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A function f defined on stacks of integers satisfies the following properties. f(∅) = 0 and f (push (S, i)) = max (f(S), 0) + i for all stacks S and integers i.
If a stack S contains the integers 2, -3, 2, -1, 2 in order from bottom to top, what is f(S)?
- a)6
- b)4
- c)3
- d)2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A function f defined on stacks of integers satisfies the following pro...
i Element to be pushed
Initial State f(φ) = 0 For Empty Stack F(S) is 0.
Then we push each element ( )one by one and calculate f(s)for each insertion as given
Is the function to compute F(s) for each insertions
1. INSERT 2 into Stack
Similarly ,
The value of F(s) after inserting all elements into stack is 3
Most Upvoted Answer
A function f defined on stacks of integers satisfies the following pro...
Solution:
Given, f() = 0 and f(push(S, i)) = max(f(S), 0) + i for all stacks S and integers i.
Let's calculate f(S) for the given stack S containing the integers 2, -3, 2, -1, 2 in order from bottom to top.
1. Pushing 2 onto the empty stack:
f(push({}, 2)) = max(f({}), 0) + 2
= max(0, 0) + 2
= 2
2. Pushing -3 onto the stack:
f(push({2}, -3)) = max(f({2}), 0) - 3
= max(2, 0) - 3
= -1
3. Pushing 2 onto the stack:
f(push({2, -3}, 2)) = max(f({2, -3}), 0) + 2
= max(2, 0) + 2
= 4
4. Pushing -1 onto the stack:
f(push({2, -3, 2}, -1)) = max(f({2, -3, 2}), 0) - 1
= max(4, 0) - 1
= 3
5. Pushing 2 onto the stack:
f(push({2, -3, 2, -1}, 2)) = max(f({2, -3, 2, -1}), 0) + 2
= max(3, 0) + 2
= 5
Therefore, f(S) = 3 for the given stack S containing the integers 2, -3, 2, -1, 2 in order from bottom to top.
Hence, the correct answer is option (c) 3.
Given, f() = 0 and f(push(S, i)) = max(f(S), 0) + i for all stacks S and integers i.
Let's calculate f(S) for the given stack S containing the integers 2, -3, 2, -1, 2 in order from bottom to top.
1. Pushing 2 onto the empty stack:
f(push({}, 2)) = max(f({}), 0) + 2
= max(0, 0) + 2
= 2
2. Pushing -3 onto the stack:
f(push({2}, -3)) = max(f({2}), 0) - 3
= max(2, 0) - 3
= -1
3. Pushing 2 onto the stack:
f(push({2, -3}, 2)) = max(f({2, -3}), 0) + 2
= max(2, 0) + 2
= 4
4. Pushing -1 onto the stack:
f(push({2, -3, 2}, -1)) = max(f({2, -3, 2}), 0) - 1
= max(4, 0) - 1
= 3
5. Pushing 2 onto the stack:
f(push({2, -3, 2, -1}, 2)) = max(f({2, -3, 2, -1}), 0) + 2
= max(3, 0) + 2
= 5
Therefore, f(S) = 3 for the given stack S containing the integers 2, -3, 2, -1, 2 in order from bottom to top.
Hence, the correct answer is option (c) 3.
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A function f defined on stacks of integers satisfies the following properties. f(∅) = 0 and f (push (S, i)) = max (f(S), 0) + i for all stacks S and integers i.If a stack S contains the integers 2, -3, 2, -1, 2 in order from bottom to top, what is f(S)?a)6b)4c)3d)2Correct answer is option 'C'. Can you explain this answer?
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