How to Ensure Positive Results When Using the Modulus Operator with Negative Numbers?

Cleverly solve the problem of taking modulo negative numbers

Many programming languages ​​provide the modulo operator (%), which is used to calculate the remainder after dividing one number by another. However, when this operator is applied to negative numbers, unexpected results may occur.

For example, when executing -1 % 3 in a language like C or Java, the result is -1 instead of the expected 2. This is because the modulo operator usually returns the remainder of a division operation, which may be negative for a negative dividend.

To overcome this problem and get the desired behavior, a custom mod function can be implemented:

<code class="language-c++">int mod(int x, int m) {
    return (x % m + m) % m;
}</code>

Using this function, the following calculation results are as expected:

输入	预期输出	函数输出
-1 % 3	2	mod(-1, 3) = 2
-2 % 3	1	mod(-2, 3) = 1
-3 % 3	0	mod(-3, 3) = 0

How this function works is that it ensures that the result is always positive by adding the modulus to any negative value obtained by the initial modulo operation.

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