A palindrome is a word, sentence, or sequence that reads the same forward and backward — ignoring differences in capitalization for word-level palindromes. Examples: “racecar”, “GADAG”, “level”, “9009”. The most efficient check uses a two-pointer approach: one pointer starts at the left end, one at the right, and they advance toward each other until they …
The transpose of a matrix is formed by flipping it over its main diagonal — rows become columns and columns become rows. If the original matrix is of order M×N, its transpose is of order N×M, where element A[i][j] becomes B[j][i]. Matrix A (3×2): Transpose B (2×3): 1 2 1 3 5 3 4 → …
This program reads two matrices of the same order, computes either their sum or difference (user’s choice), and then finds the trace of the result. The trace of a matrix is the sum of its main diagonal elements (positions where row index equals column index). It is defined for any matrix, not just square ones …
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 …