Wednesday, September 7, 2016

Minimum cost to fill given weight in a bag - GeeksforGeeks


Minimum cost to fill given weight in a bag - GeeksforGeeks
You are given a bag of size W kg and you are provided costs of packets different weights of oranges in array cost[] where cost[i] is basically cost of 'i' kg packet of oranges. Where cost[i] = -1 means that 'i' kg packet of orange is unavailable
Find the minimum total cost to buy exactly W kg oranges and if it is not possible to buy exactly W kg oranges then print -1. It may be assumed that there is infinite supply of all available packet types.
Note : array starts from index 1.

This problem is can be reduced to 0-1 Knapsack Problem. So in cost array, we first ignore those packets which are not available i.e; cost is -1 and then traverse the cost array and create two array val[] for storing cost of ‘i’ kg packet of orange and wt[] for storing weight of corresponding packet. Suppose cost[i] = 50 so weight of packet will be i and cost will be 50.
Algorithm :


  • Create matrix min_cost[n+1][W+1], where n is number of distinct weighted packets of orange and W is maximum capacity of bag.
  • Initialize 0th row with INF (infinity) and 0th Column with 0.
  • Now fill the matrix
    • if wt[i-1] > j then min_cost[i][j] = min_cost[i-1][j] ;
    • if wt[i-1] >= j then min_cost[i][j] = min(min_cost[i-1][j], val[i-1] + min_cost[i][j-wt[i-1]]);
  • If min_cost[n][W]==INF then output will be -1 because this means that we cant not make make weight W by using these weights else output will be min_cost[n][W].
// cost[] initial cost array including unavailable packet
// W capacity of bag
int MinimumCost(int cost[], int n, int W)
{
    // val[] and wt[] arrays
    // val[] array to store cost of 'i' kg packet of orange
    // wt[] array weight of packet of orange
    vector<int> val, wt;
 
    // traverse the original cost[] array and skip
    // unavailable packets and make val[] and wt[]
    // array. size variable tells the available number
    // of distinct weighted packets
    int size = 0;
    for (int i=0; i<n; i++)
    {
        if (cost[i]!= -1)
        {
            val.push_back(cost[i]);
            wt.push_back(i+1);
            size++;
        }
    }
 
    n = size;
    int min_cost[n+1][W+1];
 
    // fill 0th row with infinity
    for (int i=0; i<=W; i++)
        min_cost[0][i] = INF;
 
    // fill 0'th coloumn with 0
    for (int i=1; i<=n; i++)
        min_cost[i][0] = 0;
 
    // now check for each weight one by one and fill the
    // matrix according to the condition
    for (int i=1; i<=n; i++)
    {
        for (int j=1; j<=W; j++)
        {
            // wt[i-1]>j means capacity of bag is
            // less then weight of item
            if (wt[i-1] > j)
                min_cost[i][j] = min_cost[i-1][j];
 
            // here we check we get minimum cost either
            // by including it or excluding it
            else
                min_cost[i][j] = min(min_cost[i-1][j],
                     min_cost[i][j-wt[i-1]] + val[i-1]);
        }
    }
 
    // exactly weight W can not be made by given weights
    return (min_cost[n][W]==INF)? -1: min_cost[n][W];
}

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