mirror of
https://github.com/BlackLight/Snort_AIPreproc.git
synced 2024-11-14 20:57:15 +01:00
414 lines
13 KiB
JavaScript
414 lines
13 KiB
JavaScript
/*
|
|
* Various algorithms and data structures, licensed under the MIT-license.
|
|
* (c) 2010 by Johann Philipp Strathausen <strathausen@gmail.com>
|
|
* http://strathausen.eu
|
|
*
|
|
*/
|
|
|
|
|
|
|
|
/*
|
|
Path-finding algorithm Bellman-Ford
|
|
|
|
finds the shortest paths from one node to all nodes
|
|
- runs in O( |E| · |V| ), where E = edges and V = vertices (nodes)
|
|
- can run on graphs with negative edge weights as long as they do not have
|
|
any negative weight cycles
|
|
*/
|
|
function bellman_ford(g, source) {
|
|
|
|
/* STEP 1: initialisation */
|
|
for(var n in g.nodes)
|
|
g.nodes[n].distance = Infinity;
|
|
/* predecessors are implicitly null */
|
|
source.distance = 0;
|
|
g.snapShot("Initiallisation: Set all distances are infinite and all predecessors are null.");
|
|
|
|
/* STEP 2: relax each edge (this is at the heart of Bellman-Ford) */
|
|
/* repeat this for the number of nodes minus one */
|
|
for(var i = 1; i < g.nodes.length; i++)
|
|
/* for each edge */
|
|
for(var e in g.edges) {
|
|
var edge = g.edges[e];
|
|
if(edge.source.distance + edge.weight < edge.target.distance) {
|
|
g.snapShot("Relax edge between "+edge.source.id+" and "+edge.target.id+".");
|
|
edge.target.distance = edge.source.distance + edge.weight;
|
|
edge.target.predecessor = edge.source;
|
|
}
|
|
}
|
|
|
|
g.snapShot("Ready.");
|
|
|
|
/* STEP 3: TODO Check for negative cycles */
|
|
/* For now we assume here that the graph does not contain any negative
|
|
weights cycles. (this is left as an excercise to the reader[tm]) */
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
Path-finding algorithm Dijkstra
|
|
|
|
- worst-case running time is O( |E| + |V| · log |V| ) thus better than
|
|
Bellman-Ford, but cannot handle negative edge weights
|
|
*/
|
|
function dijkstra(g, source) {
|
|
/* initially, all distances are infinite and all predecessors are null */
|
|
for(var n in g.nodes)
|
|
g.nodes[n].distance = Infinity;
|
|
/* predecessors are implicitly null */
|
|
source.distance = 0;
|
|
var counter=0;
|
|
/* set of unoptimized nodes, sorted by their distance (but a Fibonacci heap
|
|
would be better) */
|
|
var q = new BinaryMinHeap(g.nodes, "distance");
|
|
|
|
var node;
|
|
/* get the node with the smallest distance */
|
|
/* as long as we have unoptimized nodes */
|
|
|
|
while(q.min()!=undefined) {
|
|
/* remove the latest */
|
|
node=q.extractMin();
|
|
node.optimized=true;
|
|
|
|
/* no nodes accessible from this one, should not happen */
|
|
if(node.distance == Infinity)
|
|
throw "Orphaned node!";
|
|
|
|
/* for each neighbour of node */
|
|
for(e in node.edges) {
|
|
if(node.edges[e].target.optimized)
|
|
continue;
|
|
|
|
/* look for an alternative route */
|
|
var alt = node.distance + node.edges[e].weight;
|
|
|
|
/* update distance and route if a better one has been found */
|
|
if (alt < node.edges[e].target.distance) {
|
|
|
|
/* update distance of neighbour */
|
|
node.edges[e].target.distance = alt;
|
|
|
|
/* update priority queue */
|
|
q.heapify();
|
|
|
|
/* update path */
|
|
node.edges[e].target.predecessor = node;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
/* Runs at worst in O(|V|³) and at best in Omega(|V|³) :-)
|
|
complexity Sigma(|V|²) */
|
|
/* This implementation is not yet ready for general use, but works with the
|
|
Dracula graph library. */
|
|
function floyd_warshall(g, source) {
|
|
|
|
/* Step 1: initialising empty path matrix (second dimension is implicit) */
|
|
var path = [];
|
|
var next = [];
|
|
var n = g.nodes.length;
|
|
|
|
/* construct path matrix, initialize with Infinity */
|
|
for(j in g.nodes) {
|
|
path[j] = [];
|
|
next[j] = [];
|
|
for(i in g.nodes)
|
|
path[j][i] = j == i ? 0 : Infinity;
|
|
}
|
|
|
|
/* initialize path with edge weights */
|
|
for(e in g.edges)
|
|
path[g.edges[e].source.id][g.edges[e].target.id] = g.edges[e].weight;
|
|
|
|
/* Note: Usually, the initialisation is done by getting the edge weights
|
|
from a node matrix representation of the graph, not by iterating through
|
|
a list of edges as done here. */
|
|
|
|
/* Step 2: find best distances (the heart of Floyd-Warshall) */
|
|
for(k in g.nodes){
|
|
for(i in g.nodes) {
|
|
for(j in g.nodes)
|
|
if(path[i][j] > path[i][k] + path[k][j]) {
|
|
path[i][j] = path[i][k] + path[k][j];
|
|
/* Step 2.b: remember the path */
|
|
next[i][j] = k;
|
|
}
|
|
}
|
|
}
|
|
/* Step 3: Path reconstruction */
|
|
function getPath(i, j) {
|
|
if(path[i][j] == Infinity)
|
|
throw "There is no path.";
|
|
var intermediate = next[i][j];
|
|
if(intermediate == undefined)
|
|
return null;
|
|
else
|
|
return getPath(i, intermediate)
|
|
.concat([intermediate])
|
|
.concat(getPath(intermediate, j));
|
|
}
|
|
// console&&console.log(path);
|
|
// console&&console.log(next);
|
|
|
|
/* TODO use the knowledge */
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
A simple binary min-heap serving as a priority queue
|
|
- takes an array as the input, with elements having a key property
|
|
- elements will look like this:
|
|
{
|
|
key: "... key property ...",
|
|
value: "... element content ..."
|
|
}
|
|
- provides insert(), min(), extractMin() and heapify()
|
|
- example usage (e.g. via the Firebug console):
|
|
var x = {foo:20,hui:"bla"};
|
|
var a = new BinaryMinHeap([x,{foo:3},{foo:10},{foo:20},{foo:30},{foo:6},{foo:1},{foo:3}],"foo");
|
|
console.log(a.extractMin());
|
|
console.log(a.extractMin());
|
|
x.ma=0;
|
|
a.heapify(); // call this when key updated
|
|
console.log(a.extractMin());
|
|
console.log(a.extractMin());
|
|
- can also be used on a simple array, like [9,7,8,5]
|
|
*/
|
|
function BinaryMinHeap(array, key) {
|
|
|
|
/* Binary tree stored in an array, no need for a complicated data structure */
|
|
var tree = [];
|
|
|
|
var key = key || 'key';
|
|
|
|
/* Calculate the index of the parent or a child */
|
|
var parent = function(index) { return Math.floor((index - 1)/2); };
|
|
var right = function(index) { return 2 * index + 2; };
|
|
var left = function(index) { return 2 * index + 1; };
|
|
|
|
/* Helper function to swap elements with their parent
|
|
as long as the parent is bigger */
|
|
function bubble_up(i) {
|
|
var p = parent(i);
|
|
while((p >= 0) && (tree[i][key] < tree[p][key])) {
|
|
/* swap with parent */
|
|
tree[i] = tree.splice(p, 1, tree[i])[0];
|
|
/* go up one level */
|
|
i = p;
|
|
p = parent(i);
|
|
}
|
|
}
|
|
|
|
/* Helper function to swap elements with the smaller of their children
|
|
as long as there is one */
|
|
function bubble_down(i) {
|
|
var l = left(i);
|
|
var r = right(i);
|
|
|
|
/* as long as there are smaller children */
|
|
while(tree[l] && (tree[i][key] > tree[l][key]) || tree[r] && (tree[i][key] > tree[r][key])) {
|
|
|
|
/* find smaller child */
|
|
var child = tree[l] ? tree[r] ? tree[l][key] > tree[r][key] ? r : l : l : l;
|
|
|
|
/* swap with smaller child with current element */
|
|
tree[i] = tree.splice(child, 1, tree[i])[0];
|
|
|
|
/* go up one level */
|
|
i = child;
|
|
l = left(i);
|
|
r = right(i);
|
|
}
|
|
}
|
|
|
|
/* Insert a new element with respect to the heap property
|
|
1. Insert the element at the end
|
|
2. Bubble it up until it is smaller than its parent */
|
|
this.insert = function(element) {
|
|
|
|
/* make sure there's a key property */
|
|
(element[key] == undefined) && (element = {key:element});
|
|
|
|
/* insert element at the end */
|
|
tree.push(element);
|
|
|
|
/* bubble up the element */
|
|
bubble_up(tree.length - 1);
|
|
}
|
|
|
|
/* Only show us the minimum */
|
|
this.min = function() {
|
|
return tree.length == 1 ? undefined : tree[0];
|
|
}
|
|
|
|
/* Return and remove the minimum
|
|
1. Take the root as the minimum that we are looking for
|
|
2. Move the last element to the root (thereby deleting the root)
|
|
3. Compare the new root with both of its children, swap it with the
|
|
smaller child and then check again from there (bubble down)
|
|
*/
|
|
this.extractMin = function() {
|
|
var result = this.min();
|
|
|
|
/* move the last element to the root or empty the tree completely */
|
|
/* bubble down the new root if necessary */
|
|
(tree.length == 1) && (tree = []) || (tree[0] = tree.pop()) && bubble_down(0);
|
|
|
|
return result;
|
|
}
|
|
|
|
/* currently unused, TODO implement */
|
|
this.changeKey = function(index, key) {
|
|
throw "function not implemented";
|
|
}
|
|
|
|
this.heapify = function() {
|
|
for(var start = Math.floor((tree.length - 2) / 2); start >= 0; start--) {
|
|
bubble_down(start);
|
|
}
|
|
}
|
|
|
|
//this.debug = function() {console&&console.log("----");for(i in tree){console&&console.log(tree[i].id,tree[i].distance);};}
|
|
/* insert the input elements one by one only when we don't have a key property (TODO can be done more elegant) */
|
|
// if (key=="key")
|
|
for(i in (array || []))
|
|
this.insert(array[i]);
|
|
// else {
|
|
// this.tree = array; // TODO there's an error here, maybe the array needs to be cloned or copied, because all reference is lost after this assignment
|
|
// this.heapify();
|
|
// }
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
Quick Sort:
|
|
1. Select some random value from the array, the median.
|
|
2. Divide the array in three smaller arrays according to the elements
|
|
being less, equal or greater than the median.
|
|
3. Recursively sort the array containg the elements less than the
|
|
median and the one containing elements greater than the median.
|
|
4. Concatenate the three arrays (less, equal and greater).
|
|
5. One or no element is always sorted.
|
|
Note: This could be implemented more efficiently by using only one array.
|
|
*/
|
|
function quickSort(arr) {
|
|
/* recursion anchor: one element is always sorted */
|
|
if(arr.length <= 1) return arr;
|
|
/* randomly selecting some value */
|
|
var median = arr[Math.floor(Math.random() * arr.length)];
|
|
var arr1 = [], arr2 = [], arr3 = [];
|
|
for(var i in arr) {
|
|
arr[i] < median && arr1.push(arr[i]);
|
|
arr[i] == median && arr2.push(arr[i]);
|
|
arr[i] > median && arr3.push(arr[i]);
|
|
}
|
|
/* recursive sorting and assembling final result */
|
|
return quickSort(arr1).concat(arr2).concat(quickSort(arr3));
|
|
}
|
|
|
|
/*
|
|
Selection Sort:
|
|
1. Select the minimum and remove it from the array
|
|
2. Sort the rest recursively
|
|
3. Return the minimum plus the sorted rest
|
|
4. An array with only one element is already sorted
|
|
*/
|
|
function selectionSort(arr) {
|
|
/* recursion anchor: one element is always sorted */
|
|
if(arr.length == 1) return arr;
|
|
var minimum = Infinity;
|
|
var index;
|
|
for(var i in arr) {
|
|
if(arr[i] < minimum) {
|
|
minimum = arr[i];
|
|
index = i; /* remember the minimum index for later removal */
|
|
}
|
|
}
|
|
/* remove the minimum */
|
|
arr.splice(index, 1);
|
|
/* assemble result and sort recursively (could be easily done iteratively as well)*/
|
|
return [minimum].concat(selectionSort(arr));
|
|
}
|
|
|
|
/*
|
|
Merge Sort:
|
|
1. Cut the array in half
|
|
2. Sort each of them recursively
|
|
3. Merge the two sorted arrays
|
|
4. An array with only one element is already sorted
|
|
|
|
*/
|
|
function mergeSort(arr) {
|
|
/* merges two sorted arrays into one sorted array */
|
|
function merge(a, b) {
|
|
/* result set */
|
|
var c = [];
|
|
/* as long as there are elements in the arrays to be merged */
|
|
while(a.length > 0 || b.length > 0){
|
|
/* are there elements to be merged, if yes, compare them and merge */
|
|
var n = a.length > 0 && b.length > 0 ? a[0] < b[0] ? a.shift() : b.shift() : b.length > 0 ? b.shift() : a.length > 0 ? a.shift() : null;
|
|
/* always push the smaller one onto the result set */
|
|
n != null && c.push(n);
|
|
}
|
|
return c;
|
|
}
|
|
/* this mergeSort implementation cuts the array in half, wich should be fine with randomized arrays, but introduces the risk of a worst-case scenario */
|
|
median = Math.floor(arr.length / 2);
|
|
var part1 = arr.slice(0, median); /* for some reason it doesn't work if inserted directly in the return statement (tried so with firefox) */
|
|
var part2 = arr.slice(median - arr.length);
|
|
return arr.length <= 1 ? arr : merge(
|
|
mergeSort(part1), /* first half */
|
|
mergeSort(part2) /* second half */
|
|
);
|
|
}
|
|
|
|
/* Balanced Red-Black-Tree */
|
|
function RedBlackTree(arr) {
|
|
|
|
}
|
|
|
|
function BTree(arr) {
|
|
|
|
}
|
|
|
|
function NaryTree(n, arr) {
|
|
|
|
}
|
|
|
|
|
|
/**
|
|
* Curry - Function currying
|
|
* Copyright (c) 2008 Ariel Flesler - aflesler(at)gmail(dot)com | http://flesler.blogspot.com
|
|
* Licensed under BSD (http://www.opensource.org/licenses/bsd-license.php)
|
|
* Date: 10/4/2008
|
|
*
|
|
* @author Ariel Flesler
|
|
* @version 1.0.1
|
|
*/
|
|
|
|
function curry( fn ){
|
|
return function(){
|
|
var args = curry.args(arguments),
|
|
master = arguments.callee,
|
|
self = this;
|
|
|
|
return args.length >= fn.length ? fn.apply(self,args) : function(){
|
|
return master.apply( self, args.concat(curry.args(arguments)) );
|
|
};
|
|
};
|
|
};
|
|
|
|
curry.args = function( args ){
|
|
return Array.prototype.slice.call(args);
|
|
};
|
|
|
|
Function.prototype.curry = function(){
|
|
return curry(this);
|
|
};
|