Hi guys im learning c# currently and Im trying to run threw some interview questions to try and understand them and learn in the process.
I found a question, How do you find the missing number in a given integer array of 1 to 100?
I think I get the General Idea of having to get the sum, Then the Sum of the Sequence then Minus X - Y;
But im confused about the code example below, Why is he using * (arr.Length + 2) When the Equation is n*(n+1)/2 I know its correct but shouldnt this be (arr.Length + 1) * (arr.Length) / 2 According tot he formula
Im terribly confused.
//array to find the missing number between 1 and 10
// Simplicity, We will take number 1 to 10 i where Number 5 is missing in the sequence.
int[] arr = { 1, 2, 3, 4, 6, 7, 8, 9, 10 };
int missingNumber,Totalsum;
// Accoreding to series rule, calculating sum of total numbers upto 10
//sum of first n natutal numbers=n*(n+1)/2
Totalsum = (arr.Length + 1) * (arr.Length + 2) / 2;
// Missing number is calculating.
foreach (int item in arr)
{
Totalsum = Totalsum - item;
}
missingNumber = Totalsum;
Console.WriteLine("missing number : {0}",missingNumber);
Not a Assignment. Just someone trying to learn programming by them selves looking up random questions to learn practically
Where i got the question
https://simpleprogrammer.com/programming-interview-questions/
The Explanation I found
https://www.interviewsansar.com/find-missing-number-between-1-to-n-in-array-in-c/
The comment gives the answer to your question:
// Accoreding to series rule, calculating sum of total numbers upto 10
//sum of first n natutal numbers=n*(n+1)/2
It's just that it's a number sequence that "should have 10 numbers but actually only has 9"
The formula needs n to be 10, but the array has a length of 9. 9+1 is n, 9+2 is n+1
Related
The original problem is located at Project Euler Largest palindrome product and is below.
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers.
The question in context is found at
Dmitry Answering Largest palindrome product - C#. I got the correct answer but did it from min to max instead of max to min so I looked for a more efficient answer to study. I understand what all the code does, but I can't figure out where Dmitry started to get the formula to get the minimum multiplicand from the maximum multiplicand constant. I'm blitzing through several coding challenge websites in preparation for some technical interviews.
This line:
const int NMin = NMax - (NMax + 1) / 10 + 1;
OF
// Store the maximum palindrome number here:
long maxNumber = 0;
// The maximum multiplicand (typically: 9...9):
const int NMax = 999;
// The minimum multiplicand.
// Obviously, it couldn't be less than 90...0:
const int NMin = NMax - (NMax + 1) / 10 + 1;
for (int i = NMax; i > NMin; i--)
{
// Starting from i since i * j = j * i for any i, j:
for (int j = i; j > NMin; j--)
{
long number = Math.BigMul(i, j);
// The fastest condition should be the first in the `if` statement:
if (number > maxNumber && isPalindome(number))
{
maxNumber = number;
Console.WriteLine("{0} = {1} * {2}", number, i, j);
break; // Leave the `j` loop, because it's guaranteed that there is
// no numbers greater than `number` for the current `i`
}
}
}
The websites I've been going through include:
Advent Of Code
HackerEarth and HackerRank
Leetcode I've been attempting to finish the Comprehensive Study Plans
Project Euler Only on Problem #4 right now
As stated in problem 4 the largest palindrome for the product of two-digit numbers is 91*99. I believe Dmitry recognized that of all max palindromes for a given digit range (3, 4, or 5 as he calculated but realistically to infinity) must be 9x -> 9y (where x represents 0's and y represents 9's). The amount of x and y needed is digit - 1 if you always want the highest palindrome. The lower 90% here is simply not worth checking for palindromes because they won't produce the highest multiplication.
Thus he can calculate the minimum every time given the equation he provided:
NMin = NMax - (NMax + 1) / 10 + 1 // NMin = 900 if NMax = 999
In the case of 4-digit palindrome, this produces 9,000 -> 9,999 or 90,000 -> 99,999 for 5.
The important thing to note here is he could have hard-coded NMin or picked a larger minimum number.
So for example we have 1, 5, and 10 and we want to interpolate between these with 12 points, we should get:
1.0000
1.7273
2.4545
3.1818
3.9091
4.6364
5.4545
6.3636
7.2727
8.1818
9.0909
10.0000
say we have 5, 10, and 4 and again 12 points, we should get:
5.0000
5.9091
6.8182
7.7273
8.6364
9.5455
9.4545
8.3636
7.2727
6.1818
5.0909
4.0000
This is a generalized solution that works by these principles:
Performs linear interpolation
It calculates a "floating point index" into the input array
This index is used to select 1 (if the fractional parts is very close to 0) or 2 numbers from the input array
The integer part of this index is the base input array index
The fractional part says how far towards the next array element we should move
This should work with whatever size input arrays and output collections you would need.
public IEnumerable<double> Interpolate(double[] inputs, int count)
{
double maxCountForIndexCalculation = count - 1;
for (int index = 0; index < count; index++)
{
double floatingIndex = (index / maxCountForIndexCalculation) * (inputs.Length - 1);
int baseIndex = (int)floatingIndex;
double fraction = floatingIndex - baseIndex;
if (Math.Abs(fraction) < 1e-5)
yield return inputs[baseIndex];
else
{
double delta = inputs[baseIndex + 1] - inputs[baseIndex];
yield return inputs[baseIndex] + fraction * delta;
}
}
}
It produces the two collections of outputs you showed in your question but beyond that, I have not tested it. Little error checking is performed so you should add the necessary bits.
The problem is an interpolation of two straight lines with different slopes given the end points and the intersection.
Interpolation is defined as following : In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
I'm tired of people giving negative points for solutions to hard problems. This is not a simply problem, but a problem that require "thinking out of the box". lets looks at the solution for following input : 1 12 34
I picked these numbers because the results are all integers
The step size L (Lower) = distance of elements from 1 to 12 = 2
The step size H (Higher) = distance of elements from 12 to 34 = 4
So the answer is : 1 3 5 7 9 11 [12] 14 18 22 26 30 34
Notice the distance between the 6th point 11 and center is 1 (half of L)
Notice the distance between the center point 12 and the 7th point is 2 (half of H)
Finally notice the distance between the 6th and 7th points is 3.
My results are scaled exactly the same as the OPs first example.
It is hard to see the sequence with the fractional inputs the OP posted. If you look at the OP first example and calculate the step distance of the first 6 points you get 0.72. The last 6 points the distance is 0.91. Then calculate the distance from the 6th point to the center is .36 (half 0.72). Then center to 7th point 0.45 (half 0.91). Excuse me for rounding the numbers a little bit.
It is a sequence problem just like the in junior high school where you learned arithmetic and geometric sequences. Then as a bonus question you got the sequence 23, 28, 33, 42,51,59,68,77,86 which turns out to be the train stations on the NYC 3rd Ave subway system. Solving problems like this you need to think "Outside the Box" which comes from the tests IBM gives to Job Applicants. These are the people who can solve the Nine Point Problem : http://www.brainstorming.co.uk/puzzles/ninedotsnj.html
I did the results when the number of points is EVEN which in you case is 12. You will need to complete the code if the number of points is ODD.
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace ConsoleApplication1
{
class Program
{
const int NUMBER_POINTS = 12;
static void Main(string[] args)
{
List<List<float>> tests = new List<List<float>>() {
new List<float>() { 1,5, 10},
new List<float>() { 5,10, 4}
};
foreach (List<float> test in tests)
{
List<float> output = new List<float>();
float midPoint = test[1];
if(NUMBER_POINTS % 2 == 0)
{
//even number of points
//add lower numbers
float lowerDelta = (test[1] - test[0])/((NUMBER_POINTS / 2) - .5F);
for (int i = 0; i < NUMBER_POINTS / 2; i++)
{
output.Add(test[0] + (i * lowerDelta));
}
float upperDelta = (test[2] - test[1]) / ((NUMBER_POINTS / 2) - .5F); ;
for (int i = 0; i < NUMBER_POINTS / 2; i++)
{
output.Add(test[1] + (i * upperDelta) + (upperDelta / 2F));
}
}
else
{
}
Console.WriteLine("Numbers = {0}", string.Join(" ", output.Select(x => x.ToString())));
}
Console.ReadLine();
}
}
}
As the title says, I'm developing in C#.
I'd like to generate a number which has more than 9 numbers, so I thought about generating numbers, follow by 9.
For instance, if I want to generate a number which has 10 digits - I'd generate first a number which has 9 numbers, and then a number which has 1 digit.
If I generate the number 20, I'd generate first 2 numbers with 9 digits each, and then a number with 2 digits.
This is what I've tried:
for (int i = 0, j = (int.Parse(inputRandom.Text) % 9 == 0 ? int.Parse(inputRandom.Text) % 9 : int.Parse(inputRandom.Text) % 9 + 1); i < j; i++)
if (i < (int.Parse(inputRandom.Text) % 9 == 0 ? j % 9 : j % 9 + 1) - 1)
numToSend += (BigInteger)r.Next(int.Parse(1 + Zero((int.Parse(inputRandom.Text) % 9 + 8) * (inputRandom.Text.Length - 1))));
else
numToSend += (BigInteger)r.Next(int.Parse(1 + Zero(int.Parse(inputRandom.Text) % 9 * 9)));
The method Zero returns a string with 0, times the number specified in. I.e Zero(1) would return: "0"
I need this method because the method Next(Int32) can return a number, up to what specified between the brackets. I.e Next(10) would return a number between 0 and 9.
My goal
I want to generate a number with a number of digit above 9, and put the number into the string numToSend. I cannot simply do this, because the method Next() can only generate ints.
Even after your edit, I don't find the question very clear. However, I do think I understand that you are essentially trying to generate a random BigInteger value, and that you want the random value to be within a range defined by some specific number of digits.
For example, if you ask for a 10-digit value, some value between 0 and 9999999999 should be returned. If you ask for a 20-digit value, some value between 0 and 99999999999999999999 should be returned.
Based on that understanding, I believe this method should accomplish what you are asking:
BigInteger NextRandom(Random random, int digitCount)
{
BigInteger result = 0;
while (digitCount-- > 0)
{
result = result * 10 + random.Next(10);
}
return result;
}
Note that the number returned could have fewer than digitCount actual digits in it. In fact, there's always a 1-in-10 chance of that happening. And a 1-in-100 chance of the result having fewer than (digitCount - 1) digits, etc.
If you want something different from that, please be more specific about the exact requirements of the output you want (read https://stackoverflow.com/help/how-to-ask for advice on how to present your question in a clear, answerable way).
For example, the above won't generate a random value within some arbitrary range; the (exclusive) max value can only ever be a power of 10. Also, due to the way BigInteger works, if you are looking for a value with a specific number of binary digits, you can do that simply by using the Random.NextBytes() method, passing the resulting array (making modifications as appropriate to ensure e.g. positive values).
See also C# A random BigInt generator for more inspiration (I would've voted as that for a duplicate, but it seems from your description that you might be looking for a slightly different result than what's requested in that question).
I have a maths issue within my program. I think the problem is simple but I'm not sure what terms to use, hence my own searches returned nothing useful.
I receive some values in a method, the only thing I know (in terms of logic) is the numbers will be something which can be duplicated.
In other words, the numbers I could receive are predictable and would be one of the following
1
2
4
16
256
65536
etc
I need to know at what index they appear at. In othewords, 1 is always at index 0, 2 at index 1, 4 at index 3, 16 is at index 4 etc.
I know I could write a big switch statement but I was hoping a formula would be tidier. Do you know if one exists or any clues as the names of the math forumula's I'm using.
The numbers you listed are powers of two. The inverse function of raising a number to a power is the logarithm, so that's what you use to go backwards from (using your terminology here) a number to an index.
var num = 256;
var ind = Math.Log(num, 2);
Above, ind is the base-2 logarithm of num. This code will work for any base; just substitute that base for 2. If you are only going to be working with powers of 2 then you can use a special-case solution that is faster based on the bitwise representation of your input; see What's the quickest way to compute log2 of an integer in C#?
Try
Math.Log(num, base)
where base is 2
MSDN: http://msdn.microsoft.com/en-us/library/hd50b6h5.aspx
Logarithm will return to You power of base from you number.
But it's in case if your number really are power of 2,
otherwise you have to understand exactly what you have, what you need
It also look like numbers was powered to 2 twice, so that try this:
private static int getIndexOfSeries(UInt64 aNum)
{
if (aNum == 1)
return 0;
else if (aNum == 2)
return 1;
else
{
int lNum = (int)Math.Log(aNum, 2);
return 1+(int)Math.Log(lNum, 2);
}
}
Result for UInt64[] Arr = new UInt64[] { 1, 2, 4, 16, 256, 65536, 4294967296 } is:
Num[0] = 1
Num[1] = 2
Num[2] = 4
Num[3] = 16
Num[4] = 256
Num[5] = 65536
Num[6] = 4294967296 //65536*65536
where [i] - index
You should calculate the base 2 logarithm of the number
Hint: For the results:
0 2
1 4
2 16
3 256
4 65536
5 4294967296
etc.
The formula is, for a give integer x:
Math.Pow(2, Math.Pow(2, x));
that is
2 to the power (2 to the power (x) )
Once the formula is known, one could solve it for x (I won't go through that since you already got an answer).
This question already has answers here:
Closed 10 years ago.
Possible Duplicate:
Finding all possible combinations of numbers to reach a given sum
I have to create method which from array of numbers selects numbers, which sum will be exact as required one or if such doesn't exist select the minimal greater one.
What would be the algorithm of this function?
public int[] selectExactSum(int[] X, int SUM) {
}
example:
numbers are: {5, 2, 8, 4, 6} and required sum is 12.
The result would be: {2, 4, 6}
If required sum is 13, the result would be:{2, 8, 4} - so, the sum would be in this case 14 - the first minimal greater one.
If Required sum is 15, the possible results would be: {5, 2, 8} or {5, 4, 6}. In this case return the one of your choice - probably the first one you get.
What would be the algorithm for custom numbers and sum?
Thanks,
Simon
This is a generalized case of the problem called subset sum. It's an NP-complete problem, thus the best known algorithm is pseudo-polynomial.
If you understand the above linked algorithm, you can deduct the modification necessary to solve your problem.
How about recursively?
public static int[] SelectExactSum(int[] x, int sum) {
int[]
rest = x.Skip(1).ToArray(),
with = x.Length == 1 ? x : x.Take(1).Concat(SelectExactSum(rest, sum - x[0])).ToArray(),
without = x.Length == 1 ? new int[0] : SelectExactSum(rest, sum);
int withSum = with.Sum(), withoutSum = without.Sum();
return
withSum >= sum ? (withoutSum >= sum ? (withSum < withoutSum ? with : without) : with) :
withoutSum >= sum ? without : new int[0];
}
Note: Calling SelectExactSum(new int[] {5,2,8,4,6}, 13) doesn't return {2,8,4} as stated in the question, but {5,8} as that actually sums up to 13.
Took me about 15 minutes to made it, you can see it running here:
http://jesuso.net/projects/selectExactSum/index.php?numbers=5%2C2%2C8%2C4%2C6&reqSum=15
And here's the code:
http://jesuso.net/projects/selectExactSum/selectExactSum.txt
I made it as simple as possible, but its made on PHP, let me know if you need some help translating it to c#.