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7/21/2019 Algorithms_ Dynamic Programming - Matrix Chain Multiplication With C Program Source Code - The Learning Point
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great
books
for
Computer
Science,
Programming
and
Tech
Interviews!
To go
through
the C
program /
source-
code,
scroll
down to
the end of
this page
Matrix
Chain
Multiplication
Dynamic
Programming
solves
problems
by
Sorting- at a glance
Bubble Sort - One of the mostelementary sorting algorithms to
implement - and also very
inefficient. Runs in quadratic
time. A good starting point to
understand sorting in general,
before moving on to more
advanced techniques and
algorithms. A general idea of
how the algorithm works and a
the code for a C program.
Insertion Sort - Another
quadratic time sorting algorithm
- an example of dynamic
programming. An explanation
and step through of how the
algorithm works, as well as the
source code for a C program
which performs insertion sort.
Selection Sort - Another
quadratic time sorting algorithm
- an example of a greedy
algorithm. An explanation and
step through of how the
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Popular articles
Exposing CBSE/ICSE Marking
Scams(2013)
Exposing CBSE/ICSE: A follow-up
(2015)
CBSE Score manipulation over a
decade
Mathematics
Quizzes on Progressions
MCQ #1: Arithmetic Progression
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combining
the
solutions
to
subproblems
just like
the divide
and
conquer
method. Dynamic
programming
method is
used to
solve theproblem
of
multiplication
of a chain
of matrices
so that
the fewest
totalscalar
multiplications
are
performed.
Given a
chain (A1,
A2, A3,
A4….An)
of n
matrices,
we wish
to
compute
algorithm works, as well as the
source code for a C program
which performs selection sort.
Shell Sort- An inefficient but
interesting algorithm, the
complexity of which is not
exactly known.
Merge Sort An example of a
Divide and Conquer algorithm.
Works in O(n log n) time. The
memory complexity for this is a
bit of a disadvantage.
Quick Sort In the average case,
this works in O(n log n) time. Noadditional memory overhead -
so this is better than merge sort
in this regard. A partition
element is selected, the array is
restructured such that all
elements greater or less than
the partition are on opposite
sides of the partition. These two
parts of the array are then
sorted recursively.
Heap Sort- Efficient sorting
algorithm which runs in O(n log
n) time. Uses the Heap data
structure.
Binary Search Algorithm-
Commonly used algorithm usedto find the position of an
element in a sorted array. Runs
in O(log n) time.
Basic Data Structures and
Algorithms
MCQ #2: Geometric Progression
MCQ #3 : More on Geometric
Progressions.
MCQ #4 : Harmonic
Progressions.
MCQ #5: More on Harmonic
Progression
MCQ #6: Mixed Progressions
Coordinate Geometry - Straight
Lines
MCQ #1: Cartesian Planes,
Straight Line Basics
MCQ #2 on Straight Lines
MCQ #3 on Straight Lines
MCQ #4 on Straight Lines
Circles
1 MCQ #1 on Circles.
2 MCQ #2 on Circles.
3 MCQ #3 on Circles.
Conic Sections- Parabola,
Hyperbola, Ellipse
1 MCQ- The Basics of Conic
Sections
2 MCQ on Parabola..
3 MCQ on Hyperbola
4 MCQ on Ellipses.
Probability
MCQ #1 on Basic Probability
MCQ #2: More Challenging
Problems on Probability
MCQ #3- Conditional Probability
and Bayes Theorem
Complex Numbers
MCQ #1
MCQ #2: More on Complex
Numbers
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the
product. A
product
of matrices
is fully
parenthesized
if it is
either a
single
matrix or
the
product of
fully
parenthesized matrixproducts,
surrounded
by
parenthesis.
Since,
matrix
multiplication
isassociative
all parenthesizations
yield the
same
product.
But, the
way we
parenthesize
a chain of
matrices
have an
impact on
the cost
of
Stacks Last In First Out data
structures ( LIFO ). Like a stack of
cards from which you pick up the
one on the top ( which is the last
one to be placed on top of the
stack ). Documentation of the
various operations and the
stages a stack passes through
when elements are inserted or
deleted. C program to help you
get an idea of how a stack is
implemented in code.
Queues First in First Out data
structure (FIFO). Like people
waiting to buy tickets in a queue
- the first one to stand in the
queue, gets the ticket first and
gets to leave the queue first.
Documentation of the various
operations and the stages a
queue passes through as
elements are inserted or deleted.
C Program source code to help
you get an idea of how a queueis implemented in code.
Single Linked List A self
referential data structure. A list
of elements, with a head and a
tail; each element points to
another of its own kind.
Double Linked List - A self
referential data structure. A list
of elements, with a head and a
tail; each element points to
another of its own kind in front
of it, as well as another of its
own kind, which happens to be
behind it in the sequence.
Quadratic Equations
MCQ Quadratic Equations
Quadratic In-equations
MCQ Quadratic In-equations
Computer Science
Quizzes on Basic Object Oriented
Programming with C++
1 MCQ #1: C++ and OOPS
2 MCQ #2: Inheritance in C++
Quizzes on C Programming-
Arrays, Strings and Pointers
1 C Programming MCQ #1:
Strings- 1
2 C Programming MCQ #2:
Strings (2)
3 C Programming MCQ #3:
Strings (3)
4 C Programming MCQ #4:
Arrays(1)
5 C Programming MCQ #5:
Arrays (2)
6 C Programming MCQ #6:
Arrays (3)
7 C Programming MCQ #7:
Pointers (1)
8 C Programming MCQ #8:
Pointers (2)
Quizzes on Java Programming
1 Java MCQ #1- Classes,
Inheritances and Interfaces
2 Java MCQ #2- Collections
3 Java MCQ #3- Threading
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evaluating
the
product.
We divide
a chain of
matrices
to be
multiplied into
two
optimal
sub-
chains,
and then
theoptimal
parenthesizations
of the
sub-
chains
must
be composed
of optimalchains.
Algorithm
- this has
been
covered in
the
tutorial
document:
A block of
memory
cache is
Circular Linked List Linked list
with no head and tail - elements
point to each other in a circular
fashion.
Binary Search Trees A basic
form of tree data structures.
Inserting and deleting
elements in them. Different
kind of binary tree traversal
algorithms.
Heaps - A tree like data
structure where every element
is lesser (or greater) than the
one above it. Heap formation,sorting using heaps in O(n log
n) time.
Height Balanced
Trees - Ensuring that trees
remain balanced to optimize
complexity of operations which
are performed on them.
Graphs
Depth First Search - Traversing
through a graph using Depth
First Search in which unvisited
Quizzes on Data Structures,
Algorithms and Complexity
1 MCQ #1: The Basics of Sorting
Algorithms- Quadratic Sorts
2 MCQ #2: Efficient Sorting
Algorithms- Quick sort, Merge
Sort, Heap Sort
3 MCQ #3- The Radix Sort
4 MCQ #4: Divide and Conquer
5 MCQ #5- Dynamic
Programming
6 MCQ #6- Complexity of
Algorithms
7 MCQ #7- Application of
Master's Theorem
8 MCQ #8: Binary Search Trees
9 MCQ #9: B-Trees
10 MCQ #9: AVL-Trees
11 MCQ #10: Representing
Graphs as Data Structures
12 MCQ #11: Spanning Trees
13 MCQ #12: Algorithms -
Graphs: Spanning Trees -
Kruskal and Prim Algorithms
14 MCQ #13: Algorithms -
Graphs: Depth and Breadth First
Search
Basic English Grammar
English Online: Articles (Quiz #1)
English Online: Articles (Quiz #2)
English Online: Articles (Quiz #3)
English Grammar- The Tenses:
Quiz #1
English Grammar- The Tenses:
Quiz #2
English Grammar- The Tenses:
Quiz #3
English Grammar- The Tenses:
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used to
store the
result of
the
function
for
specific
values. If
cache[i][j]
= -1 then
we do not
know the
result. If it
is somenumber
then that
denotes
the return
value
of multiply
(i,j). We
store it toavoid
computing
the same
again.
Input
Format:
First
integer
must be
the
number of
matrices.
It has to
neighbors of the current vertex
are pushed into a stack and
visited in that order.
Breadth First Search -
Traversing through a graph using
Breadth First Search in which
unvisited neighbors of the
current vertex are pushed into a
queue and then visited in that
order.
Minimum Spanning Trees:
Kruskal Algorithm- Finding the
Minimum Spanning Tree using
the Kruskal Algorithm which is a
greedy technique. Introducing
the concept of Union Find.
Minumum Spanning Trees: Prim's
Algorithm- Finding the Minimum
Spanning Tree using the Prim's
Algorithm.
Dijkstra Algorithm for Shortest
Paths- Popular algorithm for
finding shortest paths : Dijkstra
Algorithm.
Floyd Warshall Algorithm for
Shortest Paths- All the all
Quiz #4
English Grammar- The Tenses:
Quiz #5
English Grammar: The Parts of
Speech (Quiz #1)
English Grammar: The Parts of
Speech (Quiz #2)
English Grammar: The Parts of
Speech (Quiz #3)
English Grammar: The Parts of
Speech (Quiz #4)
English Grammar: The Parts of
Speech (Quiz #5)
English Grammar: The Parts of
Speech (Quiz #6)
English Grammar: The Parts of
Speech (Quiz #7)
English Grammar: The Parts of
Speech (Quiz #8)
English Grammar: The Parts of
Speech (Quiz #9)
English Grammar: The Parts of
Speech (Quiz #10)
0
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be
followed
by rows of
first matrix,
columns
of first
matrix,
columns
for second
matrix,
columns
for third
matrix
and so on.
Complete
Tutorial
with
Examples
:
shortest path algorithm: Floyd
Warshall Algorithm
Bellman Ford Algorithm -
Another common shortest path
algorithm : Bellman Ford
Algorithm.
Dynamic Programming A
technique used to solve
optimization problems, based
on identifying and solving sub-
parts of a problem first.
Integer Knapsack problemAn
elementary problem, often
used to introduce the concept
of dynamic programming.
Matrix Chain
Multiplication Given a long
chain of matrices of varioussizes, how do you parenthesize
them for the purpose of
multiplication - how do you
chose which ones to start
multiplying first?
Longest Common
Subsequence Given two
strings, find the longest
common sub sequence
between them.
Elementary cases : Fractional
Knapsack Problem, Task
Scheduling - Elementary
7/21/2019 Algorithms_ Dynamic Programming - Matrix Chain Multiplication With C Program Source Code - The Learning Point
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Matrix
Chain
Multiplication
- C Program
Source Code
#include<string.h>
problems in Greedy algorithms -
Fractional Knapsack, Task
Scheduling. Along with C
Program source code.
Data Compression using
Huffman TreesCompression
using Huffman Trees. A greedy
technique for encoding
information.
7/21/2019 Algorithms_ Dynamic Programming - Matrix Chain Multiplication With C Program Source Code - The Learning Point
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#include<stdio.h>
#include<limits.h>
int min(int a,int b)
return a < b ? a:b;
/*d[i] is used to store the dimension of the mSo for no loss of generality we will put d[0] t
start the index from 1
*/
int d[100100];
/* Cache is used to store the result of the fu
do not know the result. If it is some number
We store it to avoid computing the same ag*/
int cache[1024][1024];
int multiply(int from,int to)
if(from==to)return 0;
if(cache[from][to]!=-1)
return cache[from][to];
int iter,result = INT_MAX;
/*We put the paranthesis at every possi
is minimum */
for(iter=from;iter<to;iter++)
/* Update the result every time */
result= min(result,multiply(from,ite
return result;
/* Input Format: First integer must be the nu
rows of first matrix, columns of first matri
*/
7/21/2019 Algorithms_ Dynamic Programming - Matrix Chain Multiplication With C Program Source Code - The Learning Point
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int main()
/*Initialising cache to -1 */
memset(cache, -1,sizeof(cache));
int number_of_matrices;
scanf("%d",&number_of_matrices);
scanf("%d",&d[0]); int iter;
for(iter=1;iter<=number_of_matrices;ite
scanf("%d",&d[iter]);
printf("%d\n",multiply(1,number_of_mat
Related
Tutorials
(common
examples
of
Dynamic
Programming):
Integer
Knapsack
problem
An elementary
problem, often
used to introduce
the concept of
dynamic
programming.
Matrix Chain
Multiplication
Given a long
chain of matrices
of various sizes,
how do you
parenthesize
them for the
purpose of
7/21/2019 Algorithms_ Dynamic Programming - Matrix Chain Multiplication With C Program Source Code - The Learning Point
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11/30/2015 Algorithms: Dynamic Programming - Matrix Chain Multiplication with C Program Source Code - the learning point
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multiplication -
how do you chose
which ones to
start multiplying
first?
Longest
Common
Subsequence
Given two
strings, find the
longest
common sub
sequence between
them.
Some
Important
Data
Structures
and
Algorithms,
at a
glance:
Arrays :
Popular
Sorting
and
Searching
Algorithms
Bubble
Sort
Insertion
Sort
Selection
Sort
Shell
Sort
Merge Quick
Heap
Binary
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Sort Sort Sort Search
Algorithm
Basic Data
Structures
and
Operations
on them
Stacks Queues Single
Linked
List
Double
Linked
List
Circular
Linked
List
1.
Tree Data
Structures
Binary
Search Trees
Heaps Height
Balanced
Trees
Graphs and
Graph
Algorithms
Depth First
Search
Breadth
First Search
Minimum
Spanning
Trees: Kruskal
Algorithm
Minumum
Spanning
Trees: Prim's
Algorithm
Dijkstra
Algorithm for
Shortest
Paths
Floyd
Warshall
Algorithm
for Shortest
Paths
Bellman Ford
Algorithm
Popular
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Algorithms in
Dynamic
Programming
Dynamic
Programming
Integer
Knapsack
problem
Matrix Chain
Multiplication
Longest
Common
Subsequence
Greedy
Algorithms
Elementary
cases :
Fractional
Knapsack
Problem,
Task
Scheduling
Data
Compression
using
Huffman
Trees
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