Is the solution of 5.1 in Cracking the Coding Interview wrong?

Question

For I have a coming technical interview, I start to study the book "Cracking the Coding Interview" recently.

When I was practicing the question of 5.1, I found the solution of the book is different from mine.

The question is:

You are given two 32-bit numbers, N and M, and two bit positions, i and j. Write a method to set all bits between i and j in N equal to M (eg, M becomes a substring of N located at i and starting at j). EXAMPLE:

Input: N = 10000000000, M = 10101, i = 2, j = 6
Output: N = 10001010100

The solution is:

public static int updateBits2(int n, int m, int i, int j) {
    int max = ~0;
    int left =  max - ((1 << j) - 1);
    int right = (1 << i) - 1;
    int mask = left | right;
    int maskN = mask & n;
    int result = maskN | (m << i);
    return result;
}

The key point is to create a mask to set the bit from i to j of n to 0, and left shift m to i position and OR the m and n.

When the input is n=89, m=3, i=2, j=4, the answer should be 77, for:

n = 1011001
m = 011
n with 2 to 4 set by m = 1001101 = 77 

but the result of the solution is 93.

Then I found out that the mask create by the solution lacks one 0 bit in the left side. For example, the mask should be 1100011 with the given inputs above. But the mask created by the solution is 1110011.

I fix this by change this line

int left =  max - ((1 << j) - 1);

to

int left =  max - ((1 << j + 1) - 1);

So my question is, is the solution wrong or do I miss something?

Answer 1

You can tell by the EXAMPLE, where i=2, j=6, and 5 bits are changed, that [i,j] is meant to be an inclusive range. So if you have i=2 and j=4, you should be setting 3 bits, not 2.

So the function you posted (I can't tell if it's yours or the referenced one) called updateBits2 is incorrect.

However, your fix fails when j==31 , and that is something they would bug you about in a coding interview. Instead of (1<<(j+1))-1 , use (1<<j)|((1<<j)-1) , or shorten the whole line to left = -2<<j;

Answer 2

I came across the same issue. I think the solution was wrong.

int left =  max - ((1 << j) - 1);

should be changed to:

int left =  max - ((1 << j + 1) - 1);