[2051] | 1 | /* |
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| 2 | * Copyright 1997, Regents of the University of Minnesota |
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| 3 | * |
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| 4 | * mfm2.c |
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| 5 | * |
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| 6 | * This file contains code that implements the edge-based FM refinement |
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| 7 | * |
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| 8 | * Started 7/23/97 |
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| 9 | * George |
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| 10 | * |
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| 11 | * $Id: mfm2.c,v 1.2 1998/11/30 14:50:44 karypis Exp $ |
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| 12 | */ |
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| 13 | |
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| 14 | #include <metis.h> |
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| 15 | |
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| 16 | |
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| 17 | /************************************************************************* |
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| 18 | * This function performs an edge-based FM refinement |
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| 19 | **************************************************************************/ |
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| 20 | void MocFM_2WayEdgeRefine2(CtrlType *ctrl, GraphType *graph, float *tpwgts, float *orgubvec, |
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| 21 | int npasses) |
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| 22 | { |
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| 23 | int i, ii, j, k, l, kwgt, nvtxs, ncon, nbnd, nswaps, from, to, pass, me, limit, tmp, cnum; |
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| 24 | idxtype *xadj, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind; |
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| 25 | idxtype *moved, *swaps, *perm, *qnum; |
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| 26 | float *nvwgt, *npwgts, origdiff[MAXNCON], origbal[MAXNCON], minbal[MAXNCON]; |
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| 27 | PQueueType parts[MAXNCON][2]; |
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| 28 | int higain, oldgain, mincut, initcut, newcut, mincutorder; |
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| 29 | float *maxwgt, *minwgt, ubvec[MAXNCON], tvec[MAXNCON]; |
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| 30 | |
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| 31 | nvtxs = graph->nvtxs; |
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| 32 | ncon = graph->ncon; |
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| 33 | xadj = graph->xadj; |
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| 34 | nvwgt = graph->nvwgt; |
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| 35 | adjncy = graph->adjncy; |
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| 36 | adjwgt = graph->adjwgt; |
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| 37 | where = graph->where; |
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| 38 | id = graph->id; |
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| 39 | ed = graph->ed; |
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| 40 | npwgts = graph->npwgts; |
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| 41 | bndptr = graph->bndptr; |
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| 42 | bndind = graph->bndind; |
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| 43 | |
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| 44 | moved = idxwspacemalloc(ctrl, nvtxs); |
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| 45 | swaps = idxwspacemalloc(ctrl, nvtxs); |
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| 46 | perm = idxwspacemalloc(ctrl, nvtxs); |
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| 47 | qnum = idxwspacemalloc(ctrl, nvtxs); |
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| 48 | |
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| 49 | limit = amin(amax(0.01*nvtxs, 15), 100); |
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| 50 | |
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| 51 | Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, origbal); |
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| 52 | for (i=0; i<ncon; i++) { |
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| 53 | origdiff[i] = fabs(tpwgts[0]-npwgts[i]); |
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| 54 | ubvec[i] = amax(origbal[i], orgubvec[i]); |
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| 55 | } |
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| 56 | |
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| 57 | /* Setup the weight intervals of the two subdomains */ |
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| 58 | minwgt = fwspacemalloc(ctrl, 2*ncon); |
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| 59 | maxwgt = fwspacemalloc(ctrl, 2*ncon); |
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| 60 | |
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| 61 | for (i=0; i<2; i++) { |
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| 62 | for (j=0; j<ncon; j++) { |
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| 63 | maxwgt[i*ncon+j] = tpwgts[i]*ubvec[j]; |
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| 64 | minwgt[i*ncon+j] = tpwgts[i]*(1.0/ubvec[j]); |
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| 65 | } |
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| 66 | } |
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| 67 | |
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| 68 | /* Initialize the queues */ |
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| 69 | for (i=0; i<ncon; i++) { |
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| 70 | PQueueInit(ctrl, &parts[i][0], nvtxs, PLUS_GAINSPAN+1); |
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| 71 | PQueueInit(ctrl, &parts[i][1], nvtxs, PLUS_GAINSPAN+1); |
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| 72 | } |
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| 73 | for (i=0; i<nvtxs; i++) |
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| 74 | qnum[i] = samax(ncon, nvwgt+i*ncon); |
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| 75 | |
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| 76 | |
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| 77 | if (ctrl->dbglvl&DBG_REFINE) { |
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| 78 | printf("Parts: ["); |
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| 79 | for (l=0; l<ncon; l++) |
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| 80 | printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); |
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| 81 | printf("] T[%.3f %.3f], Nv-Nb[%5d, %5d]. ICut: %6d, LB: ", tpwgts[0], tpwgts[1], |
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| 82 | graph->nvtxs, graph->nbnd, graph->mincut); |
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| 83 | for (i=0; i<ncon; i++) |
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| 84 | printf("%.3f ", origbal[i]); |
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| 85 | printf("\n"); |
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| 86 | } |
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| 87 | |
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| 88 | idxset(nvtxs, -1, moved); |
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| 89 | for (pass=0; pass<npasses; pass++) { /* Do a number of passes */ |
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| 90 | for (i=0; i<ncon; i++) { |
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| 91 | PQueueReset(&parts[i][0]); |
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| 92 | PQueueReset(&parts[i][1]); |
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| 93 | } |
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| 94 | |
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| 95 | mincutorder = -1; |
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| 96 | newcut = mincut = initcut = graph->mincut; |
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| 97 | Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, minbal); |
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| 98 | |
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| 99 | ASSERT(ComputeCut(graph, where) == graph->mincut); |
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| 100 | ASSERT(CheckBnd(graph)); |
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| 101 | |
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| 102 | /* Insert boundary nodes in the priority queues */ |
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| 103 | nbnd = graph->nbnd; |
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| 104 | RandomPermute(nbnd, perm, 1); |
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| 105 | for (ii=0; ii<nbnd; ii++) { |
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| 106 | i = bndind[perm[ii]]; |
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| 107 | ASSERT(ed[i] > 0 || id[i] == 0); |
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| 108 | ASSERT(bndptr[i] != -1); |
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| 109 | PQueueInsert(&parts[qnum[i]][where[i]], i, ed[i]-id[i]); |
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| 110 | } |
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| 111 | |
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| 112 | for (nswaps=0; nswaps<nvtxs; nswaps++) { |
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| 113 | SelectQueue2(ncon, npwgts, tpwgts, &from, &cnum, parts, maxwgt); |
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| 114 | to = (from+1)%2; |
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| 115 | |
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| 116 | if (from == -1 || (higain = PQueueGetMax(&parts[cnum][from])) == -1) |
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| 117 | break; |
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| 118 | ASSERT(bndptr[higain] != -1); |
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| 119 | |
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| 120 | newcut -= (ed[higain]-id[higain]); |
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| 121 | saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); |
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| 122 | saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1); |
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| 123 | |
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| 124 | Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, tvec); |
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| 125 | if ((newcut < mincut && AreAllBelow(ncon, tvec, ubvec)) || |
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| 126 | (newcut == mincut && IsBetter2wayBalance(ncon, tvec, minbal, ubvec))) { |
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| 127 | mincut = newcut; |
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| 128 | for (i=0; i<ncon; i++) |
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| 129 | minbal[i] = tvec[i]; |
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| 130 | mincutorder = nswaps; |
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| 131 | } |
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| 132 | else if (nswaps-mincutorder > limit) { /* We hit the limit, undo last move */ |
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| 133 | newcut += (ed[higain]-id[higain]); |
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| 134 | saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1); |
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| 135 | saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); |
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| 136 | break; |
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| 137 | } |
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| 138 | |
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| 139 | where[higain] = to; |
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| 140 | moved[higain] = nswaps; |
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| 141 | swaps[nswaps] = higain; |
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| 142 | |
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| 143 | if (ctrl->dbglvl&DBG_MOVEINFO) { |
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| 144 | printf("Moved %6d from %d(%d). Gain: %5d, Cut: %5d, NPwgts: ", higain, from, cnum, ed[higain]-id[higain], newcut); |
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| 145 | for (l=0; l<ncon; l++) |
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| 146 | printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); |
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| 147 | |
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| 148 | printf(", LB: "); |
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| 149 | for (i=0; i<ncon; i++) |
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| 150 | printf("%.3f ", tvec[i]); |
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| 151 | if (mincutorder == nswaps) |
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| 152 | printf(" *\n"); |
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| 153 | else |
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| 154 | printf("\n"); |
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| 155 | } |
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| 156 | |
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| 157 | |
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| 158 | /************************************************************** |
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| 159 | * Update the id[i]/ed[i] values of the affected nodes |
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| 160 | ***************************************************************/ |
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| 161 | SWAP(id[higain], ed[higain], tmp); |
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| 162 | if (ed[higain] == 0 && xadj[higain] < xadj[higain+1]) |
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| 163 | BNDDelete(nbnd, bndind, bndptr, higain); |
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| 164 | |
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| 165 | for (j=xadj[higain]; j<xadj[higain+1]; j++) { |
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| 166 | k = adjncy[j]; |
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| 167 | oldgain = ed[k]-id[k]; |
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| 168 | |
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| 169 | kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]); |
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| 170 | INC_DEC(id[k], ed[k], kwgt); |
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| 171 | |
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| 172 | /* Update its boundary information and queue position */ |
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| 173 | if (bndptr[k] != -1) { /* If k was a boundary vertex */ |
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| 174 | if (ed[k] == 0) { /* Not a boundary vertex any more */ |
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| 175 | BNDDelete(nbnd, bndind, bndptr, k); |
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| 176 | if (moved[k] == -1) /* Remove it if in the queues */ |
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| 177 | PQueueDelete(&parts[qnum[k]][where[k]], k, oldgain); |
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| 178 | } |
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| 179 | else { /* If it has not been moved, update its position in the queue */ |
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| 180 | if (moved[k] == -1) |
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| 181 | PQueueUpdate(&parts[qnum[k]][where[k]], k, oldgain, ed[k]-id[k]); |
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| 182 | } |
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| 183 | } |
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| 184 | else { |
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| 185 | if (ed[k] > 0) { /* It will now become a boundary vertex */ |
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| 186 | BNDInsert(nbnd, bndind, bndptr, k); |
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| 187 | if (moved[k] == -1) |
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| 188 | PQueueInsert(&parts[qnum[k]][where[k]], k, ed[k]-id[k]); |
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| 189 | } |
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| 190 | } |
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| 191 | } |
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| 192 | |
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| 193 | } |
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| 194 | |
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| 195 | |
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| 196 | /**************************************************************** |
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| 197 | * Roll back computations |
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| 198 | *****************************************************************/ |
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| 199 | for (i=0; i<nswaps; i++) |
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| 200 | moved[swaps[i]] = -1; /* reset moved array */ |
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| 201 | for (nswaps--; nswaps>mincutorder; nswaps--) { |
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| 202 | higain = swaps[nswaps]; |
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| 203 | |
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| 204 | to = where[higain] = (where[higain]+1)%2; |
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| 205 | SWAP(id[higain], ed[higain], tmp); |
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| 206 | if (ed[higain] == 0 && bndptr[higain] != -1 && xadj[higain] < xadj[higain+1]) |
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| 207 | BNDDelete(nbnd, bndind, bndptr, higain); |
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| 208 | else if (ed[higain] > 0 && bndptr[higain] == -1) |
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| 209 | BNDInsert(nbnd, bndind, bndptr, higain); |
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| 210 | |
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| 211 | saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); |
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| 212 | saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+((to+1)%2)*ncon, 1); |
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| 213 | for (j=xadj[higain]; j<xadj[higain+1]; j++) { |
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| 214 | k = adjncy[j]; |
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| 215 | |
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| 216 | kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]); |
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| 217 | INC_DEC(id[k], ed[k], kwgt); |
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| 218 | |
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| 219 | if (bndptr[k] != -1 && ed[k] == 0) |
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| 220 | BNDDelete(nbnd, bndind, bndptr, k); |
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| 221 | if (bndptr[k] == -1 && ed[k] > 0) |
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| 222 | BNDInsert(nbnd, bndind, bndptr, k); |
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| 223 | } |
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| 224 | } |
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| 225 | |
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| 226 | if (ctrl->dbglvl&DBG_REFINE) { |
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| 227 | printf("\tMincut: %6d at %5d, NBND: %6d, NPwgts: [", mincut, mincutorder, nbnd); |
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| 228 | for (l=0; l<ncon; l++) |
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| 229 | printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); |
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| 230 | printf("], LB: "); |
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| 231 | Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, tvec); |
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| 232 | for (i=0; i<ncon; i++) |
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| 233 | printf("%.3f ", tvec[i]); |
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| 234 | printf("\n"); |
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| 235 | } |
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| 236 | |
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| 237 | graph->mincut = mincut; |
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| 238 | graph->nbnd = nbnd; |
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| 239 | |
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| 240 | if (mincutorder == -1 || mincut == initcut) |
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| 241 | break; |
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| 242 | } |
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| 243 | |
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| 244 | for (i=0; i<ncon; i++) { |
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| 245 | PQueueFree(ctrl, &parts[i][0]); |
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| 246 | PQueueFree(ctrl, &parts[i][1]); |
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| 247 | } |
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| 248 | |
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| 249 | idxwspacefree(ctrl, nvtxs); |
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| 250 | idxwspacefree(ctrl, nvtxs); |
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| 251 | idxwspacefree(ctrl, nvtxs); |
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| 252 | idxwspacefree(ctrl, nvtxs); |
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| 253 | fwspacefree(ctrl, 2*ncon); |
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| 254 | fwspacefree(ctrl, 2*ncon); |
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| 255 | |
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| 256 | } |
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| 257 | |
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| 258 | |
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| 259 | /************************************************************************* |
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| 260 | * This function selects the partition number and the queue from which |
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| 261 | * we will move vertices out |
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| 262 | **************************************************************************/ |
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| 263 | void SelectQueue2(int ncon, float *npwgts, float *tpwgts, int *from, int *cnum, |
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| 264 | PQueueType queues[MAXNCON][2], float *maxwgt) |
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| 265 | { |
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| 266 | int i, j, maxgain=0; |
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| 267 | float diff, max, maxdiff=0.0; |
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| 268 | |
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| 269 | *from = -1; |
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| 270 | *cnum = -1; |
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| 271 | |
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| 272 | /* First determine the side and the queue, irrespective of the presence of nodes */ |
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| 273 | for (j=0; j<2; j++) { |
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| 274 | for (i=0; i<ncon; i++) { |
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| 275 | diff = npwgts[j*ncon+i]-maxwgt[j*ncon+i]; |
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| 276 | if (diff >= maxdiff) { |
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| 277 | maxdiff = diff; |
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| 278 | *from = j; |
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| 279 | *cnum = i; |
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| 280 | } |
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| 281 | } |
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| 282 | } |
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| 283 | |
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| 284 | if (*from != -1 && PQueueGetSize(&queues[*cnum][*from]) == 0) { |
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| 285 | /* The desired queue is empty, select a node from that side anyway */ |
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| 286 | for (i=0; i<ncon; i++) { |
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| 287 | if (PQueueGetSize(&queues[i][*from]) > 0) { |
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| 288 | max = (npwgts[(*from)*ncon+i] - maxwgt[(*from)*ncon+i]); |
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| 289 | *cnum = i; |
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| 290 | break; |
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| 291 | } |
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| 292 | } |
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| 293 | |
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| 294 | for (i++; i<ncon; i++) { |
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| 295 | diff = npwgts[(*from)*ncon+i] - maxwgt[(*from)*ncon+i]; |
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| 296 | if (diff > max && PQueueGetSize(&queues[i][*from]) > 0) { |
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| 297 | max = diff; |
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| 298 | *cnum = i; |
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| 299 | } |
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| 300 | } |
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| 301 | } |
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| 302 | |
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| 303 | /* Check to see if you can focus on the cut */ |
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| 304 | if (maxdiff <= 0.0 || *from == -1) { |
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| 305 | maxgain = -100000; |
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| 306 | |
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| 307 | for (j=0; j<2; j++) { |
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| 308 | for (i=0; i<ncon; i++) { |
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| 309 | if (PQueueGetSize(&queues[i][j]) > 0 && PQueueGetKey(&queues[i][j]) > maxgain) { |
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| 310 | maxgain = PQueueGetKey(&queues[i][j]); |
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| 311 | *from = j; |
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| 312 | *cnum = i; |
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| 313 | } |
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| 314 | } |
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| 315 | } |
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| 316 | |
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| 317 | /* printf("(%2d %2d) %3d\n", *from, *cnum, maxgain); */ |
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| 318 | } |
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| 319 | } |
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| 320 | |
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| 321 | |
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| 322 | /************************************************************************* |
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| 323 | * This function checks if the newbal is better than oldbal given the |
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| 324 | * ubvector ubvec |
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| 325 | **************************************************************************/ |
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| 326 | int IsBetter2wayBalance(int ncon, float *newbal, float *oldbal, float *ubvec) |
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| 327 | { |
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| 328 | int i, j; |
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| 329 | float max1=0.0, max2=0.0, sum1=0.0, sum2=0.0, tmp; |
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| 330 | |
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| 331 | for (i=0; i<ncon; i++) { |
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| 332 | tmp = (newbal[i]-1)/(ubvec[i]-1); |
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| 333 | max1 = (max1 < tmp ? tmp : max1); |
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| 334 | sum1 += tmp; |
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| 335 | |
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| 336 | tmp = (oldbal[i]-1)/(ubvec[i]-1); |
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| 337 | max2 = (max2 < tmp ? tmp : max2); |
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| 338 | sum2 += tmp; |
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| 339 | } |
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| 340 | |
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| 341 | if (max1 < max2) |
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| 342 | return 1; |
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| 343 | else if (max1 > max2) |
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| 344 | return 0; |
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| 345 | else |
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| 346 | return sum1 <= sum2; |
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| 347 | } |
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| 348 | |
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| 349 | |
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