Question

Given a search problem where some elements are searched more
than others, it is more important to minimize the total cost of
several searches rather than the worst-case cost of a single
search. If x is a more frequent search target than y, building a
tree where the depth of x is smaller than the depth of y will work
better, even if that means increasing the overall depth of the
tree. A perfectly balanced tree is not the best choice if some
items are significantly more popular than others.

Suppose we are given a sorted array of keys A[1..n] and an array of
corresponding access frequencies f[1..n]. Build the binary search
tree that minimizes the total search time, assuming that there will
be exactly f[i] searches for each key A[i]. Suggest a recursive
definition of the cost function, such that Cost(T, f[1..n]]=...,
where T is the tree.

Answer #1

1. This is very famous dynamic programming problem known as optimal cost binary search tree.

Lets understand problem with a example

suppose keys = [ 5,7]

frequency = [10 , 14)

so we can have trees in these two forms

5 or 7

\ /

7 5

Cost = 10*1 + 14*2 = 38 cost = 14*1 + 10*2 = 34

So in right side of tree cost of searching is minimum.

Here cost[i][j] denotes min cost binary search tree which can we formed taking R as a root and

freq[i...j] denotes sum of frequency of keys from i to j.

Base case

i == j only one element so return freq[i]

i>j return 0. As no elements occur between [j,i]

Here we are calculating cost[i][j] using cost[i][R] and cost[R+1][j] as this problems satisfy optimal substructure property.

Feel free to ask doubts in comments if any

1. Given an
n-element array A, Algorithm X executes an
O(n)-time computation for each even
number in A and an O(log n)-time computation for
each odd number in A.
What is the best-case running time of Algorithm X?
What is the worst-case running time of Algorithm X?
2. Given an array,
A, of n integers, give an O(n)-time algorithm that finds
the longest subarray of A such that all the numbers in that
subarray are in sorted order. Your algorithm...

1. We consider the two-point boundary problem uy00(t) + vy0(t) +
wy(t) = f(t), where a ≤ t ≤ b and y(a) = α, y(b) = β Here u,v,w,
are constants and f(t) is a given function. We assume that u 6=
0.
(a) Using the numerical techniques discussed in the book (or class)
show how an approximation to y(t) on the interval a ≤ t ≤ b may be
generated by solving a tridiagonal system of linear equations of...

1.- While insecurity causes losses for some, it generates
profits for others. "From a couple of years to now, the search for
us has skyrocketed. Before, it was us looking for clients, making
them see the need to hire private, specialized and armed security,"
Fuentes said. Miguel Ángel Silva Gómez, Code Uno's chief operating
officer, with 16 years in the market, indicated that, although
there is more demand for these services, they have not been able to
increase the price...

Are some cities more windy than others? Does Chicago deserve to
be nicknamed "The Windy City"? Given below are the average wind
speeds (in miles per hour) for 45 selected cities.
8.7
12.3
8.6
11.5
9.1
8.8
35.1
6.1
7.0
7.2
11.8
10.9
7.6
9.2
9.1
8.1
9.0
8.9
9.2
10.7
10.5
9.6
7.8
11.4
9.5
7.7
8.8
8.8
12.9
8.3
7.8
5.9
10.4
10.4
9.6
8.7
10.1
10.5
7.9
10.6
8.5
8.8
9.4
8.8
9.3
(a)
Calculate
y
and...

Match the statement to the correct answer. (Some reagents can be
used more than once.) The flowchart along with the report sheets in
experiment 5 should be very helpful.
A
6M Nitric Acid (HNO3)
B
Colbalt Nitrate (Co(NO3)2)
C
Disodium EDTA (Na2EDTA)
D
Aluminum Nitrate (Al(NO3)3)
E
Zinc Nitrate (Zn(NO3)2
F
Barium Nitrate (Ba(NO3)2)
G
6M Hydrochloric Acid (HCl)
H
OH-, CO32-, and
PO43-
I
Lead chloride (PbCl2(s))
J
0.1M sodium carbonate (Na2CO3)
K
NH4+(aq) and OH-(aq)
L
Silver chloride...

Why do we naturally tend to trust some strangers more than
others? One group of researchers decided to study the relationship
between eye color and trustworthiness. In their experiment the
researchers took photographs of 80 students (20 males with brown
eyes, 20 males with blue eyes, 20 females with brown eyes, and 20
females with blue eyes), each seated in front of a white background
looking directly at the camera with a neutral expression. These
photos were cropped so the...

Why do we naturally tend to trust some strangers more than
others? One group of researchers decided to study the relationship
between eye color and trustworthiness. In their experiment the
researchers took photographs of 80 students (20 males with brown
eyes, 20 males with blue eyes, 20 females with brown eyes, and 20
females with blue eyes), each seated in front of a white background
looking directly at the camera with a neutral expression. These
photos were cropped so the...

Why do we naturally tend to trust some strangers more than
others? One group of researchers decided to study the relationship
between eye color and trustworthiness. In their experiment the
researchers took photographs of 80 students (20 males with brown
eyes, 20 males with blue eyes, 20 females with brown eyes, and 20
females with blue eyes), each seated in front of a white background
looking directly at the camera with a neutral expression. These
photos were cropped so the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago