Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Minimum Cost to cut a board into squares in C++
Concept
Suppose a board of length p and width q is given, we require to break this board into p*q squares such that cost of breaking is least. For this board,cutting cost for each edge will be given. In a nutshell, we require selecting such a sequence of cutting such that cost is minimized.
Examples
With respect of above board optimal way to cut into square is −
Total minimum cost in above case is 65. It is computed evaluated implementing following steps.
Initial Value : Total_cost = 0 Total_cost = Total_cost + edge_cost * total_pieces Cost 5 Horizontal cut Cost = 0 + 5*1 = 5 Cost 5 Vertical cut Cost = 5 + 5*2 = 15 Cost 4 Vertical cut Cost = 15 + 4*2 = 23 Cost 3 Horizontal cut Cost = 23 + 3*3 = 32 Cost 3 Vertical cut Cost = 32 + 3*3 = 41 Cost 2 Horizontal cut Cost = 41 + 2*4 = 49 Cost 2 Vertical cut Cost = 49 + 2*4 = 57 Cost 2 Vertical cut Cost = 57 + 2*4 = 65
Method
This type of problem can be solved implementing greedy approach. If total cost is treated by S, then S = b1x1 + b2x2 … + bkxk, where xi is treated as a cost of certain edge cutting and bi is corresponding coefficient, The coefficient bi is determined by thetotal number of cuts we have competed implementing edge xi at the end of the cutting process.
We should notice that sum of the coefficients are always constant, hence we want to compute a distribution of bi obtainable such that S is least. To do so we accomplish cuts on largest cost edge as soon as possible, which will reach to optimal S. If we encounter several edges having the equal cost, we can remove or cut any one of them first.
C++ Program
Following is the solution implementing above approach, first we sorted the edge cutting costs in reverse order, and then we loop in them from higher cost to lower cost building our solution. Each time we select an edge, counterpart count is incremented by 1, which is to be multiplied each time with corresponding edge cutting cost.
Example
// C++ program to divide a board into p*q squares
#include <bits/stdc++.h>
using namespace std;
int minimumCostOfBreaking(int X1[], int Y1[], int p, int q){
int res1 = 0;
sort(X1, X1 + p, greater<int>());
sort(Y1, Y1 + q, greater<int>());
int hzntl = 1, vert = 1;
int i = 0, j = 0;
while (i < p && j < q){
if (X1[i] > Y1[j]){
res1 += X1[i] * vert;
hzntl++;
i++;
}
else{
res1 += Y1[j] * hzntl;
vert++;
j++;
}
}
int total = 0;
while (i < p)
total += X1[i++];
res1 += total * vert;
total = 0;
while (j < q)
total += Y1[j++];
res1 += total * hzntl;
return res1;
}
int main(){
int p = 6, q = 4;
int X1[p-1] = {3, 2, 4, 2, 5};
int Y1[q-1] = {5, 2, 3};
cout << minimumCostOfBreaking(X1, Y1, p-1, q-1);
return 0;
}Output
65
215 Views
