我正在寻找针对JavaScript或类似内容的Blossom算法的实现。
我有一组配对
A - B
A - C
B - D
我需要选择对，假设每个字母只能在输出中结束一次。在上面的场景中，正确的结果将是
A - C
B - D
因为A，B，C和D都以结果结束。
的结果不正确A - B
会使C和D离开。
答案 0 :(得分：2)
当然，为什么不呢？
/*
Edmonds's maximum matching algorithm
Complexity: O(v^3)
Written by Felipe Lopes de Freitas
Adapted to JavaScript from C++ (http://pastebin.com/NQwxv32y) by גלעד ברקן
*/
var MAX = 100,
undef = -2,
empty = -1,
noEdge = 0,
unmatched = 1,
matched = 2,
forward = 0,
reverse = 0;
//Labels are the key to this implementation of the algorithm.
function Label(){ //An even label in a vertex means there's an alternating path
this.even = undefined; //of even length starting from the root node that ends on the
this.odd = new Array(2); //vertex. To find this path, the backtrace() function is called,
}; //constructing the path by following the content of the labels.
//Odd labels are similar, the only difference is that base nodes
//of blossoms inside other blossoms may have two. More on this later.
function elem(){ //This is the element of the queue of labels to be analyzed by
this.vertex = undefined;
this.type = undefined; //the augmentMatching() procedure. Each element contains the vertex
}; //where the label is and its type, odd or even.
var g = new Array(MAX); //The graph, as an adjacency matrix.
for (var i=0; i<MAX; i++){
g[i] = new Array(MAX);
}
//blossom[i] contains the base node of the blossom the vertex i
var blossom = new Array(MAX); //is in. This, together with labels eliminates the need to
//contract the graph.
//The path arrays are where the backtrace() routine will
var path = new Array(2);
for (var i=0; i<2; i++){
path[i] = new Array(MAX);
}
var endPath = new Array(2); //store the paths it finds. Only two paths need to be
//stored. endPath[p] denotes the end of path[p].
var match = new Array(MAX); //An array of flags. match[i] stores if vertex i is in the matching.
//label[i] contains the label assigned to vertex i. It may be undefined,
var label = new Array(MAX); //empty (meaning the node is a root) and a node might have even and odd
//labels at the same time, which is the case for nonbase nodes of blossoms
for (var i=0; i<MAX; i++){
label[i] = new Label();
}
var queue = new Array(2*MAX); //The queue is necessary for efficiently scanning all labels.
var queueFront,queueBack; //A label is enqueued when assigned and dequeued after scanned.
for (var i=0; i<2*MAX; i++){
queue[i] = new elem();
}
function initGraph(n){
for (var i=0; i<n; i++)
for (var j=0; j<n; j++) g[i][j]=noEdge;
}
function readGraph(){
var n = graph.n,
e = graph.e;
//int n,e,a,b;
//scanf(" %d %d",&n,&e); //The graph is read and its edges are unmatched by default.
initGraph(n); //Since C++ arrays are 0..n-1 and input 1..n , subtractions
for (var i=0; i<e; i++){ //are made for better memory usage.
//scanf(" %d %d",&a,&b);
var a = graph[i][0],
b = graph[i][1];
if (a!=b)
g[a-1][b-1]=g[b-1][a-1]=unmatched;
}
return n;
}
function initAlg(n){ //Initializes all data structures for the augmentMatching()
queueFront=queueBack=0; //function begin. At the start, all labels are undefined,
for (var i=0; i<n; i++){ //the queue is empty and a node alone is its own blossom.
blossom[i]=i;
label[i].even=label[i].odd[0]=label[i].odd[1]=undef;
}
}
function backtrace (vert, pathNum, stop, parity, direction){
if (vert==stop) return; //pathNum is the number of the path to store
else if (parity==0){ //vert and parity determine the label to be read.
if (direction==reverse){
backtrace(label[vert].even,pathNum,stop,(parity+1)%2,reverse);
path[pathNum][endPath[pathNum]++]=vert;
} //forward means the vertices called first enter
else if (direction==forward){ //the path first, reverse is the opposite.
path[pathNum][endPath[pathNum]++]=vert;
backtrace(label[vert].even,pathNum,stop,(parity+1)%2,forward);
}
}
/*
stop is the stopping condition for the recursion.
Recursion is necessary because of the possible dual odd labels.
having empty at stop means the recursion will only stop after
the whole tree has been climbed. If assigned to a vertex, it'll stop
once it's reached.
*/
else if (parity==1 && label[vert].odd[1]==undef){
if (direction==reverse){
backtrace(label[vert].odd[0],pathNum,stop,(parity+1)%2,reverse);
path[pathNum][endPath[pathNum]++]=vert;
}
else if (direction==forward){
path[pathNum][endPath[pathNum]++]=vert;
backtrace(label[vert].odd[0],pathNum,stop,(parity+1)%2,forward);
}
}
/*
Dual odd labels are interpreted as follows:
There exists an odd length alternating path starting from the root to this
vertex. To find this path, backtrace from odd[0] to the top of the tree and
from odd[1] to the vertex itself. This, put in the right order, will
constitute said path.
*/
else if (parity==1 && label[vert].odd[1]!=undef){
if (direction==reverse){
backtrace(label[vert].odd[0],pathNum,empty,(parity+1)%2,reverse);
backtrace(label[vert].odd[1],pathNum,vert,(parity+1)%2,forward);
path[pathNum][endPath[pathNum]++]=vert;
}
else if (direction==forward){
backtrace(label[vert].odd[1],pathNum,vert,(parity+1)%2,reverse);
backtrace(label[vert].odd[0],pathNum,empty,(parity+1)%2,forward);
path[pathNum][endPath[pathNum]++]=vert;
}
}
}
function enqueue (vert, t){
var tmp = new elem(); //Enqueues labels for scanning.
tmp.vertex=vert; //No label that's dequeued during the execution
tmp.type=t; //of augmentMatching() goes back to the queue.
queue[queueBack++]=tmp; //Thus, circular arrays are unnecessary.
}
function newBlossom (a, b){ //newBlossom() will be called after the paths are evaluated.
var i,base,innerBlossom,innerBase;
for (i=0; path[0][i]==path[1][i]; i++); //Find the lowest common ancestor of a and b
i--; //it will be used to represent the blossom.
base=blossom[path[0][i]]; //Unless it's already contained in another...
//In this case, all will be put in the older one.
for (var j=i; j<endPath[0]; j++) blossom[path[0][j]]=base;
for (var j=i+1; j<endPath[1]; j++) blossom[path[1][j]]=base; //Set all nodes to this
for (var p=0; p<2; p++){ //new blossom.
for (var j=i+1; j<endPath[p]-1; j++){
if (label[path[p][j]].even==undef){ //Now, new labels will be applied
label[path[p][j]].even=path[p][j+1]; //to indicate the existence of even
enqueue(path[p][j],0); //and odd length paths.
}
else if (label[path[p][j]].odd[0]==undef && label[path[p][j+1]].even==undef){
label[path[p][j]].odd[0]=path[p][j+1];
enqueue(path[p][j],1); //Labels will only be put if the vertex
} //doesn't have one.
else if (label[path[p][j]].odd[0]==undef && label[path[p][j+1]].even!=undef){
/*
If a vertex doesn't have an odd label, but the next one in the path
has an even label, it means that the current vertex is the base node
of a previous blossom and the next one is contained within it.
The standard labeling procedure will fail in this case. This is fixed
by going to the last node in the path inside this inner blossom and using
it to apply the dual label.
Refer to backtrace() to know how the path will be built.
*/
innerBlossom=blossom[path[p][j]];
innerBase=j;
for (; blossom[j]==innerBlossom && j<endPath[p]-1; j++);
j--;
label[path[p][innerBase]].odd[0]=path[p][j+1];
label[path[p][innerBase]].odd[1]=path[p][j];
enqueue(path[p][innerBase],1);
}
}
}
if (g[a][b]==unmatched){ //All nodes have received labels, except
if (label[a].odd[0]==undef){ //the ones that called the function in
label[a].odd[0]=b; //the first place. It's possible to
enqueue(a,1); //find out how to label them by
} //analyzing if they're in the matching.
if (label[b].odd[0]==undef){
label[b].odd[0]=a;
enqueue(b,1);
}
}
else if (g[a][b]==matched){
if (label[a].even==undef){
label[a].even=b;
enqueue(a,0);
}
if (label[b].even==undef){
label[b].even=a;
enqueue(b,0);
}
}
}
function augmentPath (){ //An augmenting path has been found in the matching
var a,b; //and is contained in the path arrays.
for (var p=0; p<2; p++){
for (var i=0; i<endPath[p]-1; i++){
a=path[p][i]; //Because of labeling, this path is already
b=path[p][i+1]; //lifted and can be augmented by simple
if (g[a][b]==unmatched) //changing of the matching status.
g[a][b]=g[b][a]=matched;
else if (g[a][b]==matched)
g[a][b]=g[b][a]=unmatched;
}
}
a=path[0][endPath[0]-1];
b=path[1][endPath[1]-1];
if (g[a][b]==unmatched) g[a][b]=g[b][a]=matched;
else if (g[a][b]==matched) g[a][b]=g[b][a]=unmatched;
//After this, a and b are included in the matching.
match[path[0][0]]=match[path[1][0]]=true;
}
function augmentMatching (n){ //The main analyzing function, with the
var node,nodeLabel; //goal of finding augmenting paths or
initAlg(n); //concluding that the matching is maximum.
for (var i=0; i<n; i++) if (!match[i]){
label[i].even=empty;
enqueue(i,0); //Initialize the queue with the exposed vertices,
} //making them the roots in the forest.
while (queueFront<queueBack){
node=queue[queueFront].vertex;
nodeLabel=queue[queueFront].type;
if (nodeLabel==0){
for (var i=0; i<n; i++) if (g[node][i]==unmatched){
if (blossom[node]==blossom[i]);
//Do nothing. Edges inside the same blossom have no meaning.
else if (label[i].even!=undef){
/*
The tree has reached a vertex with a label.
The parity of this label indicates that an odd length
alternating path has been found. If this path is between
roots, we have an augmenting path, else there's an
alternating cycle, a blossom.
*/
endPath[0]=endPath[1]=0;
backtrace(node,0,empty,0,reverse);
backtrace(i,1,empty,0,reverse);
//Call the backtracing function to find out.
if (path[0][0]==path[1][0]) newBlossom(node,i);
/*
If the same root node is reached, a blossom was found.
Start the labelling procedure to create pseudo-contraction.
*/
else {
augmentPath();
return true;
/*
If the roots are different, we have an augmenting path.
Improve the matching by augmenting this path.
Now some labels might make no sense, stop the function,
returning that it was successful in improving.
*/
}
}
else if (label[i].even==undef && label[i].odd[0]==undef){
//If an unseen vertex is found, report the existing path
//by labeling it accordingly.
label[i].odd[0]=node;
enqueue(i,1);
}
}
}
else if (nodeLabel==1){ //Similar to above.
for (var i=0; i<n; i++) if (g[node][i]==matched){
if (blossom[node]==blossom[i]);
else if (label[i].odd[0]!=undef){
endPath[0]=endPath[1]=0;
backtrace(node,0,empty,1,reverse);
backtrace(i,1,empty,1,reverse);
if (path[0][0]==path[1][0]) newBlossom(node,i);
else {
augmentPath();
return true;
}
}
else if (label[i].even==undef && label[i].odd[0]==undef){
label[i].even=node;
enqueue(i,0);
}
}
}
/*
The scanning of this label is complete, dequeue it and
keep going to the next one.
*/
queueFront++;
}
/*
If the function reaches this point, the queue is empty, all
labels have been scanned. The algorithm couldn't find an augmenting
path. Therefore, it concludes the matching is maximum.
*/
return false;
}
function findMaximumMatching (n){
//Initialize it with the empty matching.
for (var i=0; i<n; i++) match[i]=false;
//Run augmentMatching(), it'll keep improving the matching.
//Eventually, it will no longer find a path and break the loop,
//at this point, the current matching is maximum.
while (augmentMatching(n));
}
function main(){
var n;
n=readGraph();
findMaximumMatching(n);
for (var i=0; i<n; i++){
for (var j=i+1; j<n; j++) if (g[i][j]==matched)
console.log(i+1,j+1);
}
return 0;
}
输出：
var graph = [[1,2]
,[1,3]
,[2,4]];
graph["n"] = 4;
graph["e"] = 3;
main()
1 3
2 4
答案 1 :(得分：1)
只是为了好玩 - FIDDLE。
它读取div的内容，然后创建一个包含所有可能排列的数组，＆＃34; pair＆＃34; （3＆＃39;变量＆＃39;一次取2个。）
然后解析出构成div内容的各个字母。
然后将每个字母与这些字母匹配以查看它出现的次数 - 如果它对于每一对只有一次，那么特定的对＃＆＃39;被添加到解决方案数组中。
分析完所有组合后，会显示解决方案阵列。
不是很优雅，但似乎有用。
JS
var totaldivs = $('div').length; //count total divs or objects
console.log("Total divs = " + totaldivs);
var elements = []; //Read objects from the divs and assign to array elements
for(var i = 0; i < totaldivs; i++ )
{
elements[i] = $( 'div:eq(' + i + ')' ).text();
elements[i] = elements[i].replace(/\s+/g, '');
console.log(elements[i]);
}
var objects = []; //make array of all individual objects
var loopvar = 0;
for(var n = 0; n < totaldivs; n++)
{
poshyphen = elements[n].indexOf('-');
objects[loopvar] = elements[n].substring(0, poshyphen);
objects[loopvar+1] = elements[n].substring(poshyphen+1, elements[n].length);
loopvar = loopvar + 2;
}
$('.putmehere2').html(objects);
var pair = [];
var pairindex = 0; //make and array of all combinations of objects - pair
for(var r = 0; r < totaldivs; r++)
{
for(var s = 0; s <totaldivs; s++)
{
if(elements[r] != elements[s])
{
pair[pairindex] = elements[r] + '-' + elements[s];
pairindex++;
}
}
}
$('.putmehere').html(pair);
var solution = [];
var sol = 0;
var count = [];
var reg = new RegExp("regex","g");
for( var q = 0; q < pair.length; q++)
{
for( var r = 0; r < 4; r++)
{
var regex = new RegExp( objects[r], 'g' );
count[r] = (pair[q].match( regex )||[]).length;
console.log("Pair= " + pair[q] + " Objects = " + objects[r] + " Count= " + count[r]);
}
if( count[0] == 1 && count[1] == 1 && count[2] == 1 && count[3] == 1 )
{
solution.push( pair[q]);
}
}
$('.putmehere2').html(solution);