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58<span id="Multidimensional-Arrays"></span><div class="header">
59<p>
60Next: <a href="Constructing-Array-Values.html" accesskey="n" rel="next">Constructing Array Values</a>, Previous: <a href="Limitations-of-C-Arrays.html" accesskey="p" rel="prev">Limitations of C Arrays</a>, Up: <a href="Arrays.html" accesskey="u" rel="up">Arrays</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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62<hr>
63<span id="Multidimensional-Arrays-1"></span><h3 class="section">16.7 Multidimensional Arrays</h3>
64<span id="index-multidimensional-arrays"></span>
65<span id="index-array_002c-multidimensional"></span>
66
67<p>Strictly speaking, all arrays in C are unidimensional. However, you
68can create an array of arrays, which is more or less equivalent to a
69multidimensional array. For example,
70</p>
71<div class="example">
72<pre class="example">struct chesspiece *board[8][8];
73</pre></div>
74
75<p>declares an array of 8 arrays of 8 pointers to <code>struct
76chesspiece</code>. This data type could represent the state of a chess
77game. To access one square&rsquo;s contents requires two array index
78operations, one for each dimension. For instance, you can write
79<code>board[row][column]</code>, assuming <code>row</code> and <code>column</code>
80are variables with integer values in the proper range.
81</p>
82<p>How does C understand <code>board[row][column]</code>? First of all,
83<code>board</code> is converted automatically to a pointer to the zeroth
84element (at index zero) of <code>board</code>. Adding <code>row</code> to that
85makes it point to the desired element. Thus, <code>board[row]</code>&rsquo;s
86value is an element of <code>board</code>&mdash;an array of 8 pointers.
87</p>
88<p>However, as an expression with array type, it is converted
89automatically to a pointer to the array&rsquo;s zeroth element. The second
90array index operation, <code>[column]</code>, accesses the chosen element
91from that array.
92</p>
93<p>As this shows, pointer-to-array types are meaningful in C.
94You can declare a variable that points to a row in a chess board
95like this:
96</p>
97<div class="example">
98<pre class="example">struct chesspiece *(*rowptr)[8];
99</pre></div>
100
101<p>This points to an array of 8 pointers to <code>struct chesspiece</code>.
102You can assign to it as follows:
103</p>
104<div class="example">
105<pre class="example">rowptr = &amp;board[5];
106</pre></div>
107
108<p>The dimensions don&rsquo;t have to be equal in length. Here we declare
109<code>statepop</code> as an array to hold the population of each state in
110the United States for each year since 1900:
111</p>
112<div class="example">
113<pre class="example">#define NSTATES 50
114{
115 int nyears = current_year - 1900 + 1;
116 int statepop[NSTATES][nyears];
117 <span class="roman">&hellip;</span>
118}
119</pre></div>
120
121<p>The variable <code>statepop</code> is an array of <code>NSTATES</code> subarrays,
122each indexed by the year (counting from 1900). Thus, to get the
123element for a particular state and year, we must subscript it first
124by the number that indicates the state, and second by the index for
125the year:
126</p>
127<div class="example">
128<pre class="example">statepop[state][year - 1900]
129</pre></div>
130
131<span id="index-array_002c-layout-in-memory"></span>
132<p>The subarrays within the multidimensional array are allocated
133consecutively in memory, and within each subarray, its elements are
134allocated consecutively in memory. The most efficient way to process
135all the elements in the array is to scan the last subscript in the
136innermost loop. This means consecutive accesses go to consecutive
137memory locations, which optimizes use of the processor&rsquo;s memory cache.
138For example:
139</p>
140<div class="example">
141<pre class="example">int total = 0;
142float average;
143
144for (int state = 0; state &lt; NSTATES, ++state)
145 {
146 for (int year = 0; year &lt; nyears; ++year)
147 {
148 total += statepop[state][year];
149 }
150 }
151
152average = total / nyears;
153</pre></div>
154
155<p>C&rsquo;s layout for multidimensional arrays is different from Fortran&rsquo;s
156layout. In Fortran, a multidimensional array is not an array of
157arrays; rather, multidimensional arrays are a primitive feature, and
158it is the first index that varies most rapidly between consecutive
159memory locations. Thus, the memory layout of a 50x114 array in C
160matches that of a 114x50 array in Fortran.
161</p>
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164<p>
165Next: <a href="Constructing-Array-Values.html" accesskey="n" rel="next">Constructing Array Values</a>, Previous: <a href="Limitations-of-C-Arrays.html" accesskey="p" rel="prev">Limitations of C Arrays</a>, Up: <a href="Arrays.html" accesskey="u" rel="up">Arrays</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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