Space complexity of recursive function (Time & Space)
There is recursion function below, and I did not calculated time & space complexity. I looked at some resources, but it was not clear enough for me the understanding. Could anyone explain the way of solving in the simplest way, and answers the question?
By the way, I tried to solve time complexity, and I found O(2^n). Is it correct?
int func(int n) {
if (n < 3)
return 3;
else {
return func(n-3)*func(n-3);
}
}
c algorithm time-complexity space-complexity
edited Nov 18 '18 at 21:03
user10605163
2,848624
asked Nov 18 '18 at 14:14
Kaan Taha KökenKaan Taha Köken
154215
add a comment |
There is recursion function below, and I did not calculated time & space complexity. I looked at some resources, but it was not clear enough for me the understanding. Could anyone explain the way of solving in the simplest way, and answers the question?
By the way, I tried to solve time complexity, and I found O(2^n). Is it correct?
int func(int n) {
if (n < 3)
return 3;
else {
return func(n-3)*func(n-3);
}
}
c algorithm time-complexity space-complexity
edited Nov 18 '18 at 21:03
user10605163
2,848624
asked Nov 18 '18 at 14:14
Kaan Taha KökenKaan Taha Köken
154215
2
Interestingly, replacingreturn func(x-3)*func(x-3)byz= func(x-3); return z*z;lowers the complexity to O(n) while keeping the same result.
– Yves Daoust
Nov 18 '18 at 15:05
add a comment |
There is recursion function below, and I did not calculated time & space complexity. I looked at some resources, but it was not clear enough for me the understanding. Could anyone explain the way of solving in the simplest way, and answers the question?
By the way, I tried to solve time complexity, and I found O(2^n). Is it correct?
int func(int n) {
if (n < 3)
return 3;
else {
return func(n-3)*func(n-3);
}
}
c algorithm time-complexity space-complexity
edited Nov 18 '18 at 21:03
user10605163
2,848624
asked Nov 18 '18 at 14:14
Kaan Taha KökenKaan Taha Köken
154215
There is recursion function below, and I did not calculated time & space complexity. I looked at some resources, but it was not clear enough for me the understanding. Could anyone explain the way of solving in the simplest way, and answers the question?
By the way, I tried to solve time complexity, and I found O(2^n). Is it correct?
int func(int n) {
if (n < 3)
return 3;
else {
return func(n-3)*func(n-3);
}
}
c algorithm time-complexity space-complexity
c algorithm time-complexity space-complexity
edited Nov 18 '18 at 21:03
user10605163
2,848624
asked Nov 18 '18 at 14:14
Kaan Taha KökenKaan Taha Köken
154215
edited Nov 18 '18 at 21:03
user10605163
2,848624
asked Nov 18 '18 at 14:14
Kaan Taha KökenKaan Taha Köken
154215
edited Nov 18 '18 at 21:03
user10605163
2,848624
edited Nov 18 '18 at 21:03
user10605163
2,848624
edited Nov 18 '18 at 21:03
user10605163
2,848624
2,848624
asked Nov 18 '18 at 14:14
Kaan Taha KökenKaan Taha Köken
154215
asked Nov 18 '18 at 14:14
Kaan Taha KökenKaan Taha Köken
154215
asked Nov 18 '18 at 14:14
Kaan Taha KökenKaan Taha Köken
154215
154215
2
Interestingly, replacingreturn func(x-3)*func(x-3)byz= func(x-3); return z*z;lowers the complexity to O(n) while keeping the same result.
– Yves Daoust
Nov 18 '18 at 15:05
add a comment |
2
Interestingly, replacingreturn func(x-3)*func(x-3)byz= func(x-3); return z*z;lowers the complexity to O(n) while keeping the same result.
– Yves Daoust
Nov 18 '18 at 15:05
2
2
Interestingly, replacing
return func(x-3)*func(x-3) by z= func(x-3); return z*z; lowers the complexity to O(n) while keeping the same result.– Yves Daoust
Nov 18 '18 at 15:05
Interestingly, replacing
return func(x-3)*func(x-3) by z= func(x-3); return z*z; lowers the complexity to O(n) while keeping the same result.– Yves Daoust
Nov 18 '18 at 15:05
add a comment |
1 Answer
1
active
oldest
votes
Yes, the time complexity is indeed O(2 ^ n).
The recurrence relation for time complexity is:
T(n) = 2 * T(n - 3)
Applying the above equation k times:
T(n) = 2 * 2 * 2 ... k times * T(n - 3 * k) = 2 ^ k * T(n - 3k)
When k is n/3, T(n) = 2 ^ k = 2 ^ (n / 3) = O(2 ^ n)
There's only one function running at a time and stack depth can be k at max.
So, space complexity is n / 3 or O(n)
answered Nov 18 '18 at 14:25
merlynmerlyn
1,59511222
add a comment |
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1 Answer
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active
oldest
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oldest
votes
active
oldest
votes
Yes, the time complexity is indeed O(2 ^ n).
The recurrence relation for time complexity is:
T(n) = 2 * T(n - 3)
Applying the above equation k times:
T(n) = 2 * 2 * 2 ... k times * T(n - 3 * k) = 2 ^ k * T(n - 3k)
When k is n/3, T(n) = 2 ^ k = 2 ^ (n / 3) = O(2 ^ n)
There's only one function running at a time and stack depth can be k at max.
So, space complexity is n / 3 or O(n)
answered Nov 18 '18 at 14:25
merlynmerlyn
1,59511222
add a comment |
Yes, the time complexity is indeed O(2 ^ n).
The recurrence relation for time complexity is:
T(n) = 2 * T(n - 3)
Applying the above equation k times:
T(n) = 2 * 2 * 2 ... k times * T(n - 3 * k) = 2 ^ k * T(n - 3k)
When k is n/3, T(n) = 2 ^ k = 2 ^ (n / 3) = O(2 ^ n)
There's only one function running at a time and stack depth can be k at max.
So, space complexity is n / 3 or O(n)
answered Nov 18 '18 at 14:25
merlynmerlyn
1,59511222
add a comment |
Yes, the time complexity is indeed O(2 ^ n).
The recurrence relation for time complexity is:
T(n) = 2 * T(n - 3)
Applying the above equation k times:
T(n) = 2 * 2 * 2 ... k times * T(n - 3 * k) = 2 ^ k * T(n - 3k)
When k is n/3, T(n) = 2 ^ k = 2 ^ (n / 3) = O(2 ^ n)
There's only one function running at a time and stack depth can be k at max.
So, space complexity is n / 3 or O(n)
answered Nov 18 '18 at 14:25
merlynmerlyn
1,59511222
Yes, the time complexity is indeed O(2 ^ n).
The recurrence relation for time complexity is:
T(n) = 2 * T(n - 3)
Applying the above equation k times:
T(n) = 2 * 2 * 2 ... k times * T(n - 3 * k) = 2 ^ k * T(n - 3k)
When k is n/3, T(n) = 2 ^ k = 2 ^ (n / 3) = O(2 ^ n)
There's only one function running at a time and stack depth can be k at max.
So, space complexity is n / 3 or O(n)
answered Nov 18 '18 at 14:25
merlynmerlyn
1,59511222
answered Nov 18 '18 at 14:25
merlynmerlyn
1,59511222
answered Nov 18 '18 at 14:25
merlynmerlyn
1,59511222
answered Nov 18 '18 at 14:25
merlynmerlyn
1,59511222
1,59511222
add a comment |
add a comment |
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2
Interestingly, replacing
return func(x-3)*func(x-3)byz= func(x-3); return z*z;lowers the complexity to O(n) while keeping the same result.– Yves Daoust
Nov 18 '18 at 15:05