1
Question
A function f defined on stacks of integers satisfies the following properties. f(ϕ)=0 and f (push(S)) = max (f(S), 0) + i for all stack S and integers. If a stack S contains the integers 2, -3, 2, -1, 2 in order from bottom to top. What is f(S)?
A function f defined on stacks of integers satisfies the following properties. f(ϕ)=0 and f (push(S)) = max (f(S), 0) + i for all stack S and integers. If a stack S contains the integers 2, -3, 2, -1, 2 in order from bottom to top. What is f(S)?
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Solution
The correct option is C 3
i : The element to be pushed in Stack S
Initially f(S) = 0
f(S)
max(f(S),0)
i
Updated_f(S)=max(f(S),0)+i
0
0
2
2
2
2
-3
-1
-1
0
2
2
2
2
-1
1
1
1
2
3
i : The element to be pushed in Stack S
Initially f(S) = 0
| f(S) | max(f(S),0) | i |
Updated_f(S)=max(f(S),0)+i |
| 0 | 0 | 2 | 2 |
| 2 | 2 | -3 | -1 |
| -1 | 0 | 2 | 2 |
| 2 | 2 | -1 | 1 |
| 1 | 1 | 2 | 3 |
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