ভগ্নাংশ ন্যাপস্যাক সমস্যায়, আইটেমগুলির একটি সেট দেওয়া হয়, প্রতিটির একটি ওজন এবং একটি মান রয়েছে। ন্যাপস্যাকের মোট মূল্য সর্বাধিক করার জন্য আমাদের আইটেমগুলি ভাঙতে হবে এবং এটি লোভী পদ্ধতিতে করা যেতে পারে।
অ্যালগরিদম
Begin Take an array of structure Item Declare value, weight, knapsack weight and density Calculate density=value/weight for each item Sorting the items array on the order of decreasing density We add values from the top of the array to total value until the bag is full, i.e; total value <= W End
উদাহরণ কোড
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
typedef struct {
int v;
int w;
float d;
} Item;
void input(Item items[],int sizeOfItems) {
cout << "Enter total "<< sizeOfItems <<" item's values and weight" <<
endl;
for(int i = 0; i < sizeOfItems; i++) {
cout << "Enter "<< i+1 << " V ";
cin >> items[i].v;
cout << "Enter "<< i+1 << " W ";
cin >> items[i].w;
}
}
void display(Item items[], int sizeOfItems) {
int i;
cout << "values: ";
for(i = 0; i < sizeOfItems; i++) {
cout << items[i].v << "\t";
}
cout << endl << "weight: ";
for (i = 0; i < sizeOfItems; i++) {
cout << items[i].w << "\t";
}
cout << endl;
}
bool compare(Item i1, Item i2) {
return (i1.d > i2.d);
}
float knapsack(Item items[], int sizeOfItems, int W) {
int i, j;
float totalValue = 0, totalWeight = 0;
for (i = 0; i < sizeOfItems; i++) {
items[i].d = (float)items[i].v / items[i].w; //typecasting done (v is int and w is also int so we get final value of d as int)
}
sort(items, items+sizeOfItems, compare);
/*
uncomment if u need to check the data after sortingis done
cout << "values : ";
for(i = 0; i < sizeOfItems; i++) {
cout << items[i].v << "\t";
}
cout << endl << "weights: ";
for (i = 0; i < sizeOfItems; i++) {
cout << items[i].w << "\t";
}
cout << endl << "ratio : ";
for (i = 0; i < sizeOfItems; i++) {
cout << items[i].d << "\t";
}
cout << endl;
*/
for(i=0; i<sizeOfItems; i++) {
if(totalWeight + items[i].w<= W) {
totalValue += items[i].v ;
totalWeight += items[i].w;
} else {
int wt = W-totalWeight;
totalValue += (wt * items[i].d);
totalWeight += wt;
break;
}
}
cout << "Total weight in bag " << totalWeight<<endl;
return totalValue;
}
int main() {
int W;
Item items[4];
input(items, 4);
cout << "Entered data \n";
display(items,4);
cout<< "Enter Knapsack weight \n";
cin >> W;
float mxVal = knapsack(items, 4, W);
cout << "Max value for "<< W <<" weight is "<< mxVal;
} আউটপুট
Enter total 4 item's values and weight Enter 1 V Enter 1 W Enter 2 V Enter 2 W Enter 3 V Enter 3 W Enter 4 V Enter 4 W Entered data values: 2 0 0 0 weight: 0 490642064 0 4196544 Enter Knapsack weight Total weight in bag 0 Max value for 0 weight is 2
