I hear and I forget.
I see and I remember.
I do and I understand.
-- Confucius
- [MARTIN] R. Martin, The Clean Coder
- [SEDGEWICK] R. Sedgewick, K. Wayne, Algorithms (4th ed.)
- [CORMEN] T. Cormen, Ch. Leiserson, R. Rivest, C. Stein, Introduction to Algorithms (2rd ed.)
- [WIRTH] N. Wirth, Algorithmen und Datenstrukturen
- [LAAK] G. Laakman-McDowell, Cracking the Coding Interview: 150 Programming Questions and Solutions
- [G4G] www.geeksforgeeks.org
My solutions to algorithmic problems are grouped in distinct packages:
Implement a converter of an integer to its binary representation eg.:
- 5 as binary is: 101
- 6 as binary is: 110
(Use the Deque interface.)
Compute Newton (binomial) coefficient with limits:
- cap their value if it is going to be bigger than 1_000_000_000,
- ensure there is no arithmetic overflow,
- do not use the BigDecimal / BigInteger classes of Java.
Implement a solution to the Dining Philosophers problem.
Note: threads should avoid circular deadlocks, so there are several directed graph representing synchronisation on forks is a correct solution.
Implement a generalized solution to this problem. Any valid graph representing philosophers taking forks should define the "protocol" of fork-usage.
Suppose a graph is represented in a 2-dimensional matrix. Write an algorithm that detects whether a directed graph has a cycle.
Implement Max-Heap along with its operations:
- insert into heap
- delete from root
- build heap / heapify
- sift up
- sift down.
- Implement basic operations on one-directional pointer list.
- Implement also the following additional operations:
- get the kth element to the end of the list (see [LAAK], ex. 2.2).
- check if a given list is a palindrome.
- There is an array of integers A[0..n]. Create and populate an array of boolean values according to the following rule (predicate): for each i in [0..n]: B[i] == true <=> exists j in [0..i): A[j]==i and exists j in (i..n]: A[j]==i. (The solution must be linear O(n) in computation time and space.)
Implement an algorithm that counts the number of countries represented by areas of the same value reachable by moving North, East, West, South finite number of steps (ie. that are in each other's von Neumann surroundings) within a 2D-array.
Implement this algorithm in multiple ways:
- using recursion
- without recursion but with a queue/deque.
Observe which approach is:
- the fastest,
- the most capable of handling big data.
Find three numbers a, b, c (a "troika" in Russian;) ) such that:
- a < b < c
- exists i<j<k in [0..n]: nums[i]=a && nums[j]=b && nums[k]=c for a given array of integers
nums.
Implement an algorithm that for a given 2D array simulates a flood by changing its fields according to the following rules:
- floodable fields are those that have the same value as the initial flooding field
- and that can be reached only by moving north/east/south/west from an already flooded field.
Top 75 Programming Interview Questions, no 57: write a program to print Floyd’s Triangle.
Find the longest plateau (constant value segment in a table.
If a set is represented as a monotonic array, implement CRUD operations on a set:
- union of sets
- union of sets without duplicates
- intersection
- minus (exception)
Construct a 2-dim. array like this for a given number > 0 (below an example for 3):
[1, 1, 1, 1, 1]
[1, 2, 2, 2, 1]
[1, 2, 3, 2, 1]
[1, 2, 2, 2, 1]
[1, 1, 1, 1, 1]
Write an algorithm that calculates the length of the longest segment A[l..r] of an array (sequence) of integers A[0..n] (l,r in [0..n]) for which the following conditions holds:
for all i,j in [l..r]:
abs( A[i] - A[j] ) <= tol
where tol (tolerance) is a positive integer. The algorithm should be O(n^2) fast.
A couple is two adjacent identical items in a sequence. You are to remove all couples, then process the list recursively to remove any additional couples formed by the removal of the original couples. For instance, given the list {red blue green green blue red yellow}, first remove the green couple, leaving {red blue blue red yellow}, then remove the blue couple, leaving {red red yellow}, and finally remove the red couple, leaving {yellow}.
In an array, we begin with any bar-chart (or row of close-packed 'towers', each of unit width), and then it rains,
completely filling all convex enclosures in the chart with water. In the following example below, a bar chart
representing the values [5, 3, 7, 2, 6, 4, 5, 9, 1, 2] has filled, collecting 14 units of water:
X
X
X@@@@X
X@X@@X
X@X@X@XX
X@X@XXXX
XXX@XXXX
XXXXXXXX@X
XXXXXXXXXX
(where X is enclosure and @ is a quantity of water).
Implement the Dijkstra algorithm to evaluate arithmetic infix expressions.
- "2+(1+2)*(3-3)" ->
- "(1+((2+3)(45)))" -> 101.0
Write an evaluator of postfix arithmetic expressions. For example, it should return the following results given postfix expressions:
- postfix("7 3 +") = 7 + 3 = 10
- postfix("7 3 + 8 1 - *") = (7 + 3) * (8 - 1) = 70.
Tokenize an expression given the list of tokens eg.:
- "(1+sqrt(5))/2" --> ["(","1","+","sqrt","(","5",")",")","/","2"]
- "1 + (2 - 3)" --> ["1","+","(","2","-","3",")"]
A binary search tree can be described using the following notation "Grammar":
- _ ∈ Grammar
- X ∈ Integers => (X _ _) ∈ Grammar
- X ∈ Integers, L ∈ Grammar, R ∈ Grammar => (X L R).
Implement an algoritm that creates a Binary Tree given an expression from tha above described grammar. For example:
|1|
/ \
|2| |3|
/ \
|4| |5|
\
|6|
is represented by:
(1 (2 (4 _ _) _) (3 _ (5 _ (6 _ _))))
- Implement the binary search that finds the first and the last occurence of a value in a table, use it to get the number of occurrences.
- Implement an algorithm that finds an index i in a ascending (monothonic) array A of unique integers where A[i]==i ( see [LAAK], ex. 9.3).
Use binary search to find the maximum value in a bitonic table.
Use binary search to find the minimum value in an antibitonic table. A table A[0..n] of Integers is antibitonic when there exists an index i (0<i<n) for which:
- A[0..i] forms a strictly decreasing sequence
- A[i..n] forms a strictly increasing sequence. (So the graph of i->A[i] is similar to the letter "V".)
Implement HeapSort (use previously implemented max-heap).
Find the length of the longest balanced substring of a given string. If a string does not have any balanced substring, then return -1. A string is considered balanced if for any character it contains, it contains both the lower case variant and the upper case variant of the character (in any amount) eg:
- "aaaaaA" - is balanced,
- "baBASssssa" - is balanced,
- "s" - is not balanced,
- "SsSx" - is not balanced,
- "sSxXX" - is balanced, etc.
Check if a given string is a cyclic transformation of another, eg.:
- abbbc <-> bbbca
- aabb <-> bbaa.
Write a stack client Parentheses.java that reads a string of parentheses, square brackets, and curly braces from
standard input and uses a stack to determine whether they are properly balanced. For example, your program should
print true for "[()]{}{[()()]()}" and false for "[(])".
Implement a breadth-first algorithm. A binary tree should be represented as a pointer-based data structure. The algorithm should use a queue. For example, a tree:
|a|
/ \
|b| |c|
/ \ \
|d| |e| |f|
\
|g|
should be printed as: a b c d e f g.
Binary Search Trees:
- Implement an algorithm that finds a successor of a given element of a binary search tree.
Find the k-th largest element in a binary search tree (see: [G4G]).
Implement an algorithm that computes length of the longest unique path in a binary tree that begins in the tree root. For example, in given tree:
|1|
/ \
|2| |3|
/ \ \
|4| |3| |1|
\
|8|
the longest path is 1-2-4 or 1-2-3
Implement an algorithm that prints a binary tree in: pre-order, in-rder and post-order.
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