Assignment 3

CS 452/652/752 Advanced Algorithms and Applications

Out: 19 October 2019, Due: 28 October 2019

Upload the aftercited files, (a) a PDF (preferably, generated from latex)

containing the defenses control perfect programming scrutinys. (b) Regulation control perfect programming problems. The regulation should embrace patchwork and deterrent instructions. Use concepts of Dynamic programming to unfold these scrutinys.

CS452 unfold any 6. The 6 scrutinys you unfold conquer be merit (100/6) points.

The fostering couple scrutinys can be unfoldd control cumulative extra merit of 10

points.

CS652 and CS752 unfold any 7. Perfect scrutinys merit (100/7) points. The

fostering scrutiny can be unfoldd control an extra merit of 10 points.

Programming problems

Scrutiny 1

FibDP of integer n is defined to be unite of FibDP of n – 1 pretended to FibDP

of n – 2. The principal couple collection of the FibDP train are 5 and 6. The principal 5

provisions are: 5, 6, 11, 17, 28, … Take into consequence the collection in the FibDP

train whose values are refereffectual further than 50000000000. What is the unite of the

odd-valued provisions?

Scrutiny 2

Starting in the apex left recess of a 2 × 2 grid, and barely life effectual to change to

the straight and down, there are accurately 6 routes to the depth straight recess.

How numerous such routes are there through a 21 × 21 grid?

1

Scrutiny 3

You are at the apex of a triangle mountain made with collection. While moving

down, you can barely change to neighboring collection in the dignity beneath. There are

numerous practices to arrive-at the depth from the apex. Pick the method that maximizes

the incorporate. Control issue, control the enumerate mountain beneath, the utmost incorporate

you can arrive-at is 23.

What is the utmost incorporate you can finish control the immovable dataset

[triangles.txt] ?

Scrutiny 4

In India the vogue is made up of Rupees (R), and Paise (P), and there are

eight coins in public circulation:

5P, 10P, 25P, 50P, 1R (100P), 2R (200p), 5R (500P), and 10R (1000P)

One practice to produce 2R is as follows: 1 × 1R + 1 × 50P + 2 × 25P

How numerous divergent practices can you produce 5R, ardent you enjoy infinite

supply of coins?

Scrutiny 5

In the 5×5 matrix beneath, the minimal method unite from the apex left to the depth

right, by barely moving to the straight and down, is involved in doughty red and is equal

to 2427.

Control the immovable 80 × 80 matrix [matrix.txt], ascertain the minimal method

sum.

Scrutiny 6

You are ardent a substantial integer n, violate it into the unite of at last couple substantial

integers and maximize the fruit of those integers. Return the utmost

2

fruit you can procure. (Issue Input: 10, Output: 36, Explanation: 10 = 3 3

4 = 36). What is your defense control n = 82.

Scrutiny 7

Catalan collection are recursively defined as follows:

What is Catalan enumerate 20.

Scrutiny 8

A binomial coefficient C(n, k) gives the enumerate of practices, inconsiderate prescribe,

that k objects can be selected from floating n objects. What is C(40, 5) ?

http://mathworld.wolfram.com/BinomialCoefficient.html

3

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