How does the decay of single-dimensional and multidimensional arrays in C differ?

Decay of Array Types in C

In C , arrays inherently decay into pointers when used in certain contexts. However, this decay behavior differs between single-dimensional and multidimensional arrays.

Single-Dimensional Array Decay: int[] to int*

When a single-dimensional array is used in a context requiring a pointer, it effectively decays into a pointer to its first element. For example, consider the following code:

<code class="cpp">std::is_same<int*, std::decay<int[]>::type>::value; // true</code>

This returns true because the decay of an int[] type results in an int* type.

Multidimensional Array Decay: int[][1] to int

In contrast, when a multidimensional array is used in a similar context, it does not decay into a pointer to a pointer. Instead, it decays into a pointer to its first element, which is itself an array. For example:

<code class="cpp">std::is_same<int**, std::decay<int[][1]>::type>::value; // false</code>

This returns false because the decay of an int[][1] type results in an int* type, not an int** type.

Decay of Pointer Arrays: int*[] to int

Interestingly, when an array of pointers is created, it decays into a pointer to a pointer. This is evident from the following code:

<code class="cpp">std::is_same<int**, std::decay<int*[]>::type>::value; // true</code>

This observation holds true for any type within an array of pointers, as long as the last dimension is an array. For example, int***[] decays into int*** (or int****), which is a pointer to a pointer to a pointer.

Reason for Decay Differences

The reason for this discrepancy in decay behavior lies in the concept of pointer arithmetic. Single-dimensional arrays naturally align with the behavior of pointers, allowing for efficient pointer arithmetic operations. However, the same is not true for multidimensional arrays, as each dimension represents a different level of indirection. Attempting pointer arithmetic on decaying multidimensional arrays would result in invalid memory access and unpredictable behavior.

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