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int main() { double x[] = { 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9 }; int n=8; print(x,n); double m = mean(x,n); double s = stdev(x,n); cout << "mean = " << m << ", std dev = " << s << endl; for (int i=0; i<n; i++) cout << "x[" << i << "] = " << x[i] << ", z[" << i << "] = " << (x[i] - m)/s << endl; } int main() { double x[] = { 2.5, 4.5, 6.3, 6.7, 7.2, 7.5, 7.8, 9.9 }; int n=8; print(x,n); double m = mean(x,n); double s = stdev(x,n); cout << "mean = " << m << ", std dev = " << s << endl; for (int i=0; i<n; i++) { double z = (x[i] - m)/s; cout << "x[" << i << "] = " << x[i] << ", z[" << i << "] = " << z; if (z >= 1.5) cout << " = A" << endl; else if (z >= 0.5) cout << " = B" << endl; else if (z >= -0.5) cout << " = C" << endl; else if (z >= -1.5) cout << " = D" << endl; else cout << " = F" << endl; } } void build_pascal(int p[][SIZE], int n) { assert(n > 0 && n < SIZE); for (int i=0; i<SIZE; i++) for (int j=0; j<SIZE; j++) if (i>n || j>i) p[i][j] = 0; else if (j==0 || j==i) p[i][j] = 1; else p[i][j] = p[i-1][j-1] + p[i-1][j]; } double max_of_col(Matrix m, int n, int j) { double max=m[0][j]; for (int i=1; i<n; i++) if (m[i][j]>max) max = m[i][j]; return max; } double minimax(Matrix m, int n) { assert(n>0 && n < SIZE); double minimax=max_of_col(m,n,0); for (int j=1; j<n; j++) { double mm = max_of_col(m,n,j); if (mm<minimax) minimax = mm; } return minimax; }
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7.1 THE REFERENCE OPERATOR Computer memory can be imagined as a very large array of bytes. For example, a computer with 256 MB of RAM (256 megabytes of random-access memory) actually contains an array of 268,435,456 (228) bytes. As an array, these bytes are indexed from 0 to 268,435,455. The index of each byte is its memory address. So a 256 MB computer has memory addresses ranging from 0 to 268,435,455, which is 0x00000000 to 0x0fffffff in hexadecimal (see Appendix G). The diagram at right represents that array of bytes, each with its hexadecimal address. A variable declaration associates three fundamental attributes to the variable: its name, its type, and its memory address. For example, the declaration
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0x00000000 0x00000001 0x00000002 0x00000003 0x00000004 0x00000005 0x00000006 0x00000007 0x00000008 0x0064fdee 0x0064fdef 0x0064fdf0 0x0064fdf1 0x0064fdf2 0x0064fdf3 0x0064fdf4 0x0064fdf5 0x0064fdf6 0x0064fdf7 0x0064fdf8 0x0064fdf9 0x0064fdfa 0x0064fdfb 0x0064fdfc 0x0064fdfd 0x0064fdfe 0x0064fdff 0x0064fe00 0x0064fe01 0x0ffffff7 0x0ffffff8 0x0ffffff9 0x0ffffffa 0x0ffffffb 0x0ffffffc 0x0ffffffd 0x0ffffffe 0x0fffffff
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associates the name n, the type int, and the address of some location in memory where the value of n is stored. Suppose that address is 0x0064fdf0. Then we can visualize n like this:
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0x0064fdf0
The variable itself is represented by the box. The variable s name n is on the left of the box, the variable s address 0x0064fdf0 is above the box, and the variable s type int is below the box. On most computers, variables of type int occupy 4 bytes in memory. 0x0064fdee 0x0064fdef So the variable n shown above would occupy the 4-byte block of 0x0064fdf0 0x0064fdf1 0x0064fdf2 memory represented by the shaded rectangle in the diagram at right, 0x0064fdf3 0x0064fdf4 using bytes 0x0064fdf0, 0x0064fdf1, 0x0064fdf2, and 0x0064fdf3. 0x0064fdf5 0x0064fdf6 Note that the address of the object is the address of the first byte in the block of memory where the object is stored. If the variable is initialized, like this:
int n=44;
then the two representations look like this:
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