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Algorithm Design approaches

Algorithm Design approaches. Dr. Jey Veerasamy. Petrol cost minimization problem. You need to go from S to T by car, spending the minimum for petrol. S. T. Quick-sort . Merge-sort. Divide & Conquer - characteristics. # of stops minimization problem.

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Algorithm Design approaches

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  1. Algorithm Design approaches Dr. Jey Veerasamy

  2. Petrol cost minimization problem • You need to go from S to T by car, spending the minimum for petrol. S T

  3. Quick-sort

  4. Merge-sort

  5. Divide & Conquer - characteristics

  6. # of stops minimization problem • Similar to petrol cost minimization problem, but we are minimizing # of stops. S T

  7. Activity selection problem

  8. Fractional knapsack problem • Gold powder, silver powder, … • Thief has limited weight capacity

  9. Greedy approach - characteristics

  10. Fibonacci number problem • Definition of Fibonacci number: F(1) = 1 F(2) = 2 F(n) = F(n-1) + F(n-2), when n > 2 • Recursive solution using D&C approach: int f(int n) { if (n == 1) return 1; else if (n == 2) return 2; else return f(n-1) + f(n-2); }

  11. D&C Solution for F(6) F(6) F(4) F(5) F(4) F(3) F(3) F(2) F(3) F(2) F(2) F(1) F(2) F(1) Several subproblems are solved repeatedly - Not an efficient approach. F(2) F(1)

  12. DP solution for F(6) • DP uses a table and bottom-up approach (note that D&C used top-down approach): int fib(int n) { int f[n+1]; f[1] = 1; f[2] = 2; for (i=3 ; i<= n ; i++) f[i] = f[i-1]+f[i-2]; return f[n]; } Computations are NOT repeated! F(1) F(2) F(3) F(4) F(5) F(6)

  13. Knapsack problem • Individual pieces with specific weights, thief wants to know whether there is an exact match for his weight limit.

  14. Dynamic programming - characteristics

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