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![n 0 1 2 3
0 1 1 0 1
1 1 1 1 1
2 0 1 1 1
3 1 1 1 1
3 2
10 Graphcolor(int k)
{
for(Int c =1 ;c<=m;c++)
{
if (isSafe(k,c)){
x[k]=c;
if((k+1))<n)
Graphcolor(k+1)
else
print x[]; return
}
}
}
k =Current node
c =colour
n = total nodes
0 1 2
1 2 3X[k]=
ifSafe(int k, int c)
{
for(int i=0;i<n;i++)
{
if(G[k][i] ==1 && c==x[i])
{
return false;
}
}
return true;
}](https://image.slidesharecdn.com/daa-190131074307/75/Non-Deterministic-and-Deterministic-Problems-3-2048.jpg)
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Non Deterministic and Deterministic Problems
- 1. NP Problems (NonDeterministic problem) Department of Computer Applications School of Physical Sciences Sikkim University Presented By - : Robin Gurung 14UCA015
- 2. NP problems 1. Graphcolouring. 2. Bin Packing Problem.
- 3. n 0 12 3 0 1 1 0 1 1 1 1 1 1 2 0 1 1 1 3 1 1 1 1 3 2 10 Graphcolor(int k) { for(Int c =1 ;c<=m;c++) { if (isSafe(k,c)){ x[k]=c; if((k+1))<n) Graphcolor(k+1) else print x[]; return } } } k =Current node c =colour n = total nodes 0 1 2 1 2 3X[k]= ifSafe(int k, int c) { for(int i=0;i<n;i++) { if(G[k][i] ==1 && c==x[i]) { return false; } } return true; }
- 4. •Only feasible tosmall problem like this. •This graph colouring problem is known as NP hard problem. •This algorithm is still O(𝑚 𝑛 ) •m = no. of colours •n = no. of vertices. Conclusion of Graph colouring
- 5. Bin packing Problem •Fitting things efficiently and neatly inside a larger container. • 6 group of people ,of group size 3,1,6,4,5 and 2 need to fit onto a minibuses with capacity 7 must stay together in their groups. Find a number of buses need to pack them in efficiently and so that each group stays together.
- 6. Bin packing algorithm •LowerBound of a problem. •Perform first fit algorithm. •Perform first fit decreasing algorithm. •Full bin packing algorithm.
- 7. Lower bound 3 2 5 4 6 1 + + + + + 21 + 7 7 7 7 21 /7=3 3 is lower bound MinibusesGroups
- 8. First fit algorithm 3 2 5 4 6 1 *Occupied 4 minibuses * 7 waste spaces MinibusesGroups
- 9. First fit decreasingalgorithm MinibusesGroups
- 10.
- 11. Conclusion of binpacking algorithm • First fit algorithm :- I. quick and easy to perform. II. Does not lead to optimal solution. • First fit decreasing algorithm I. quick and easy to perform. II. Usually better than first fit algorithm. III. does not get optimal solution. • Full bin packing algorithm I. usually get good solution. II. cant be difficult to perform if numbers are awkward.