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diff --git a/01-knapsack/ks_dp-ng.c b/01-knapsack/ks_dp-ng.c
index 7830651..ddb0d04 100644
--- a/01-knapsack/ks_dp-ng.c
+++ b/01-knapsack/ks_dp-ng.c
@@ -7,12 +7,14 @@
#define NONE -1
+enum { RELAX = 0, NO_RELAX };
enum { SORT_DESC = 0, SORT_ASC };
enum { UNSORTED = 0, SORT_WR, SORT_VR, SORT_RW, SORT_RV};
static int debug;
static int sort;
static int sort_order;
+static int relax;
typedef struct _InputItem
{
@@ -25,6 +27,7 @@ typedef struct _SolverItem {
int i; /* index of the selected item */
int v; /* cumulated value */
int w; /* cumulated weight */
+ float r; /* linear relaxation best value */
} SolverItem;
typedef struct _Solver
@@ -87,11 +90,39 @@ item_cmp(const void *p1, const void *p2)
return 0;
}
+static inline float relax_item(Solver* solver, SolverItem* data, int start)
+{
+ int w;
+ int i;
+ float relax;
+ const InputItem *item;
+
+ w = data->w;
+ relax= data->v;
+ item = &solver->items[start];
+ for (i = start; i < solver->n; i++, item++)
+ {
+ if ((w + item->w) <= solver->k)
+ {
+ w += item->w;
+ relax += item->v;
+ }
+ else
+ {
+ relax += (item->v * ((solver->k - w) / (float)item->w));
+ break;
+ }
+ }
+
+ return relax;
+}
+
static void solve(Solver* solver)
{
int n, k;
int v, w;
int i, j;
+ float r;
int min_c, lower_bound;
const InputItem *item;
SolverItem *data;
@@ -105,7 +136,16 @@ static void solve(Solver* solver)
if (debug > 2)
{
- printf("\nformat V(i,W)\n");
+ printf("\nformat V(i,W,r)\n");
+ }
+
+ /* RELAXATION */
+ if (relax == RELAX)
+ {
+ data = solver->column;
+ r = relax_item(solver, data, 0);
+ for (j = 0; j <= k; j++, data++)
+ data->r = r;
}
/* SOLVE */
@@ -134,6 +174,12 @@ static void solve(Solver* solver)
data->v = v + up_left->v;
data->w = w + up_left->w;
}
+
+ /* RELAXTION must be cached */
+ if (relax == RELAX)
+ {
+ data->r = relax_item(solver, data, (i + 1));
+ }
}
if (debug > 2)
@@ -141,8 +187,8 @@ static void solve(Solver* solver)
printf("i=%d; j=k; j<=%d:\n", i, lower_bound);
data = solver->column;
for (j = 0; j <= k; j++, data++)
- printf(" %d : % 4d(% 2d % 2d)\n",
- j, data->v, data->i, data->w);
+ printf(" %d : % 4d(% 2d % 2d %.1f)\n",
+ j, data->v, data->i, data->w, data->r);
printf("\n");
}
}
@@ -152,8 +198,8 @@ static void solve(Solver* solver)
printf("i=%d:\n", solver->n - 1);
data = solver->column;
for (j = 0; j <= k; j++, data++)
- printf(" % 4d(% 2d % 2d)\n",
- data->v, data->i, data->w);
+ printf(" % 4d(% 2d % 2d %.1f)\n",
+ data->v, data->i, data->w, data->r);
}
if (debug > 0)
@@ -194,10 +240,11 @@ int main(int argc, char** argv, char** env)
InputItem *item;
debug = 0;
+ relax = NO_RELAX;
sort = UNSORTED;
sort_order = SORT_DESC;
excpected_value = NONE;
- while ((opt = getopt(argc, argv, "d:e:s:S")) != -1) {
+ while ((opt = getopt(argc, argv, "d:e:s:SR")) != -1) {
switch (opt) {
case 'd':
debug = atoi(optarg);
@@ -211,6 +258,9 @@ int main(int argc, char** argv, char** env)
case 'S':
sort_order = SORT_ASC;
break;
+ case 'R':
+ relax = RELAX;
+ break;
default: /* '?' */
fprintf(stderr, "Usage: %s [falgs] input\n",
argv[0]);
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