Transforming a signal from a function of time or space to frequency(ω) which holds within it’s unique (ω) key also the respected phase(φ) and a respected amplitude/magnitude (A), is called a fourier transform. This is possible because any signal can be represented as a sum of sinusoids. f(x) –> TransformContinue Reading
The Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space( to a new set that spans the same k-dimensional subspace as it’s original set of vectors). When the matrix is full column rank it yields the QR decomposition which is composed of aContinue Reading
This algorithm produces an unbiased permutation: every permutation is equally likely. Shuffling an array of n elements in C++: void fisherYatesShuffling(int *arr, int n_elements) { int shuffled_array[n_elements]; int ind_taken[n_elements]; for (int i = 0; i < n_elements; i++) ind_taken[i] = 0; int index; for (int i = 0; i < n;Continue Reading
Bayes’ Theorem – Is the probability Event A will happen given (|) Event B happened. P(A|B) = P(B|A) * P(A) / P(B) For example (Assume we have 3 out of 4 probabilities): Calculate a probability that an event A(Eating) will happen given (|) that an event B(Exercising) happened. P(A|B) = P(B|A)Continue Reading
Applying (pre multiplying) a matrix to a vector gives you either a rotation or a scale(strech/compress) or both a scale(strech/compress) and a rotation. This is called vector transformation, and the (pre multiplying) matrix is called the transformation matrix. No Rotation Case(Pure Scaling ; EigenValue/Eigen Vector) When a vector transformation byContinue Reading
The Euclidean algorithm is based on the principle that the greatest common divisor (GCD) of two numbers does not change if the larger number is replaced by its difference with the smaller number. This is repeated with successive smaller pairs of numbers until they both are equal, which in thatContinue Reading
Given an array nums of n integers and an integer target, find three integers in nums such that the sum is closest to target. Return the sum of the three integers. You may assume that each input would have exactly one solution. Example: Given array nums = [-1, 2, 1, -4], and target = 1. The sum thatContinue Reading
Given an array nums of n integers, are there elements a, b, c in nums such that a + b + c = 0? Find all unique triplets in the array which gives the sum of zero. Note: The solution set must not contain duplicate triplets. Example: Given array nums = [-1, 0, 1, 2, -1, -4], A solution set is: [ [-1, 0, 1], [-1,Continue Reading
Write a function to find the longest common prefix string amongst an array of strings. If there is no common prefix, return an empty string “”. Example 1: Input: [“flower”,”flow”,”flight”] Output: “fl” Example 2: Input: [“dog”,”racecar”,”car”] Output: “” Explanation: There is no common prefix among the input strings. Note: All givenContinue Reading
Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M. Symbol Value I 1 V 5 X 10 L 50 C 100 D 500 M 1000 For example, two is written as II in Roman numeral, just two one’s added together. Twelve is written as, XII, which is simply X + II. The number twenty seven is written as XXVII,Continue Reading
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