The identity matrix (also called the unit matrix) is a square matrix in which every element on the main diagonal is 1, and all off-diagonal elements are 0. It is the multiplicative identity for matrix multiplication: for any matrix A, multiplying by the identity matrix I gives IA = AI = A. This program reads …
Two matrices are equal if and only if they have the same dimensions (same number of rows and same number of columns) and every corresponding pair of elements is equal: A[i][j] == B[i][j] for all i, j. If the dimensions differ, equality is impossible. This program checks both conditions. The original had void main(), exit(1) …
Computing x raised to the power n (written xn) naively requires n multiplications. Binary exponentiation (also called fast power or exponentiation by squaring) reduces this to O(log n) multiplications by halving the exponent at each step: if n is even, compute xn/2 and square it; if n is odd, multiply x by xn-1. The original …
The standard library’s strlen() counts characters in a string by walking from the first character until it reaches the null terminator (‘\0’) — the zero byte that marks the end of every C string. Implementing strlen() yourself is a classic exercise that teaches exactly how strings work in C. The original post had two serious …
This program converts a given number of days into years, weeks, and remaining days using integer division and modulo arithmetic. The formula uses 365 days per year and 7 days per week (leap years are ignored). It is a straightforward exercise in chained division and remainder operations. The original post used void main() and broken …
A cube is a three-dimensional shape with six equal square faces. Given the side length s, the surface area is 6s² (six faces, each with area s²) and the volume is s³. This program reads the side length and computes both values using only basic arithmetic — no need for pow() and the -lm flag …