369 lines
9.5 KiB
Text
369 lines
9.5 KiB
Text
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/*
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* lap implementation
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*
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* Copyright (C) YuanJun, ZhangLiang, Li Wei, Li Ming, Andreas Nuechter,
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*
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* Released under the GPL version 3.
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*
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*/
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/**
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* @file
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* @brief
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*
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* @author Andreas Nuechter. Jacobs University Bremen, Germany
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* @author YuanJun, Wuhan University, China
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* @author ZhangLiang, Wuhan University, China
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* @author Li Wei, Wuhan University, China
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* @author Li Ming, Wuhan University, China
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*/
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#include "veloslam/lap.h"
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cost lap(int dim,
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cost **assigncost,
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col *rowsol,
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row *colsol,
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cost *u,
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cost *v)
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// input:
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// dim - problem size
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// assigncost - cost matrix
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// output:
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// rowsol - column assigned to row in solution
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// colsol - row assigned to column in solution
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// u - dual variables, row reduction numbers
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// v - dual variables, column reduction numbers
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{
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Boolean unassignedfound;
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row i, imin, numfree = 0, prvnumfree, f, i0, k, freerow, *pred, *free;
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col j, j1, j2, endofpath, last, low, up, *collist, *matches;
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cost min, h, umin, usubmin, v2, *d;
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free = new row[dim]; // list of unassigned rows.
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collist = new col[dim]; // list of columns to be scanned in various ways.
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matches = new col[dim]; // counts how many times a row could be assigned.
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d = new cost[dim]; // 'cost-distance' in augmenting path calculation.
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pred = new row[dim]; // row-predecessor of column in augmenting/alternating path.
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// init how many times a row will be assigned in the column reduction.
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for (i = 0; i < dim; i++)
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matches[i] = 0;
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// COLUMN REDUCTION
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for (j = dim-1; j >= 0; j--) // reverse order gives better results.
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{
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// find minimum cost over rows.
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min = assigncost[0][j];
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imin = 0;
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for (i = 1; i < dim; i++)
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if (assigncost[i][j] < min)
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{
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min = assigncost[i][j];
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imin = i;
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}
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v[j] = min;
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if (++matches[imin] == 1)
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{
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// init assignment if minimum row assigned for first time.
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rowsol[imin] = j;
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colsol[j] = imin;
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}
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else
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colsol[j] = -1; // row already assigned, column not assigned.
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}
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// REDUCTION TRANSFER
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for (i = 0; i < dim; i++)
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if (matches[i] == 0) // fill list of unassigned 'free' rows.
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free[numfree++] = i;
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else
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if (matches[i] == 1) // transfer reduction from rows that are assigned once.
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{
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j1 = rowsol[i];
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min = BIG;
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for (j = 0; j < dim; j++)
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if (j != j1)
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if (assigncost[i][j] - v[j] < min)
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min = assigncost[i][j] - v[j];
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v[j1] = v[j1] - min;
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}
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// AUGMENTING ROW REDUCTION
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int loopcnt = 0; // do-loop to be done twice.
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do
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{
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loopcnt++;
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// scan all free rows.
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// in some cases, a free row may be replaced with another one to be scanned next.
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k = 0;
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prvnumfree = numfree;
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numfree = 0; // start list of rows still free after augmenting row reduction.
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while (k < prvnumfree)
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{
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i = free[k];
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k++;
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// find minimum and second minimum reduced cost over columns.
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umin = assigncost[i][0] - v[0];
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j1 = 0;
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usubmin = BIG;
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for (j = 1; j < dim; j++)
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{
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h = assigncost[i][j] - v[j];
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if (h < usubmin)
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if (h >= umin)
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{
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usubmin = h;
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j2 = j;
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}
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else
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{
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usubmin = umin;
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umin = h;
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j2 = j1;
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j1 = j;
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}
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}
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i0 = colsol[j1];
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if (umin < usubmin)
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// change the reduction of the minimum column to increase the minimum
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// reduced cost in the row to the subminimum.
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v[j1] = v[j1] - (usubmin - umin);
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else // minimum and subminimum equal.
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if (i0 >= 0) // minimum column j1 is assigned.
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{
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// swap columns j1 and j2, as j2 may be unassigned.
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j1 = j2;
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i0 = colsol[j2];
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}
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// (re-)assign i to j1, possibly de-assigning an i0.
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rowsol[i] = j1;
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colsol[j1] = i;
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if (i0 >= 0) // minimum column j1 assigned earlier.
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if (umin < usubmin)
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// put in current k, and go back to that k.
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// continue augmenting path i - j1 with i0.
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free[--k] = i0;
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else
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// no further augmenting reduction possible.
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// store i0 in list of free rows for next phase.
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free[numfree++] = i0;
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}
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}
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while (loopcnt < 2); // repeat once.
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// AUGMENT SOLUTION for each free row.
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for (f = 0; f < numfree; f++)
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{
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freerow = free[f]; // start row of augmenting path.
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// Dijkstra shortest path algorithm.
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// runs until unassigned column added to shortest path tree.
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for (j = 0; j < dim; j++)
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{
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d[j] = assigncost[freerow][j] - v[j];
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pred[j] = freerow;
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collist[j] = j; // init column list.
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}
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low = 0; // columns in 0..low-1 are ready, now none.
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up = 0; // columns in low..up-1 are to be scanned for current minimum, now none.
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// columns in up..dim-1 are to be considered later to find new minimum,
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// at this stage the list simply contains all columns
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unassignedfound = FALSE;
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do
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{
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if (up == low) // no more columns to be scanned for current minimum.
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{
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last = low - 1;
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// scan columns for up..dim-1 to find all indices for which new minimum occurs.
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// store these indices between low..up-1 (increasing up).
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min = d[collist[up++]];
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for (k = up; k < dim; k++)
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{
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j = collist[k];
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h = d[j];
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if (h <= min)
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{
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if (h < min) // new minimum.
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{
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up = low; // restart list at index low.
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min = h;
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}
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// new index with same minimum, put on undex up, and extend list.
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collist[k] = collist[up];
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collist[up++] = j;
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}
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}
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// check if any of the minimum columns happens to be unassigned.
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// if so, we have an augmenting path right away.
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for (k = low; k < up; k++)
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if (colsol[collist[k]] < 0)
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{
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endofpath = collist[k];
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unassignedfound = TRUE;
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break;
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}
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}
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if (!unassignedfound)
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{
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// update 'distances' between freerow and all unscanned columns, via next scanned column.
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j1 = collist[low];
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low++;
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i = colsol[j1];
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h = assigncost[i][j1] - v[j1] - min;
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for (k = up; k < dim; k++)
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{
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j = collist[k];
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v2 = assigncost[i][j] - v[j] - h;
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if (v2 < d[j])
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{
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pred[j] = i;
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if (v2 == min) // new column found at same minimum value
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if (colsol[j] < 0)
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{
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// if unassigned, shortest augmenting path is complete.
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endofpath = j;
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unassignedfound = TRUE;
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break;
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}
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// else add to list to be scanned right away.
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else
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{
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collist[k] = collist[up];
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collist[up++] = j;
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}
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d[j] = v2;
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}
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}
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}
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}
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while (!unassignedfound);
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// update column prices.
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for (k = 0; k <= last; k++)
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{
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j1 = collist[k];
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v[j1] = v[j1] + d[j1] - min;
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}
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// reset row and column assignments along the alternating path.
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do
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{
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i = pred[endofpath];
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colsol[endofpath] = i;
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j1 = endofpath;
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endofpath = rowsol[i];
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rowsol[i] = j1;
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}
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while (i != freerow);
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}
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// calculate optimal cost.
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cost lapcost = 0;
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for (i = 0; i < dim; i++)
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{
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j = rowsol[i];
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u[i] = assigncost[i][j] - v[j];
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lapcost = lapcost + assigncost[i][j];
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}
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// free reserved memory.
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delete[] pred;
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delete[] free;
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delete[] collist;
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delete[] matches;
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delete[] d;
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return lapcost;
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}
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void checklap(int dim,
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cost **assigncost,
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col *rowsol,
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row *colsol,
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cost *u,
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cost *v)
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{
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row i;
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col j;
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cost lapcost = 0, redcost = 0;
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Boolean *matched;
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char wait;
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matched = new Boolean[dim];
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for (i = 0; i < dim; i++)
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for (j = 0; j < dim; j++)
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if ((redcost = assigncost[i][j] - u[i] - v[j]) < 0)
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{
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printf("\n");
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printf("negative reduced cost i %d j %d redcost %d\n", i, j, redcost);
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printf("\n\ndim %5d - press key\n", dim);
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scanf("%d", &wait);
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break;
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}
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for (i = 0; i < dim; i++)
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if ((redcost = assigncost[i][rowsol[i]] - u[i] - v[rowsol[i]]) != 0)
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{
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printf("\n");
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printf("non-null reduced cost i %d soli %d redcost %d\n", i, rowsol[i], redcost);
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printf("\n\ndim %5d - press key\n", dim);
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scanf("%d", &wait);
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break;
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}
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for (j = 0; j < dim; j++)
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matched[j] = FALSE;
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for (i = 0; i < dim; i++)
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if (matched[rowsol[i]])
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{
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printf("\n");
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printf("column matched more than once - i %d soli %d\n", i, rowsol[i]);
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printf("\n\ndim %5d - press key\n", dim);
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scanf("%d", &wait);
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break;
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}
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else
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matched[rowsol[i]] = TRUE;
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for (i = 0; i < dim; i++)
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if (colsol[rowsol[i]] != i)
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{
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printf("\n");
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printf("error in row solution i %d soli %d solsoli %d\n", i, rowsol[i], colsol[rowsol[i]]);
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printf("\n\ndim %5d - press key\n", dim);
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scanf("%d", &wait);
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break;
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}
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for (j = 0; j < dim; j++)
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if (rowsol[colsol[j]] != j)
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{
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printf("\n");
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printf("error in col solution j %d solj %d solsolj %d\n", j, colsol[j], rowsol[colsol[j]]);
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printf("\n\ndim %5d - press key\n", dim);
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scanf("%d", &wait);
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break;
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}
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delete[] matched;
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return;
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}
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