A polynomial of degree N is an expression of the form: P(x) = ANxN + AN-1xN-1 + … + A1x + A0 The naïve way to evaluate this requires computing each power xk separately, which takes O(N²) multiplications in total. Horner’s method rewrites the polynomial as a nested product that requires only N multiplications and …
This program reads N integers and finds the two largest values without sorting the array, then computes their average. The key technique: maintain two variables — first (the largest seen so far) and second (the second-largest). Scan each new element and update these two variables in one pass. Time complexity: O(n). Space: O(1) — no …
Given N real numbers, this program computes three fundamental descriptive statistics: the mean (arithmetic average), the variance (how spread out the values are from the mean), and the standard deviation (the square root of variance — in the same units as the data). These are the first three statistics taught in any probability or data …
Linear search (also called sequential search) is the simplest searching algorithm: start at the first element, compare each element to the key, and stop when you find a match or exhaust the array. It makes no assumption about the data being sorted. It runs in O(n) time and O(1) space — no extra memory needed …
C Program to Find Sum and Average of an Array This program reads N integers (positive, negative, and zero) into an array and computes three values: the sum of negatives, the sum of positives, and the average of all elements. Algorithm Read N (array size) from the user. Read N integers into the array one …
This C program computes the value of cos(x) by summing its Taylor series up to a given accuracy, then checks the result against the built-in cos() library function. It’s a great exercise in loops, floating-point arithmetic, and how mathematical functions are actually approximated inside a computer. The Cosine Series The Taylor series for cosine (with …