I recently came across an implementation of Djikstra's Shortest Path algorithm online and found the following call.
given a List of nodes of type int and a Dictionary of distances, of type , what does the following call mean
nodes.Sort((x, y) => distances[x] - distances[y]);
The full code is as follows:
public List<int> shortest_path(int start, int finish)
{
var previous = new Dictionary<int, int>();
var distances = new Dictionary<int, int>();
var nodes = new List<int>();
List<int> path = null;
foreach (var vertex in vertices)
{
if (vertex.Item1 == start)
{
distances[vertex.Item1] = 0;
}
else
{
distances[vertex.Item1] = int.MaxValue / 2;
}
nodes.Add(vertex.Item1);
}
while (nodes.Count != 0)
{
nodes.Sort((x, y) => distances[x] - distances[y]);
var smallest = nodes[0];
nodes.Remove(smallest);
if (smallest == finish)
{
path = new List<int>();
while (previous.ContainsKey(smallest))
{
path.Add(smallest);
smallest = previous[smallest];
}
break;
}
if (distances[smallest] == int.MaxValue)
{
break;
}
foreach (var neighbor in vertices[smallest].Item2)
{
var alt = distances[smallest] + neighbor.Item2;
if (alt < distances[neighbor.Item1])
{
distances[neighbor.Item1] = alt;
previous[neighbor.Item1] = smallest;
}
}
}
return path;
}
I searched for the answer a lot but there doesn't seem to be any clear explanation of what it means.
I do know that in general in LINQ, a call to Array.Select((x,i)=>...) means that x is the actual element in the array and i is the index of element x in the array, but this doesn't seem to be the case above.
Would appreciate any explanation thanks.
In C#, what does a call to Sort with two parameters in brackets mean?
You have this line of code:
nodes.Sort((x, y) => distances[x] - distances[y]);
You are not passing two parameters to the sort method but you are passing one parameter which is a delegate that takes 2 parameters. You are essentially doing the following but using a lambda notation:
var nodes = new List<int>();
nodes.Sort(SortIt);
And here is the SortIt method:
private int SortIt(int x, int y)
{
return distances[x] - distances[y];
}
Keep in mind if you did it using the above approach, distances will have to be a class level field so the SortIt method can access it. With lambda expressions, this is what you have, it will just capture the distances variable and this is called a closure. Read this article if you want to know what closures are.
Sorting is implemented by comparing two items at a time.
The two parameters in parentheses are the two items the callback function should compare.
List.Sort Method takes an optional comparison delegate as a comparer.
https://msdn.microsoft.com/en-us/library/w56d4y5z(v=vs.110).aspx
in your example:
(x, y) => distances[x] - distances[y]) is a delegate that Sort uses as a comparer.
if distances[x] - distances[y] < 0; x is bigger;
if distances[x] - distances[y] > 0; y is bigger;
if distances[x] - distances[y] > 0; both are even;
This method will sort the elements in the entire List using the specified System.Comparison.
Where System.Comparison is a delegate
public delegate int Comparison<in T>(
T x,
T y
)
Think of it like this, you are passing the sort method a way to decide which element in the array is a precedent to the other. The sort function will use the compare function you specified to determine the precedence of each element in the returned sorted list. Therefore this function will get two elements and it will return a value indicating the result of the precendence.
let x be the first argument and y the second argument.
x < y -> the function will return a number less than 0
x = y -> the function will return 0
x > y -> the function will return a number bigger than 0
In conclusion, this function you pass to the Sort method will help the Sort function to sort the array as you wish it should sort it.
I'm trying to randomly get a specific integer (1) from a 2D array list filled with 0's and not many 1's. I made this, and it works:
while (wallsList[randomX, randomY] != 1)
{
randomX = randomizer.Next(34);
randomY = randomizer.Next(34);
}
The downside of it, it's that it takes too much time to just find one time the int (1), and I have to do this process over 1000 times since new 1's get added and removed to the 2D array each time. It takes about 3m to launch my program so I would like to know if there is an optimized version of this, I searched a lot and only found this solution for 1D arrays. Thanks for your time.
You have a sparse array. Why not represent it as a list of X/Y int pairs? Then, if the X/Y int pair is in the list, it's a 1, if not, it's a 0.
Then, to find a random value/cell containing 1, you just pick a random value from the list.
You could use a list like
new List <Tuple<int, int>> { new Tuple<int, int>(1, 5), new Tuple<int, int>(2, 7) }
Since most of your random guesses will fail, it would be far more efficient to build a second array of known good indexes and randomly search only those.
var randomizer = new Random();
var wallsList = new int[34, 34];
wallsList[23,11] = 1;
// Build an array of points that are known to pass
var knownHits =
(from x in Enumerable.Range(0, 34)
from y in Enumerable.Range(0, 34)
where wallsList[x, y] == 1
select new { x, y })
.ToArray();
// Pick a random point from previous array
var randomPoint = knownHits[randomizer.Next(knownHits.Length)];
var randomX = randomPoint.x;
var randomY = randomPoint.y;
Console.Write($"X = {randomX}, Y = {randomY}"); // X = 23, Y = 11
Alternatively, you could build the secondary array like this:
var knownHits = wallsList.Cast<int>()
.Select((v, i) => new { v, x = i / 34, y = i % 34 })
.Where(x => x.v == 1)
.ToArray();
There are a few approaches you can take. One would be to change your representation from a 2d array into something like a list of pairs of coordinates. Now selecting one at random is easy, but maybe some other operations you want to perform become harder. This approach and yours have the advantage that it selects one of the 1's uniformly. Another approach that would sacrifice this quality would be to choose a random x and y and then return the next 1, scanning by x or y. This is also not as efficient as the first solution.
I'm trying to randomly get a specific integer (1) from a 2D array list filled with 0's and not many
If you must do it randomly, your approach is fine. However, what you can improve it by avoiding drawing the same index again :
var randomizer = new Random();
var wallsList = new int[34, 34];
wallsList[01, 23] = 1;
var indexes =
from x in Enumerable.Range(0, 34)
from y in Enumerable.Range(0, 34)
select new { X = x, Y = y };
var result = indexes
.OrderBy(_ => randomizer.Next())
.FirstOrDefault(index => wallsList[index.X, index.Y] == 1);
if (result == null)
throw new Exception("Index not found");
Console.WriteLine("1 is found at[{0}, {1}]", result.X, result.Y);
This might sound lame, but I have not been able to find a really good explanation of Aggregate.
Good means short, descriptive, comprehensive with a small and clear example.
The easiest-to-understand definition of Aggregate is that it performs an operation on each element of the list taking into account the operations that have gone before. That is to say it performs the action on the first and second element and carries the result forward. Then it operates on the previous result and the third element and carries forward. etc.
Example 1. Summing numbers
var nums = new[]{1,2,3,4};
var sum = nums.Aggregate( (a,b) => a + b);
Console.WriteLine(sum); // output: 10 (1+2+3+4)
This adds 1 and 2 to make 3. Then adds 3 (result of previous) and 3 (next element in sequence) to make 6. Then adds 6 and 4 to make 10.
Example 2. create a csv from an array of strings
var chars = new []{"a","b","c","d"};
var csv = chars.Aggregate( (a,b) => a + ',' + b);
Console.WriteLine(csv); // Output a,b,c,d
This works in much the same way. Concatenate a a comma and b to make a,b. Then concatenates a,b with a comma and c to make a,b,c. and so on.
Example 3. Multiplying numbers using a seed
For completeness, there is an overload of Aggregate which takes a seed value.
var multipliers = new []{10,20,30,40};
var multiplied = multipliers.Aggregate(5, (a,b) => a * b);
Console.WriteLine(multiplied); //Output 1200000 ((((5*10)*20)*30)*40)
Much like the above examples, this starts with a value of 5 and multiplies it by the first element of the sequence 10 giving a result of 50. This result is carried forward and multiplied by the next number in the sequence 20 to give a result of 1000. This continues through the remaining 2 element of the sequence.
Live examples: http://rextester.com/ZXZ64749
Docs: http://msdn.microsoft.com/en-us/library/bb548651.aspx
Addendum
Example 2, above, uses string concatenation to create a list of values separated by a comma. This is a simplistic way to explain the use of Aggregate which was the intention of this answer. However, if using this technique to actually create a large amount of comma separated data, it would be more appropriate to use a StringBuilder, and this is entirely compatible with Aggregate using the seeded overload to initiate the StringBuilder.
var chars = new []{"a","b","c", "d"};
var csv = chars.Aggregate(new StringBuilder(), (a,b) => {
if(a.Length>0)
a.Append(",");
a.Append(b);
return a;
});
Console.WriteLine(csv);
Updated example: http://rextester.com/YZCVXV6464
It partly depends on which overload you're talking about, but the basic idea is:
Start with a seed as the "current value"
Iterate over the sequence. For each value in the sequence:
Apply a user-specified function to transform (currentValue, sequenceValue) into (nextValue)
Set currentValue = nextValue
Return the final currentValue
You may find the Aggregate post in my Edulinq series useful - it includes a more detailed description (including the various overloads) and implementations.
One simple example is using Aggregate as an alternative to Count:
// 0 is the seed, and for each item, we effectively increment the current value.
// In this case we can ignore "item" itself.
int count = sequence.Aggregate(0, (current, item) => current + 1);
Or perhaps summing all the lengths of strings in a sequence of strings:
int total = sequence.Aggregate(0, (current, item) => current + item.Length);
Personally I rarely find Aggregate useful - the "tailored" aggregation methods are usually good enough for me.
Super short
Aggregate works like fold in Haskell/ML/F#.
Slightly longer
.Max(), .Min(), .Sum(), .Average() all iterates over the elements in a sequence and aggregates them using the respective aggregate function. .Aggregate () is generalized aggregator in that it allows the developer to specify the start state (aka seed) and the aggregate function.
I know you asked for a short explaination but I figured as others gave a couple of short answers I figured you would perhaps be interested in a slightly longer one
Long version with code
One way to illustrate what does it could be show how you implement Sample Standard Deviation once using foreach and once using .Aggregate. Note: I haven't prioritized performance here so I iterate several times over the colleciton unnecessarily
First a helper function used to create a sum of quadratic distances:
static double SumOfQuadraticDistance (double average, int value, double state)
{
var diff = (value - average);
return state + diff * diff;
}
Then Sample Standard Deviation using ForEach:
static double SampleStandardDeviation_ForEach (
this IEnumerable<int> ints)
{
var length = ints.Count ();
if (length < 2)
{
return 0.0;
}
const double seed = 0.0;
var average = ints.Average ();
var state = seed;
foreach (var value in ints)
{
state = SumOfQuadraticDistance (average, value, state);
}
var sumOfQuadraticDistance = state;
return Math.Sqrt (sumOfQuadraticDistance / (length - 1));
}
Then once using .Aggregate:
static double SampleStandardDeviation_Aggregate (
this IEnumerable<int> ints)
{
var length = ints.Count ();
if (length < 2)
{
return 0.0;
}
const double seed = 0.0;
var average = ints.Average ();
var sumOfQuadraticDistance = ints
.Aggregate (
seed,
(state, value) => SumOfQuadraticDistance (average, value, state)
);
return Math.Sqrt (sumOfQuadraticDistance / (length - 1));
}
Note that these functions are identical except for how sumOfQuadraticDistance is calculated:
var state = seed;
foreach (var value in ints)
{
state = SumOfQuadraticDistance (average, value, state);
}
var sumOfQuadraticDistance = state;
Versus:
var sumOfQuadraticDistance = ints
.Aggregate (
seed,
(state, value) => SumOfQuadraticDistance (average, value, state)
);
So what .Aggregate does is that it encapsulates this aggregator pattern and I expect that the implementation of .Aggregate would look something like this:
public static TAggregate Aggregate<TAggregate, TValue> (
this IEnumerable<TValue> values,
TAggregate seed,
Func<TAggregate, TValue, TAggregate> aggregator
)
{
var state = seed;
foreach (var value in values)
{
state = aggregator (state, value);
}
return state;
}
Using the Standard deviation functions would look something like this:
var ints = new[] {3, 1, 4, 1, 5, 9, 2, 6, 5, 4};
var average = ints.Average ();
var sampleStandardDeviation = ints.SampleStandardDeviation_Aggregate ();
var sampleStandardDeviation2 = ints.SampleStandardDeviation_ForEach ();
Console.WriteLine (average);
Console.WriteLine (sampleStandardDeviation);
Console.WriteLine (sampleStandardDeviation2);
IMHO
So does .Aggregate help readability? In general I love LINQ because I think .Where, .Select, .OrderBy and so on greatly helps readability (if you avoid inlined hierarhical .Selects). Aggregate has to be in Linq for completeness reasons but personally I am not so convinced that .Aggregate adds readability compared to a well written foreach.
A picture is worth a thousand words
Reminder:
Func<X, Y, R> is a function with two inputs of type X and Y, that returns a result of type R.
Enumerable.Aggregate has three overloads:
Overload 1:
A Aggregate<A>(IEnumerable<A> a, Func<A, A, A> f)
Example:
new[]{1,2,3,4}.Aggregate((x, y) => x + y); // 10
This overload is simple, but it has the following limitations:
the sequence must contain at least one element,
otherwise the function will throw an InvalidOperationException.
elements and result must be of the same type.
Overload 2:
B Aggregate<A, B>(IEnumerable<A> a, B bIn, Func<B, A, B> f)
Example:
var hayStack = new[] {"straw", "needle", "straw", "straw", "needle"};
var nNeedles = hayStack.Aggregate(0, (n, e) => e == "needle" ? n+1 : n); // 2
This overload is more general:
a seed value must be provided (bIn).
the collection can be empty,
in this case, the function will yield the seed value as result.
elements and result can have different types.
Overload 3:
C Aggregate<A,B,C>(IEnumerable<A> a, B bIn, Func<B,A,B> f, Func<B,C> f2)
The third overload is not very useful IMO.
The same can be written more succinctly by using overload 2 followed by a function that transforms its result.
The illustrations are adapted from this excellent blogpost.
Aggregate is basically used to Group or Sum up data.
According to MSDN
"Aggregate Function Applies an accumulator function over a sequence."
Example 1: Add all the numbers in a array.
int[] numbers = new int[] { 1,2,3,4,5 };
int aggregatedValue = numbers.Aggregate((total, nextValue) => total + nextValue);
*important: The initial aggregate value by default is the 1 element in the sequence of collection.
i.e: the total variable initial value will be 1 by default.
variable explanation
total: it will hold the sum up value(aggregated value) returned by the func.
nextValue: it is the next value in the array sequence. This value is than added to the aggregated value i.e total.
Example 2: Add all items in an array. Also set the initial accumulator value to start adding with from 10.
int[] numbers = new int[] { 1,2,3,4,5 };
int aggregatedValue = numbers.Aggregate(10, (total, nextValue) => total + nextValue);
arguments explanation:
the first argument is the initial(starting value i.e seed value) which will be used to start addition with the next value in the array.
the second argument is a func which is a func that takes 2 int.
1.total: this will hold same as before the sum up value(aggregated value) returned by the func after the calculation.
2.nextValue: : it is the next value in the array sequence. This value is than added to the aggregated value i.e total.
Also debugging this code will give you a better understanding of how aggregate work.
In addition to all the great answers here already, I've also used it to walk an item through a series of transformation steps.
If a transformation is implemented as a Func<T,T>, you can add several transformations to a List<Func<T,T>> and use Aggregate to walk an instance of T through each step.
A more concrete example
You want to take a string value, and walk it through a series of text transformations that could be built programatically.
var transformationPipeLine = new List<Func<string, string>>();
transformationPipeLine.Add((input) => input.Trim());
transformationPipeLine.Add((input) => input.Substring(1));
transformationPipeLine.Add((input) => input.Substring(0, input.Length - 1));
transformationPipeLine.Add((input) => input.ToUpper());
var text = " cat ";
var output = transformationPipeLine.Aggregate(text, (input, transform)=> transform(input));
Console.WriteLine(output);
This will create a chain of transformations: Remove leading and trailing spaces -> remove first character -> remove last character -> convert to upper-case. Steps in this chain can be added, removed, or reordered as needed, to create whatever kind of transformation pipeline is required.
The end result of this specific pipeline, is that " cat " becomes "A".
This can become very powerful once you realize that T can be anything. This could be used for image transformations, like filters, using BitMap as an example;
Learned a lot from Jamiec's answer.
If the only need is to generate CSV string, you may try this.
var csv3 = string.Join(",",chars);
Here is a test with 1 million strings
0.28 seconds = Aggregate w/ String Builder
0.30 seconds = String.Join
Source code is here
Definition
Aggregate method is an extension method for generic collections. Aggregate method applies a function to each item of a collection. Not just only applies a function, but takes its result as initial value for the next iteration. So, as a result, we will get a computed value (min, max, avg, or other statistical value) from a collection.
Therefore, Aggregate method is a form of safe implementation of a recursive function.
Safe, because the recursion will iterate over each item of a collection and we can’t get any infinite loop suspension by wrong exit condition. Recursive, because the current function’s result is used as a parameter for the next function call.
Syntax:
collection.Aggregate(seed, func, resultSelector);
seed - initial value by default;
func - our recursive function. It can be a lambda-expression, a Func delegate or a function type T F(T result, T nextValue);
resultSelector - it can be a function like func or an expression to compute, transform, change, convert the final result.
How it works:
var nums = new[]{1, 2};
var result = nums.Aggregate(1, (result, n) => result + n); //result = (1 + 1) + 2 = 4
var result2 = nums.Aggregate(0, (result, n) => result + n, response => (decimal)response/2.0); //result2 = ((0 + 1) + 2)*1.0/2.0 = 3*1.0/2.0 = 3.0/2.0 = 1.5
Practical usage:
Find Factorial from a number n:
int n = 7;
var numbers = Enumerable.Range(1, n);
var factorial = numbers.Aggregate((result, x) => result * x);
which is doing the same thing as this function:
public static int Factorial(int n)
{
if (n < 1) return 1;
return n * Factorial(n - 1);
}
Aggregate() is one of the most powerful LINQ extension method, like Select() and Where(). We can use it to replace the Sum(), Min(). Max(), Avg() functionality, or to change it by implementing addition context:
var numbers = new[]{3, 2, 6, 4, 9, 5, 7};
var avg = numbers.Aggregate(0.0, (result, x) => result + x, response => (double)response/(double)numbers.Count());
var min = numbers.Aggregate((result, x) => (result < x)? result: x);
More complex usage of extension methods:
var path = #“c:\path-to-folder”;
string[] txtFiles = Directory.GetFiles(path).Where(f => f.EndsWith(“.txt”)).ToArray<string>();
var output = txtFiles.Select(f => File.ReadAllText(f, Encoding.Default)).Aggregate<string>((result, content) => result + content);
File.WriteAllText(path + “summary.txt”, output, Encoding.Default);
Console.WriteLine(“Text files merged into: {0}”, output); //or other log info
This is an explanation about using Aggregate on a Fluent API such as Linq Sorting.
var list = new List<Student>();
var sorted = list
.OrderBy(s => s.LastName)
.ThenBy(s => s.FirstName)
.ThenBy(s => s.Age)
.ThenBy(s => s.Grading)
.ThenBy(s => s.TotalCourses);
and lets see we want to implement a sort function that take a set of fields, this is very easy using Aggregate instead of a for-loop, like this:
public static IOrderedEnumerable<Student> MySort(
this List<Student> list,
params Func<Student, object>[] fields)
{
var firstField = fields.First();
var otherFields = fields.Skip(1);
var init = list.OrderBy(firstField);
return otherFields.Skip(1).Aggregate(init, (resultList, current) => resultList.ThenBy(current));
}
And we can use it like this:
var sorted = list.MySort(
s => s.LastName,
s => s.FirstName,
s => s.Age,
s => s.Grading,
s => s.TotalCourses);
Aggregate used to sum columns in a multi dimensional integer array
int[][] nonMagicSquare =
{
new int[] { 3, 1, 7, 8 },
new int[] { 2, 4, 16, 5 },
new int[] { 11, 6, 12, 15 },
new int[] { 9, 13, 10, 14 }
};
IEnumerable<int> rowSums = nonMagicSquare
.Select(row => row.Sum());
IEnumerable<int> colSums = nonMagicSquare
.Aggregate(
(priorSums, currentRow) =>
priorSums.Select((priorSum, index) => priorSum + currentRow[index]).ToArray()
);
Select with index is used within the Aggregate func to sum the matching columns and return a new Array; { 3 + 2 = 5, 1 + 4 = 5, 7 + 16 = 23, 8 + 5 = 13 }.
Console.WriteLine("rowSums: " + string.Join(", ", rowSums)); // rowSums: 19, 27, 44, 46
Console.WriteLine("colSums: " + string.Join(", ", colSums)); // colSums: 25, 24, 45, 42
But counting the number of trues in a Boolean array is more difficult since the accumulated type (int) differs from the source type (bool); here a seed is necessary in order to use the second overload.
bool[][] booleanTable =
{
new bool[] { true, true, true, false },
new bool[] { false, false, false, true },
new bool[] { true, false, false, true },
new bool[] { true, true, false, false }
};
IEnumerable<int> rowCounts = booleanTable
.Select(row => row.Select(value => value ? 1 : 0).Sum());
IEnumerable<int> seed = new int[booleanTable.First().Length];
IEnumerable<int> colCounts = booleanTable
.Aggregate(seed,
(priorSums, currentRow) =>
priorSums.Select((priorSum, index) => priorSum + (currentRow[index] ? 1 : 0)).ToArray()
);
Console.WriteLine("rowCounts: " + string.Join(", ", rowCounts)); // rowCounts: 3, 1, 2, 2
Console.WriteLine("colCounts: " + string.Join(", ", colCounts)); // colCounts: 3, 2, 1, 2
Everyone has given his explanation. My explanation is like that.
Aggregate method applies a function to each item of a collection. For example, let's have collection { 6, 2, 8, 3 } and the function Add (operator +) it does (((6+2)+8)+3) and returns 19
var numbers = new List<int> { 6, 2, 8, 3 };
int sum = numbers.Aggregate(func: (result, item) => result + item);
// sum: (((6+2)+8)+3) = 19
In this example there is passed named method Add instead of lambda expression.
var numbers = new List<int> { 6, 2, 8, 3 };
int sum = numbers.Aggregate(func: Add);
// sum: (((6+2)+8)+3) = 19
private static int Add(int x, int y) { return x + y; }
A short and essential definition might be this: Linq Aggregate extension method allows to declare a sort of recursive function applied on the elements of a list, the operands of whom are two: the elements in the order in which they are present into the list, one element at a time, and the result of the previous recursive iteration or nothing if not yet recursion.
In this way you can compute the factorial of numbers, or concatenate strings.