Data Structures and Programming Methodology CS61
Asymptotics
(a) We have a function
findMax
that iterates through an unsorted
int
array once and returns the maximum element found in that array. Give the tightest lower (Ω(·
)) and upper bounds (
O
(
·
)) of findMax in terms of
N
, the length of the array. Is it possible to define a Θ(
·
) bound for
findMax
?
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(b) Give the worst case and best case runtime in terms of
M
and
N
. Assume
ping
is in Θ(1) and returns an int
.
1
for
(
int
i = N; i > 0; i--) {
2
for
(
int
j = 0; j <= M; j++) {
3
if
(ping(i, j) > 64)
break
;
4 }
5 }
(c) Below we have a function that returns true if every int has a duplicate in the array, and false if there
is any unique int in the array. Assume
sort(array)
is in Θ(
N
log
N
) and returns
array
sorted.
1
public static boolean
noUniques(
int
[] array) {
2 array = sort(array);
3
int
N = array.length;
4
for
(
int
i = 0; i < N; i += 1) {
5
boolean
hasDuplicate =
false
;
6
for
(
int
j = 0; j < N; j += 1) {
7
if
(i != j && array[i] == array[j]) {
8 hasDuplicate = true
;
9 }
10 }
11
if
(!hasDuplicate)
return false
;
12 }
13
return true
;
14 }
Give the worst case and best case runtime in Θ(
·
) notation, where
N
=
array.length
.
I Am Speed
(a) For each code block below, fill in the blank(s) so that the function has the desired runtime. Do not use any commas. If the answer is impossible, just write ”impossible” in the blank. Assume that System.out.println runs in constant time. You may use Java’s
Math.pow(x, y)
to raise
x
to the power of y
.
// Desired Runtime:
Θ(
N
)
public static void
f1(
int
N) {
for
(
int
i = 1; i < N; ____________){
System.out.println("hi Teresa");
}
}
// Desired Runtime:
Θ(log
N
)
public static void
f2(
int
N) {
for
(
int
i = 1; i < N; ____________) {
System.out.println("howdy Ayati");
}
}
// Desired Runtime:
Θ(1)
public static void
f3(
int
N) {
for
(
int
i = 1; ____________; i += 1) {
System.out.println("hello Daniel");
}
}
原文地址：https://blog.csdn.net/w976j_/article/details/140605243
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