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c_hung.html
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<!DOCTYPE html>
<html lang="en">
<title>HungarianVisualizer-C</title>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="https://www.w3schools.com/w3css/4/w3.css">
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min.js"></script>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Lato">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
<style>
@import url(https://fonts.googleapis.com/css?family=Righteous);
@import url('https://fonts.googleapis.com/css2?family=Fjalla+One&family=Open+Sans&display=swap');
@import url('https://fonts.googleapis.com/css2?family=Montserrat:wght@700&display=swap');
body {font-family: 'Righteous', serif;
background-color:#f7d596;}
.mySlides {display: none}
.inTable {
max-width: 50px;
text-align: center;
}
td {
border: 1px solid black;
padding: 1vw;
text-align: center;
}
h1 {
text-align: center;
color: #E8CEBF;
}
h1 {
font-family: 'Righteous';
color: #202020;
text-transform: uppercase;
letter-spacing: -2vw;
}
h1 span {
display: block;
margin: 11px 0 17px 0;
font-size: 6vw;
line-height: 8vw;
color: #111;
text-shadow: 0 5.36px 8.896px white,0 -2px 1px #fff;
letter-spacing: -1px;
}
@media (max-width: 1200px) {
}
input[type="button"] {
background-color: #E8CEBF;
border: 2px solid black;
color: black;
padding: 16px 32px;
text-align: center;
text-decoration: none;
display: inline-block;
font-size: 1.2vw;
margin: 4px 2px;
transition-duration: 0.4s;
cursor: pointer;
}
input[type="number"],#problemType,.inTable
{
font-size: 2vw;
}
input[type="button"]:hover, input[type="button"]:focus, #printAns:hover, #printAns:focus {
background-color: white;
color: black;
border: 2px solid black;
}
#anotherQue {
background-color: #d70c38;
border: 2px solid #d70c28;
}
#anotherQue:hover, #anotherQue:focus{
background-color: #E8CEBF;
color: black;
border: 2px solid #d70c28;
}
.result {
color: #ee1139;
}
</style>
<body>
<div class="w3-top">
<div class="w3-bar w3-black w3-card">
<a class="w3-bar-item w3-button w3-padding-large w3-hide-medium w3-hide-large w3-right" href="javascript:void(0)" onclick="myFunction()" title="Toggle Navigation Menu"><i class="fa fa-bars"></i></a>
<a href="index.html" class="w3-bar-item w3-button w3-padding-large">HOME</a>
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<a href="#" class="w3-bar-item w3-button">C</a>
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</div>
<div class="w3-content" style="max-width:2000px;margin-top:46px">
<div>
<h1> <span>C CODE</span> </h1><br/>
</div>
</div>
<div >
<div style="background: #4CAF60;
color: white;
font-size: 1vw;
padding: 3vw;
width: 88vw;
height: 90vw;
overflow: scroll;
border: 1px solid #ccc;
margin-left: 5vw; ">
<pre><xmp style="">
#ifndef HUNGARIAN_H
#define HUNGARIAN_H
#ifdef __cplusplus
extern "C" {
#endif
#include <sys/types.h> // for size_t
#include <string.h>
#include <stdio.h>
#include <assert.h>
#include <stdlib.h>
#define USAGE "Usage: ./test [-m <m>] [-n <n>] [-f <fname>]"
#include <math.h>
#include <limits.h>
#include <sys/param.h>
#ifndef bzero
#define bzero(b,len) (memset((b), '\0', (len)), (void) 0)
#endif
/* are we maximizing or minimizing? */
#define HUNGARIAN_MIN 0
#define HUNGARIAN_MAX 1
typedef struct
{
int* i;
int* j;
int k;
} hungarian_sequence_t;
typedef struct
{
size_t m,n; // problem dimensions
int** r; // the rating (utility) matrix
int** q; // the Q matrix
int* u; // the U vector
int* v; // the V vector
int* ess_rows; // list of essential rows
int* ess_cols; // list of essential columns
hungarian_sequence_t seq; // sequence of i's and j's
int row_total, col_total; // row and column totals
int* a; // assignment vector
int maxutil; // maximum utility
int mode; // are we maximizing or minimizing?
} hungarian_t;
/*
* initialize the given object as an mXn problem. allocates storage, which
* should be freed with hungarian_fini().
*/
void hungarian_init(hungarian_t* prob, int* r, size_t m, size_t n, int mode);
/*
* frees storage associated with the given problem object. you must have
* called hungarian_init() first.
*/
void hungarian_fini(hungarian_t* prob);
/*
* solve the given problem. runs the Hungarian Method on the rating matrix
* to produce optimal assignment, which is stored in the vector prob->a.
* you must have called hungarian_init() first.
*/
void hungarian_solve(hungarian_t* prob);
/*
* prints out the resultant assignment in a 0-1 matrix form. also computes
* and prints out the benefit from the assignment. you must have called
* hungarian_solve() first.
*/
void hungarian_print_assignment(hungarian_t* prob);
/*
* prints out the rating matrix for the given problem. you must have called
* hungarian_solve() first.
*/
void hungarian_print_rating(hungarian_t* prob);
/*
* check whether an assigment is feasible. returns 1 if the assigment is
* feasible, 0 otherwise. you must have called hungarian_solve() first.
*/
int hungarian_check_feasibility(hungarian_t* prob);
/*
* computes and returns the benefit from the assignment. you must have
* called hungarian_solve() first.
*/
int hungarian_benefit(hungarian_t* prob);
/*
* makes and returns a pointer to an mXn rating matrix with values uniformly
* distributed between 1 and MAXUTIL
*/
int* make_random_r(size_t m, size_t n);
int* make_r_from_ORlib(char* fname, int* m, int* n);
#ifdef __cplusplus
}
#endif
#endif
typedef enum
{
HUNGARIAN_ERROR,
HUNGARIAN_ROUTINE_ONE,
HUNGARIAN_ROUTINE_TWO,
HUNGARIAN_DONE
} hungarian_code_t;
// the Q matrix is filled with instances of this type
typedef enum
{
HUNGARIAN_ZERO,
HUNGARIAN_ONE,
HUNGARIAN_STAR
} hungarian_q_t;
// some internal routines
void hungarian_make_cover(hungarian_t* prob);
void hungarian_build_q(hungarian_t* prob);
void hungarian_add_stars(hungarian_t* prob);
hungarian_code_t hungarian_routine_one(hungarian_t* prob);
hungarian_code_t hungarian_routine_two(hungarian_t* prob);
/*
* initialize the given object as an mXn problem. allocates storage, which
* should be freed with hungarian_fini()
*/
void hungarian_init(hungarian_t* prob, int* r, size_t m, size_t n, int mode)
{
int i,j;
// did we get a good object pointer?
assert(prob);
// we can't work with matrices that have more rows than columns.
//
// TODO: automatically transpose such matrices
assert(m<=n);
// init the struct
prob->m = m;
prob->n = n;
assert(prob->r = (int**)calloc(m,sizeof(int*)));
assert(prob->q = (int**)calloc(m,sizeof(int*)));
prob->mode = mode;
prob->maxutil = 0;
for(i=0;i<m;i++)
{
assert(prob->r[i] = (int*)calloc(n,sizeof(int)));
assert(prob->q[i] = (int*)calloc(n,sizeof(int)));
for(j=0;j<n;j++)
{
prob->r[i][j] = r[i*n+j];
if(prob->r[i][j] > prob->maxutil)
prob->maxutil = prob->r[i][j];
}
}
// if we're going to minimize, rather than maximize, we need to subtract
// each utility from the maximum. this operation will be reversed before
// computing the benefit.
if(mode == HUNGARIAN_MIN)
{
for(i=0;i<m;i++)
{
for(j=0;j<n;j++)
prob->r[i][j] = prob->maxutil - prob->r[i][j];
}
}
assert(prob->a = (int*)calloc(m,sizeof(int)));
assert(prob->u = (int*)calloc(m,sizeof(int)));
assert(prob->v = (int*)calloc(n,sizeof(int)));
assert(prob->seq.i = (int*)calloc(m*n,sizeof(int)));
assert(prob->seq.j = (int*)calloc(m*n,sizeof(int)));
assert(prob->ess_rows = (int*)calloc(m,sizeof(int)));
assert(prob->ess_cols = (int*)calloc(n,sizeof(int)));
}
/*
* frees storage associated with the given problem object. you must have
* called hungarian_init() first.
*/
void hungarian_fini(hungarian_t* prob)
{
int i;
assert(prob);
for(i=0;i<prob->m;i++)
{
free(prob->q[i]);
free(prob->r[i]);
}
free(prob->q);
free(prob->r);
free(prob->a);
free(prob->u);
free(prob->v);
free(prob->seq.i);
free(prob->seq.j);
free(prob->ess_rows);
free(prob->ess_cols);
}
/*
* make an initial cover
*/
void hungarian_make_cover(hungarian_t* prob)
{
int i,j;
int* row_max;
int* col_max;
assert(prob);
assert(row_max = (int*)calloc(prob->m,sizeof(int)));
assert(col_max = (int*)calloc(prob->n,sizeof(int)));
prob->row_total = prob->col_total = 0;
// find the max in each row (col) and sum them
for(i=0;i<prob->m;i++)
{
for(j=0;j<prob->n;j++)
{
if(prob->r[i][j] > row_max[i])
row_max[i] = prob->r[i][j];
}
prob->row_total += row_max[i];
}
for(j=0;j<prob->n;j++)
{
for(i=0;i<prob->m;i++)
{
if(prob->r[i][j] > col_max[j])
col_max[j] = prob->r[i][j];
}
prob->col_total += col_max[j];
}
// make u and v into an initial cover, based on row and col totals
if(prob->row_total <= prob->col_total)
memcpy(prob->u,row_max,sizeof(int)*prob->m);
else
memcpy(prob->v,col_max,sizeof(int)*prob->n);
free(row_max);
free(col_max);
}
void hungarian_build_q(hungarian_t* prob)
{
int i,j;
assert(prob);
for(i=0;i<prob->m;i++)
{
for(j=0;j<prob->n;j++)
{
if((prob->u[i] + prob->v[j]) == prob->r[i][j])
{
if(prob->q[i][j] == HUNGARIAN_ZERO)
prob->q[i][j] = HUNGARIAN_ONE;
}
else
prob->q[i][j] = HUNGARIAN_ZERO;
}
}
}
void hungarian_add_stars(hungarian_t* prob)
{
int i,j,k;
assert(prob);
if(prob->row_total <= prob->col_total)
{
for(i=0;i<prob->m;i++)
{
for(j=0;j<prob->n;j++)
{
if(prob->q[i][j] == HUNGARIAN_ONE)
{
for(k=0;k<prob->m;k++)
{
if((k!=i) && (prob->q[k][j] == HUNGARIAN_STAR))
break;
}
if(k==prob->m)
{
prob->q[i][j] = HUNGARIAN_STAR;
break;
}
}
}
}
}
else
{
for(j=0;j<prob->n;j++)
{
for(i=0;i<prob->m;i++)
{
if(prob->q[i][j] == HUNGARIAN_ONE)
{
for(k=0;k<prob->n;k++)
{
if((k!=j) && (prob->q[i][k] == HUNGARIAN_STAR))
break;
}
if(k==prob->n)
{
prob->q[i][j] = HUNGARIAN_STAR;
break;
}
}
}
}
}
}
/*
* Kuhn's Routine I
*/
hungarian_code_t hungarian_routine_one(hungarian_t* prob)
{
int i,j,k;
char jumpcase1,jumpprelim;
assert(prob);
prob->seq.k=0;
for(i=0;i<prob->m;i++)
prob->ess_rows[i]=0;
j=0;
// look for a 1* in each column
while(j<prob->n)
{
i=0;
while(i<prob->m)
{
if(prob->q[i][j] == HUNGARIAN_STAR)
{
// found a 1*; next column
break;
}
i++;
}
if(i<prob->m)
{
// found a 1*; next column
j++;
}
else
{
// didn't find a 1*; column j is eligible; search it for a 1
i=0;
while(i<prob->m)
{
if(prob->q[i][j] == HUNGARIAN_ONE)
{
// found a 1 (i,j); start recording
prob->seq.i[prob->seq.k] = i;
prob->seq.j[prob->seq.k] = j;
prob->seq.k++;
// CASE 1
jumpprelim=0;
while(!jumpprelim)
{
// look in row ik for a 1*
j=0;
jumpcase1=0;
while(j<prob->n && !jumpcase1)
{
if(prob->q[i][j] == HUNGARIAN_STAR)
{
// CASE 2
i=0;
while(!jumpcase1)
{
// found a 1* in (ik,jk); search col jk for a 1
while(i<prob->m)
{
if(prob->q[i][j] == HUNGARIAN_ONE)
{
// test i for distinctness
for(k=0;k<prob->seq.k;k++)
{
if(prob->seq.i[k] == i)
break;
}
if(k<prob->seq.k)
{
// i is not distinct
i++;
continue;
}
else
{
// i is distinct; record and back to Case 1
prob->seq.i[prob->seq.k] = prob->seq.i[prob->seq.k-1];
prob->seq.j[prob->seq.k] = j;
prob->seq.k++;
prob->seq.i[prob->seq.k] = i;
prob->seq.j[prob->seq.k] = j;
prob->seq.k++;
jumpcase1=1;
break;
}
}
else
i++;
}
if(i>=prob->m)
{
// didn't find a 1 in col jk; row ik is essential
prob->ess_rows[prob->seq.i[prob->seq.k-1]] = 1;
// delete last two elts of sequence
j=prob->seq.j[prob->seq.k-1];
i=prob->seq.i[prob->seq.k-1]+1;
if(prob->seq.k > 1)
{
// back to Case 2
prob->seq.k-=2;
continue;
}
else
{
// k==1; back to prelim search for 1 in (i1+1,j0)
prob->seq.k--;
jumpcase1=jumpprelim=1;
break;
}
}
}
}
else
j++;
}
if(j>=prob->n)
{
// didn't find a 1* in row ik; toggle and Alternative Ia
for(;prob->seq.k > 0;prob->seq.k--)
{
if(prob->q[prob->seq.i[prob->seq.k-1]][prob->seq.j[prob->seq.k-1]]
== HUNGARIAN_ONE)
{
prob->q[prob->seq.i[prob->seq.k-1]][prob->seq.j[prob->seq.k-1]]
= HUNGARIAN_STAR;
}
else
{
prob->q[prob->seq.i[prob->seq.k-1]][prob->seq.j[prob->seq.k-1]]
= HUNGARIAN_ONE;
}
}
// Alternative Ia
return(HUNGARIAN_ROUTINE_ONE);
}
}
}
else
i++;
}
// didn't find a 1 in col j; next col
j++;
}
}
// out of cols; Alternative Ib
// determine ess cols
for(j=0;j<prob->n;j++)
{
prob->ess_cols[j]=0;
for(i=0;i<prob->m;i++)
{
if(prob->q[i][j] == HUNGARIAN_STAR && !prob->ess_rows[i])
{
prob->ess_cols[j] = 1;
break;
}
}
}
return(HUNGARIAN_ROUTINE_TWO);
}
/*
* Kuhn's Routine II
*/
hungarian_code_t hungarian_routine_two(hungarian_t* prob)
{
int i,j,d,m,dtmp;
int oldsum,newsum;
assert(prob);
oldsum = 0;
for(i=0;i<prob->m;i++)
oldsum += prob->u[i];
for(j=0;j<prob->n;j++)
oldsum += prob->v[j];
d=0;
for(i=0;i<prob->m;i++)
{
if(prob->ess_rows[i])
continue;
for(j=0;j<prob->n;j++)
{
if(prob->ess_cols[j])
continue;
dtmp = prob->u[i] + prob->v[j] - prob->r[i][j];
if(dtmp<0)
{
printf("SUPERMOO: %d + %d < %d\n",
prob->u[i], prob->v[j], prob->r[i][j]);
}
if(!d || ((dtmp>0) && dtmp < d))
d = dtmp;
}
}
if(d<0)
printf("MOO: %d < 0\n", d);
//if(d<=0)
if(!d)
return(HUNGARIAN_DONE);
else
{
// is there some u[i]==0?
for(i=0;i<prob->m;i++)
{
if(!prob->u[i])
break;
}
if(i < prob->m)
{
// CASE 2; some u[i] == 0; compute m as the min of d and inessential v[j]
m = d;
for(j=0;j<prob->n;j++)
{
if((!prob->ess_cols[j]) && (prob->v[j] < m))
m = prob->v[j];
}
// adjust the cover
for(i=0;i<prob->m;i++)
{
if(prob->ess_rows[i])
prob->u[i] += m;
}
for(j=0;j<prob->n;j++)
{
if(!prob->ess_cols[j])
prob->v[j] -= m;
}
}
else
{
// CASE 1; all u[i] > 0; compute m as the min of d and inessential u[j]
m = d;
for(i=0;i<prob->m;i++)
{
if((!prob->ess_rows[i]) && (prob->u[i] < m))
m = prob->u[i];
}
// adjust the cover
for(i=0;i<prob->m;i++)
{
if(!prob->ess_rows[i])
prob->u[i] -=m;
}
for(j=0;j<prob->n;j++)
{
if(prob->ess_cols[j])
prob->v[j] += m;
}
}
}
newsum = 0;
for(i=0;i<prob->m;i++)
{
for(j=0;j<prob->n;j++)
{
if(prob->u[i]+prob->v[j]<prob->r[i][j])
{
printf("SUPERMOO (%d,%d): %d + %d < %d\n", i,j,
prob->u[i], prob->v[j], prob->r[i][j]);
}
}
}
// Alternative IIa; build new q and return to routine I
hungarian_build_q(prob);
return(HUNGARIAN_ROUTINE_ONE);
}
/*
* solve the given problem. runs the Hungarian Method on the rating matrix
* to produce optimal assignment, which is stored in the vector prob->a.
* you must have called hungarian_init() first.
*/
void
hungarian_solve(hungarian_t* prob)
{
hungarian_code_t state = HUNGARIAN_ROUTINE_ONE;
int i,j;
assert(prob);
bzero(prob->u,sizeof(int)*prob->m);
bzero(prob->v,sizeof(int)*prob->n);
prob->seq.k=0;
bzero(prob->ess_rows,sizeof(int)*prob->m);
bzero(prob->ess_cols,sizeof(int)*prob->n);
for(i=0;i<prob->m;i++)
bzero(prob->q[i],sizeof(int)*prob->n);
hungarian_make_cover(prob);
hungarian_build_q(prob);
hungarian_add_stars(prob);
while(state != HUNGARIAN_DONE)
{
if(state == HUNGARIAN_ROUTINE_ONE)
{
state = hungarian_routine_one(prob);
}
else
{
state = hungarian_routine_two(prob);
}
}
// fill in the assignment vector
for(i=0;i<prob->m;i++)
{
for(j=0;j<prob->n;j++)
{
if(prob->q[i][j] == HUNGARIAN_STAR)
{
prob->a[i] = j;
break;
}
}
}
}
/*
* prints out the current state of the Q matrix. also computes and prints
* out the benefit from the current assignment. mostly useful for
* debugging.
*/
void hungarian_print_stars(hungarian_t* prob)
{
int i,j;
int benefit=0;
assert(prob);
puts("\nQ: ");
for(i=0;i<prob->m;i++)
{
printf(" [ ");
for(j=0;j<prob->n;j++)
{
if(prob->q[i][j] == HUNGARIAN_ZERO)
printf("%4d ", 0);
else if(prob->q[i][j] == HUNGARIAN_ONE)
printf("%4d ", 1);
else
{
printf("%3d%s ", 1,"*");
if(prob->mode == HUNGARIAN_MIN)
benefit += prob->maxutil - prob->r[i][j];
else
benefit += prob->r[i][j];
}
}
puts(" ]");
}
printf("\nBenefit: %d\n\n", benefit);
}
/*
* prints out the resultant assignment in a 0-1 matrix form. you must have
* called hungarian_solve() first.
*/
void
hungarian_print_assignment(hungarian_t* prob)
{
int i,j;
assert(prob);
puts("\nA:");
for(i=0;i<prob->m;i++)
{
printf(" [ ");
for(j=0;j<prob->n;j++)
printf("%4d ", (j==prob->a[i]) ? 1 : 0);
printf(" ]\n");
}
}
/*
* prints out the rating matrix for the given problem. you must have called
* hungarian_solve() first.
*/
void
hungarian_print_rating(hungarian_t* prob)
{
int i,j;
puts("\nR: ");
for(i=0;i<prob->m;i++)
{
printf(" [ ");
for(j=0;j<prob->n;j++)
{
printf("%4d ", prob->r[i][j]);
}
puts(" ]");
}
}
/*
* check whether an assigment is feasible. returns 1 if the assigment is
* feasible, 0 otherwise. you must have called hungarian_solve() first.
*/
int
hungarian_check_feasibility(hungarian_t* prob)
{
int i,j;
char assigned;
// check for over/under assigned rows
for(i=0;i<prob->m;i++)
{
assigned=0;
for(j=0;j<prob->n;j++)
{
if(prob->q[i][j] == HUNGARIAN_STAR)
{
if(assigned)
return(0);
else
assigned=1;
}
}
if((prob->m <= prob->n) && !assigned)
return(0);
}
// check for over/under assigned cols
for(j=0;j<prob->n;j++)
{
assigned=0;
for(i=0;i<prob->m;i++)
{
if(prob->q[i][j] == HUNGARIAN_STAR)
{
if(assigned)
return(0);
else
assigned=1;
}
}
if((prob->n <= prob->m) && !assigned)
return(0);
}
return(1);
}
/*
* computes and returns the benefit from the assignment. you must have
* called hungarian_solve() first.
*/
int
hungarian_benefit(hungarian_t* prob)
{
int i;
int benefit=0;
assert(prob);
for(i=0;i<prob->m;i++)
{
if(prob->mode == HUNGARIAN_MIN)
benefit += prob->maxutil - prob->r[i][prob->a[i]];
else
benefit += prob->r[i][prob->a[i]];
}
return(benefit);
}
#ifndef max
#define max(a, b) ((a) > (b) ? (a) : (b))
#endif
// problem dimensions
int m,n;
// input data file
char input_fname[PATH_MAX];
void parse_args(int argc, char** argv);
int
main(int argc, char** argv)
{
hungarian_t prob;
/*
int r[4][4] = {{ 363, 626, 376, 46 },
{ 802, 993, 784, 953 },
{ 673, 23, 823, 207 },
{ 380, 451, 520, 646 }};
*/
int* r;
m = n = 4;
parse_args(argc,argv);
if(!strlen(input_fname))
r = make_random_r(m,n);
else
r = make_r_from_ORlib(input_fname,&m,&n);
if(!r)
{
puts("got NULL input");
exit(-1);
}
hungarian_init(&prob,(int*)r,m,n,HUNGARIAN_MIN);
hungarian_print_rating(&prob);
hungarian_solve(&prob);
hungarian_print_assignment(&prob);
printf("\nfeasible? %s\n",
(hungarian_check_feasibility(&prob)) ? "yes" : "no");
printf("benefit: %d\n\n", hungarian_benefit(&prob));
hungarian_fini(&prob);
free(r);
return(0);
}
void
parse_args(int argc, char** argv)