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knapsack.c
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knapsack.c
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#include <stdio.h>
#include <math.h>
#include <string.h>
#define max(a,b) (a > b ? a : b)
#define nitems 4
#define knapsacksize 10
int weight[4] = {5,4,6,3};
int value[4] = {10,40,30,50};
/// use recursive algorithm, easy to understand. looks like a tree
int knapsack_rec(int index, int current_size){
if (current_size + weight[index] <= knapsacksize && index < nitems){
return max(value[index] + knapsack_rec(index + 1, current_size + weight[index]),
knapsack_rec(index + 1, current_size));
}
return 0;
}
#define check_bit(index, kind) (((1 << index) & kind) >> index)
void print_footprint(int foot_print)
{
printf ("footprint: ");
int j;
for (j = 0; j < nitems; ++j){
if (check_bit(j, foot_print)){
printf ("%d ", weight[j]);
}
}
printf ("\n");
}
int knapsack_bruteforce()
{
int i, kinds = pow(2, nitems);
int max_value = 0, foot_print = 0;
for (i = 0; i < kinds; ++i){
int j, weight_sum = 0, value_sum = 0;
for (j = 0; j < nitems; ++j){
weight_sum += weight[j] * check_bit(j, i);
value_sum += value[j] * check_bit(j, i);
}
if (weight_sum <= knapsacksize && value_sum > max_value){
max_value = value_sum;
foot_print = i;
}
}
/// print_footprint(foot_print);
return max_value;
}
int dynamic_tab[nitems + 1][knapsacksize + 1] = {0};
int knapsack_dynamic()
{
int i;
for (i = 1; i <= nitems; ++i){
int j;
for (j = 1; j <= knapsacksize; ++j){
if (weight[i - 1] <= j){
dynamic_tab[i][j] = max(dynamic_tab[i - 1][j],
value[i - 1] +
dynamic_tab[i - 1][j - weight[i - 1]]);
}
else{
dynamic_tab[i][j] = dynamic_tab[i - 1][j];
}
}
}
return dynamic_tab[nitems][knapsacksize];
}
int dynamic_tab_rec[nitems + 1][knapsacksize + 1];
int knapsack_dynamic_rec(int index, int size_left)
{
int max_value = 0;
if (index == 0){
dynamic_tab_rec[index][size_left] = 0;
return 0;
}
int take = 0;
if (weight[index - 1] <= size_left){
if (dynamic_tab_rec[index - 1][size_left - weight[index - 1]] != -1){
take = value[index - 1]
+ dynamic_tab_rec[index - 1][size_left - weight[index - 1]];
}
else{
take = value[index - 1]
+ knapsack_dynamic_rec(index - 1, size_left - weight[index - 1]);
}
}
int dontake = knapsack_dynamic_rec(index - 1, size_left);
max_value = max(take, dontake);
dynamic_tab_rec[index][size_left] = max_value;
return max_value;
}
void print_footprint_from_tab(int tab[nitems + 1][knapsacksize + 1], int line_index, int column_index)
{
if (line_index == 0){
return;
}
if (column_index >= weight[line_index - 1] &&
tab[line_index][column_index] == value[line_index - 1]
+ tab[line_index - 1][column_index - weight[line_index - 1]]){
printf ("%d ", weight[line_index - 1]);
print_footprint_from_tab(tab, line_index - 1,
column_index - weight[line_index -1]);
}
else{
print_footprint_from_tab(tab, line_index - 1, column_index);
}
}
void print_tab(int tab[nitems + 1][knapsacksize + 1], int line_index, int column_index)
{
int i;
for (i = 0; i <= line_index; ++i){
int j;
for (j = 0; j <= column_index; ++j){
printf ("%d%c", tab[i][j], j != column_index? ' ':'\n');
}
}
}
int main()
{
printf ("1. rec max value = %d\n", knapsack_rec(0, 0));
printf ("2. bru max value = %d\n", knapsack_bruteforce());
printf ("3. dyn max value = %d\n", knapsack_dynamic());
memset(dynamic_tab_rec, -1, sizeof(dynamic_tab_rec));
printf ("4. dre max value = %d\n", knapsack_dynamic_rec(nitems, knapsacksize));
return 0;
}