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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,163 @@ | ||
| #include "hungarian.h" | ||
| using namespace std; | ||
|
|
||
| void Hungarian::update_labels() | ||
| { | ||
| int x, y, delta = INF; //init delta as infinity | ||
| for (y = 0; y < n; y++) //calculate delta using slack | ||
| if (!T[y]) | ||
| delta = min(delta, slack[y]); | ||
| for (x = 0; x < n; x++) //update X labels | ||
| if (S[x]) lx[x] -= delta; | ||
| for (y = 0; y < n; y++) //update Y labels | ||
| if (T[y]) ly[y] += delta; | ||
| for (y = 0; y < n; y++) //update slack array | ||
| if (!T[y]) | ||
| slack[y] -= delta; | ||
| } | ||
| void Hungarian::add_to_tree(int x, int prevx) | ||
| //x - current vertex,prevx - vertex from X before x in the alternating path, | ||
| //so we add edges (prevx, xy[x]), (xy[x], x) | ||
| { | ||
| S[x] = true; //add x to S | ||
| prev[x] = prevx; //we need this when augmenting | ||
| for (int y = 0; y < n; y++) //update slacks, because we add new vertex to S | ||
| if (lx[x] + ly[y] - cost[x][y] < slack[y]) | ||
| { | ||
| slack[y] = lx[x] + ly[y] - cost[x][y]; | ||
| slackx[y] = x; | ||
| } | ||
| } | ||
| void Hungarian::init_labels() | ||
| { | ||
| memset(lx, 0, sizeof(lx)); | ||
| memset(ly, 0, sizeof(ly)); | ||
| for (int x = 0; x < n; x++) | ||
| for (int y = 0; y < n; y++) | ||
| lx[x] = max(lx[x], cost[x][y]); | ||
| } | ||
|
|
||
| void Hungarian::augment() //main function of the algorithm | ||
| { | ||
| if (max_match == n) return; //check wether matching is already perfect | ||
| int x, y, root; //just counters and root vertex | ||
| int q[N_HUNGARIAN], wr = 0, rd = 0; //q - queue for bfs, wr,rd - write and read | ||
| //pos in queue | ||
| memset(S, false, sizeof(S)); //init set S | ||
| memset(T, false, sizeof(T)); //init set T | ||
| memset(prev, -1, sizeof(prev)); //init set prev - for the alternating tree | ||
| for (x = 0; x < n; x++) //finding root of the tree | ||
| if (xy[x] == -1) | ||
| { | ||
| q[wr++] = root = x; | ||
| prev[x] = -2; | ||
| S[x] = true; | ||
| break; | ||
| } | ||
|
|
||
| for (y = 0; y < n; y++) //initializing slack array | ||
| { | ||
| slack[y] = lx[root] + ly[y] - cost[root][y]; | ||
| slackx[y] = root; | ||
| } | ||
| while (true) //main cycle | ||
| { | ||
| while (rd < wr) //building tree with bfs cycle | ||
| { | ||
| x = q[rd++]; //current vertex from X part | ||
| for (y = 0; y < n; y++) //iterate through all edges in equality graph | ||
| if (cost[x][y] == lx[x] + ly[y] && !T[y]) | ||
| { | ||
| if (yx[y] == -1) break; //an exposed vertex in Y found, so | ||
| //augmenting path exists! | ||
| T[y] = true; //else just add y to T, | ||
| q[wr++] = yx[y]; //add vertex yx[y], which is matched | ||
| //with y, to the queue | ||
| add_to_tree(yx[y], x); //add edges (x,y) and (y,yx[y]) to the tree | ||
| } | ||
| if (y < n) break; //augmenting path found! | ||
| } | ||
| if (y < n) break; //augmenting path found! | ||
|
|
||
| update_labels(); //augmenting path not found, so improve labeling | ||
| wr = rd = 0; | ||
| for (y = 0; y < n; y++) | ||
| //in this cycle we add edges that were added to the equality graph as a | ||
| //result of improving the labeling, we add edge (slackx[y], y) to the tree if | ||
| //and only if !T[y] && slack[y] == 0, also with this edge we add another one | ||
| //(y, yx[y]) or augment the matching, if y was exposed | ||
| if (!T[y] && slack[y] == 0) | ||
| { | ||
| if (yx[y] == -1) //exposed vertex in Y found - augmenting path exists! | ||
| { | ||
| x = slackx[y]; | ||
| break; | ||
| } | ||
| else | ||
| { | ||
| T[y] = true; //else just add y to T, | ||
| if (!S[yx[y]]) | ||
| { | ||
| q[wr++] = yx[y]; //add vertex yx[y], which is matched with | ||
| //y, to the queue | ||
| add_to_tree(yx[y], slackx[y]); //and add edges (x,y) and (y, | ||
| //yx[y]) to the tree | ||
| } | ||
| } | ||
| } | ||
| if (y < n) break; //augmenting path found! | ||
| } | ||
|
|
||
| if (y < n) //we found augmenting path! | ||
| { | ||
| max_match++; //increment matching | ||
| //in this cycle we inverse edges along augmenting path | ||
| for (int cx = x, cy = y, ty; cx != -2; cx = prev[cx], cy = ty) | ||
| { | ||
| ty = xy[cx]; | ||
| yx[cy] = cx; | ||
| xy[cx] = cy; | ||
| } | ||
| augment(); //recall function, go to step 1 of the algorithm | ||
| } | ||
| }//end of augment() function | ||
|
|
||
| int Hungarian::hungarian() | ||
| { | ||
| //fix cost matrix | ||
| for(int i = 0; i < n; ++i) | ||
| { | ||
| for(int j = 0; j < n; ++j) | ||
| { | ||
| cost[i][j] = 10000 - cost[i][j]; | ||
| } | ||
| } | ||
| int ret = 0; //weight of the optimal matching | ||
| max_match = 0; //number of vertices in current matching | ||
| memset(xy, -1, sizeof(xy)); | ||
| memset(yx, -1, sizeof(yx)); | ||
| init_labels(); //step 0 | ||
| augment(); //steps 1-3 | ||
|
|
||
| for(int i = 0; i < n; ++i) | ||
| { | ||
| for(int j = 0; j < n; ++j) | ||
| { | ||
| cost[i][j] = 10000 - cost[i][j]; | ||
| } | ||
| } | ||
| for (int x = 0; x < n; x++) //forming answer there | ||
| ret += cost[x][xy[x]]; | ||
| return ret; | ||
| } | ||
|
|
||
| //main(void) | ||
| //{ | ||
|
|
||
| // /* Fill up the cost matrix cost(i,j) cost of making ith worker do jth job */ | ||
|
|
||
| // /* call Hungarian() */ | ||
|
|
||
| // /* To know job assigned to ith worker , read xy[i] */ | ||
|
|
||
| //} |
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