Math & Geometry

Matrix rotation, spiral order, number tricks, and fast exponentiation.

Reach for it when

Transform a matrix in place
Digit manipulation, overflow, big numbers as strings
Power, modulo, or cycle detection in number sequences

Core idea

Many of these reduce to a known identity: rotating a matrix 90 degrees clockwise is transpose then reverse each row; x^n is computed by squaring (n halves each step); spiral order peels the boundary layer by layer with four shrinking bounds.

Template · O(log n) for fast power; O(n²) for an n by n matrix

def my_pow(x, n):
    if n < 0:
        x, n = 1 / x, -n
    result = 1
    while n:
        if n & 1:
            result *= x
        x *= x                # square the base
        n >>= 1               # halve the exponent
    return result

double myPow(double x, long long n) {
    if (n < 0) { x = 1 / x; n = -n; }  // long long: -INT_MIN overflows int
    double result = 1;
    while (n) {
        if (n & 1) result *= x;
        x *= x;                         // square the base
        n >>= 1;                        // halve the exponent
    }
    return result;
}

Common pitfalls

Negative exponents and integer overflow in other languages
Spiral bounds: re-check top and bottom (or left and right) before the return passes

Math & Geometry

Reach for it when

Core idea

Template · O(log n) for fast power; O(n²) for an n by n matrix

Common pitfalls

Practice · 0 / 15 done