GATE C Programming formula sheet

Holds for any fixed-width integer type once its width $n$ in bits and its signedness are known. Use it to check whether a constant fits the type it is stored in.

The standard leaves this conversion implementation-defined. On the two's complement machines these notes assume, the result is the value above. For example, 200 stored in a signed 8-bit char gives $200-256=-56$. An unsigned $n$-bit type always stores $r$, and that case is defined by the standard.

For any array a with element type T. The same value is the address a + i. C arrays always start at index 0, and memory is byte-addressable.

The array is declared T a[R][C]. C is the number of COLUMNS (the row length), i is the row index and j is the column index, both starting at 0. The number of rows R does not appear.

For a function that makes exactly one recursive call, on $n-1$, and stops at n == 0 without a further call (for example, a factorial with base case n == 0). $C(n)$ counts the initial call and the base-case call. If the base case is at n == 1 instead (with $n\ge 1$), the count is $n$. Always check where the base case fires.

For a function that makes one recursive call on n / 2 (integer division) and stops at n == 0, like bin above. The calls that print or do work (those with $n\ge 1$) number $\lfloor {\log }_{2}n\rfloor +1$, which is the number of bits of $n$. The extra call is the base case n == 0.