0/1 Knapsack using Dynamic Programming Presentation, Slides of Design and Analysis of Algorithms

Download 0/1 Knapsack using Dynamic Programming Presentation and more Slides Design and Analysis of Algorithms in PDF only on Docsity!

0/1 KNAPSACK USING

DYNAMIC PRGRAMMING

HUSSAIN AFZAL [CS-87]

DYNAMIC PRGRAMMING

DYNAMIC PROGRAMMING IS A TECHNIQUE IN

COMPUTER PROGRAMMING THAT HELPS TO

EFFICIENTLY SOLVE A CLASS OF PROBLEMS

THAT HAVE OVERLAPPING SUBPROBLEMS AND

OPTIMAL SUBSTRUCTURE PROPERLY

EXAMPLE

**CONDITIONS

1. IF N=0 & W=0 (0)
2. IF W(N) > W KS(N,W) = KS (N-1,W)
3. IF W(N) <= W KS(N,W) = [N-1,W-W(N)] + P(N) KS(N,W) = KS (N-1,W)**

MAX

KNAPSACK PROBLEM

HUSSAIN AFZAL [CS-87]

• Object
  • Profit
• Weight - Capacity= - wt P w=0 w=1 w=2 w=3 w=4 w=5 w=6 w=
• n=0 - n=1 - n=2 - n=3
  • n=4 - wt P w=0 w=1 w=2 w=3 w=4 w=5 w=6 w=
• n=0 - n=1 - n=2 - n=3
  • n=4 - wt P w=0 w=1 w=2 w=3 w=4 w=5 w=6 w=
• n=0 - n=1 - n=2 - n=3
  • n=4 - wt P w=0 w=1 w=2 w=3 w=4 w=5 w=6 w=
• n=0 - n=1 - n=2 - n=3
  • n=4 - wt P w=0 w=1 w=2 w=3 w=4 w=5 w=6 w=
• n=0 - n=1 - n=2 - n=3
  • n=4 - wt P w=0 w=1 w=2 w=3 w=4 w=5 w=6 w=
• n=0 - n=1 - n=2 - n=3
  • n=4
  • OBJECT OBJ 1 OBJ 2 OBJ
    • PROFIT
• WEIGHT - P/W 1.3 1.6 1. - KNAPSACK CAPACITY (M)=

THANKS YOU FOR KEEPING ATTENTION

HUSSAIN AFZAL [CS-87]

ANY QUESTIONS?