sunny
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Not written any code for it. Just tried some examples with pen and paper. Here is the solution.
- sunny March 31, 20151. Consider an array. origArr={1,10,15,7,19,4,0}
2. Create a new array. newArr={}
3. Get first element from origArr. Insert it into newArr. So newArr={1}.
4. Get second element from origArr. Is it greater than element in newArr. (is 10 > 1). Insert it into newArr. So newArr = {1,10}. This a sorted Array. maxSum = 10-1 = 9
5. Get next element from origArr(15). Is 15 > last element of newArr (15>10).
6. If so simply replace this last element with this number. So newArr = {1,15}. maxSum = 15-1=14
7. Get next element of origArr(7). Is 7 > last element of newArr? No, so Discard 7.
8. Get next element of origArr(19). Is 19 > lastelement of newArr. Yes. So as before replace last element of newArr with 19. So newArr = {1,19} and maxSum = 19-1 = 18.
9. Get next element of orgiArr(4). Is 4 > last element of newArr. No. Discard 4.
10. Get next element of origArr(0). Is 0 > last element of newArr. No.
11. For all the comparisons where origArr[element] < newArr[lastElement] next step should be executed. (For simplicity i did not mention it in previous steps as it would have made the logic difficult to understand).
12. Is 0 < first element of newArr (1). Yes, so clear the newArr and add this element. So newArr = {0}.
13. Go to step 3 and continue the process to get maxSum.
I have tried it in 2-3 scenarios(again on paper) and logic holds good. Not sure about the complexity of the solution though. Please do comment on any flaws or problems you find in the solution provided.