Min-Max
Write an algorithm that finds both the smallest and
largest numbers in a list of n numbers and with complexity
T(n) is at most about (1.5)n comparisons.
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Answer Posted / kush singh
1. Algorithm MaxMin (i,j, max, min)
2. // a[1:n] is a global array Parameter i and j are integers,
3. // 1 „T i „T j < n. The effect is to set max and min to the
4. // largest and smallest values in a [i, j], respectively.
5. {
6. if (i=j) then max:=min:=a[i]; //small(P)
7. else if (i = j ¡V 1) then //Another case of Small (P)
8. {
9. if a [i] < a[j] then
10. {
11. max:=a[j]; min:=a[i];
12. }
13. else
14. {
15. max:=a[i]; min:=a[j]
16. }
17. }
18. else
19. {
20. // If P is not small, divide P into subproblems
21. // Find where to split the set
22. mid:= „¾(i+j)/2„Î;
23. //Solve the subproblems
24. Maxmin (i, mid, max, min);
25. MaxMin (mid+i, j, max1, min1);
26. // Combine the solutions
27. if (max<max 1) then max:=max1;
28. if(min>min1) then min:=min1;
29. }
30. }
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