为什么我们需要“ -'0'”来修改数组？

Question

This is code from C by Dennis Ritchie, chapter "Array":

#include <stdio.h>
/* count digits, white space, others */
main()
{
    int c, i, nwhite, nother;
    int ndigit[10];
    nwhite = nother = 0;
    for (i = 0; i < 10; ++i)
        ndigit[i] = 0;
    while ((c = getchar()) != EOF)
        if (c >= '0' && c <= '9')
            ++ndigit[c-'0'];
        else if (c == ' ' || c == '\n' || c == '\t')
            ++nwhite;
        else
            ++nother;
    printf("digits =");
    for (i = 0; i < 10; ++i)
        printf(" %d", ndigit[i]);
    printf(", white space = %d, other = %d\n", nwhite, nother);
}

Why do we need -'0' in this line?

++ndigit[c-'0'];

If I change it to ++ndigit[c] , the program doesn't work properly. Why can't we just write ++ndigit[c] ?

I already read the explanation of the book, but I don't understand it.

This works only if '0', '1', ..., '9' have consecutive increasing values. Fortunately, this is true for all character sets. By definition, chars are just small integers, so char variables and constants are identical to ints in arithmetic expressions. This is natural and convenient; for example c-'0' is an integer expression with a value between 0 and 9 corresponding to the character '0' to '9' stored in c, and thus a valid subscript for the array ndigit

Answer 1

to understand why we need "-'0'" you first need to understand ASCII table - http://www.asciitable.com/

now you need to understand that every character in C is represented by a number between 0 and 127 ( 255 for extended ).

for example if you'll print the character '0' for his numeric value:

printf( "%d", '0' );

output: 48

now you've declared an array of size 10 - ndigit[ 10 ] , where the n cell represent the number of times the number n was given as input.

so if you receive '0' as input you'd want to do ndigit[ 0 ]++ so you need to convert from char to integer. and you can do that by subtracting 48 ( = '0' )

thats why we use the line ++ndigit[c-'0'];

if c = '5', we will get

++ndigit['5' - '0']

++ndigit[ 53 - 48 ]

++ndigit[ 5 ]

exactly like we wanted it to be

Answer 2

c = getchar() will store the character code read to c , and it is differ from the integer that the character stands for.

Quote from N1256 5.2.1 Character sets

. In both the source and execution basic character sets, the value of each character after 0 in the above list of decimal digits shall be one greater than the value of the previous.

As this shows, the character codes for decimal digits are continuous, so you can convert the character code of decimal digits to the integer that the characters stand for by subtracting '0' , which is 0 's character code, from the character code.

In conclusion, c-'0' yields the integer that the character in c stands for.