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Browse College Algorithms

Stars indicate particularly interesting answers or good places to begin browsing.



Decimal To Fraction Conversion [06/25/1998]
I am trying to find a method (one that can be programmed on a PC) to convert the decimal part of a real number to a fraction represented by integers for the numerator and denominator.

Set Terminology [07/07/1997]
What does the terminology inf{...} mean?

Solving Problems Using Matrices [9/31/1995]
Given a current x,y,z coordinate (i.e. -60,-60,-60) and an angle (i.e. 90 degrees) and a plane to rotate about (i.e. z), what's the formula to solve for x,y,z?

Unsolvable Equations, Feedback Loops, Existence Proofs... [04/14/1997]
How do you solve equations like (9/4)^x = x^(9/4) ?

Applying Logic to an Interesting Problem on Billiard Balls [03/03/2004]
In front of you is a 100 story building. You must determine which is the highest floor you can drop a billiard ball from without it breaking. You have only two billiard balls to use as test objects. If both of them break and you don't know the answer then you have failed at your task. What is the least number of drops needed to be sure you will have determined the breaking point?

Arbitrary-Precision Arithmetic [08/08/2003]
How could I use QBasic V4.5's math to compute numbers that are greater than 10^15 in the quickest way, and yet display every single digit in the product?

Big-O Notation for Measuring Algorithm Efficiency [10/21/2004]
Can you explain the ideas behind the big-O notation?

Big-O Notation in Matrix Multiplication [12/10/2000]
How can I prove that two n x n matrices can be multiplied in O(n^3) time? Also, is there a faster way to multiply them?

Calculators - CORDIC Method [05/16/1999]
How can a computer or calculator calculate square roots, cube roots, Xth root, x^y, logarithm, sine, cosine, ...?

Complexity of Matrix Inversion [04/25/2001]
What is the computational complexity for the general case of inverting an NxN matrix?

Correlation Coefficients of Random Numbers [12/18/2000]
I have to generate random numbers that have a certain correlation coefficient.

Creating a List of Permutations with a Computer Program [07/31/2007]
I'm writing a computer program to list all the permutations of a given set of numbers, but am not sure of the best way to do it. Any ideas?

Data Compression [08/10/2003]
Is there an algorithm that can reduce any binary number to a much smaller binary number, then later be reversed to regain the original number? It has to work for any binary number.

Elliptic Curves: Algorithms [03/11/1999]
Find the number of points on the curve over F sub p for an elliptic curve y^2 = x^3 + 1.

Equation Solving with Newton-Raphson Method [07/23/2004]
Is there a way to solve F = A*(((1+i)^n) - 1)/i for i, such that we have i = ...? I'm thinking I need to use a logarithm, but I'm stuck.

Erlang B [10/22/2002]
I need to know how to calculate the addition of numbers using logarithms: 1 + 2 + 3. There is a step that requires adding numbers that exceed Excel's limits. How can I use logs to add the numbers?

Euclidean Algorithm [5/13/1996]
How can we prove that Euclid's method for finding the highest common factor for two numbers will work for all values?

Euclidean Algorithms [3/13/1996]
What is the Euclidean algorithm? What is a "constructible" number? What can you tell me about Diophantine equations?

Euclidean and Division Algorithms [11/26/1997]
Can you show and explain the proofs of the Euclidean Algorithm and the Division Algorithm?

Euclidean Modular Inverse Algorithm [08/26/1997]
How to program an algorithm for finding the modular inverse... the number that when multiplied by the original number produces bar 1?

Euler's Phi Function Applied to Large Numbers [08/23/2004]
I'm trying to find the phi value of a large (10-digit) composite number. Can it be done in polynomial time, and if so, is there an algorithm?

Explaining the Euclidean Algorithm [10/27/1998]
In the Euclidean Algorithm (or the Division Algorithm), why is the last divisor the greatest common factor?

Factoring Large Numbers [10/26/1998]
Can you give me an algorithm for factoring large numbers? What about the Pollard Rho Factoring Algorithm?

Factoring Polynomials over Real and Complex Numbers [07/17/2006]
I am having difficulties factoring polynomials like x^4 - 15x^2 - 75. It is irreducible over the integers but its graph suggests there are in fact roots. How can I factor over the real and complex numbers?

Fast Multiplication Algorithms for Large Integers [08/16/1997]
Are there elementary algorithms for computing the product of 2 n-digit numbers in less than O(n^1.58) time?

Ferrari's Method for Quartics [04/16/1999]
Could you explain Ferrari's method for quartics?

Finding a Series Given the Sum [09/27/1999]
How can I find all series of consecutive integers whose sum is a given value x?

A Formula for Iterating [10/11/2002]
Find the value of x if 3 = sqrt(x+sqrt(x_sqrt(x+sqrt(x)))).

Fraction Algorithm [03/19/2002]
I have been having trouble making an application that can convert a finite decimal to a fraction without doing 78349/1000000.

Generating Random Numbers [02/24/2001]
Would you know of any congruential models for the generation of random numbers?

Greatest Common Factor [03/28/1997]
How do you find the greatest common factor?

How a CPU Adds Decimal Numbers [10/22/2000]
How does an 8-bit CPU add up two four-digit decimal numbers, and why does it take four operations to do so?

How to Solve Equations with No Analytic Solution Method [10/26/2005]
A discussion of solving equations that can't be solved analytically by using iterative estimation methods including bisection, false position, and Newton's method. The equation x(e^x) = 3 is used as an example.

The Hungarian Job Assignment [03/10/2011]
A company owner writes in for help cost-efficiently assigning tasks to different employees when each one commands her own fee for every job. Invoking a little graph theory, Doctor Jacques introduces the Hungarian algorithm and walks through an application to an example assignment.

An Introduction to Basic Diophantine Equations [08/27/2007]
A birdcage contains both 2-legged and 1-legged birds, and there are a total of 11 legs in the cage. Use a Diophantine equation to find all possible combinations of birds.

Inverses in the Field GF(2^8) [11/07/2000]
How can I get the multiplicative inverse of a byte in the polynomial field GF(2^8)?

An Iterative Method of Calculating Pi [06/09/2004]
I recently saw a method of calculating pi that involves an iterative function, P(n + 1) = P(n) + sin(P(n)) where P(n) is the approximation of pi at the nth iteration.

Julian to Calendar Date Conversion [02/24/2001]
Can you show me an algorithm to convert Julian date values to calendar date values? For example, Julian date 2451964 = 02/24/2001.

Karatsuba Multiplication [10/15/2007]
Can you explain the ideas and steps behind the Karatsuba method of multiplying?

Matching Invoices with Report Totals [10/31/2000]
I have 14 invoice values and 2 report totals. The sum of the invoices for each report should be the report total. Is there a fast way of finding which invoices go with each report, or determining if it is even possible?

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