != 0)
{
maze[r, c+2] = 2;
maze[r, c+1] = 2;
MazeDigger(maze, r, c+1);
}
break;
case 3:
if(r+2 >= MazeHeight - 1)
{
continue;
}
if(maze[r+2, c] != 0)
{
maze[r+2, c] = 2;
maze[r+1, c] = 2;
MazeDigger(maze, r+2, c);
}
break;
case 4:
if(c-2 <= 0)
{
continue;
}
if(maze[r, c-2] != 0)
{
maze[r, c-2] = 2;
maze[r, c-1] = 2;
MazeDigger(maze, r, c-2);
}
break;
}
}
}
It's pretty simple really. I create an array with four directions, I randomly shuffle through them and then use a for loop to run through the array. There is a switch statement inside which will basically mark different points in the maze as being = 2. This is because a different section of the code uses modulus to generate cubes at those locations. Any help would be appreciated and please let me know if I did not provide enough information thank you!
There is no exit condition or you messed up the check.
You mark every visited cell with 2, but you will visit it again if it is unequal to 0. Never ending story :)
The 3x3 maze works, because every cell fails your border check and no recursion happens.
The 4x4 maze should already fail, but it may work for certain starting conditions.