Careercup | Chapter 5

5.1 You are given two 32-bit numbers, N andM, and two bit positions, i and j. Write a method to insert M into Nsuch that M starts at bit j and ends at bit i. You can assume that the bits j through i have enough space to fit all ofM. That is, ifM= 10011, you can assume that there are at least 5 bits between j and i. You would not, for example, have j-3 and i=2, because M could not fully fit between bit 3 and bit 2.

update某一位的时候，记得要把该位清零先。

Method 1: mask = ~((1<<(i-j+1)-1)<<i)

Method 2：mask=(~0<<(j+1)) | ((1<<i) - 1)

5.2 Given a real number between 0 and 7 (e.g., 0.72) that is passed in as a double, print the binary representation. If the number cannot be represented accurately in binary with at most 32 characters, print "ERROR."

小数的表示啊。用除法得到的是reverse的串。用乘法可以得到正串。

5.3 Given a positive integer, print the next smallest and the next largest number that have the same number of 7 bits in their binary representation.

用位操作方法很直观，用算术方法比较巧妙一些。arithmetically。 

getNext: n + (1 << c0) + (1 << (c1-1)) - 1;

getPrev: n - (1 << c1) - (1 << (c0-1)) + 1; 

 5.4 Explain what the following code does: ((n & (n-1)) == 0).

check一下n是不是2的k次方。

也可以用来检验二进制中1的个数。

5.5 Write a function to determine the number of bits required to convert integer A to integer B.

就是用n&(n-1)来计算。这个操作每次可以把least significant bit为1的给清零。

5.6 Write a program to swap odd and even bits in an integer with as few instructions as possible (e.g., bit 0 and bit! are swapped, bit 2 and bit 3 are swapped, and so on)

巧妙。移偶数位，移奇数位。

5.7 An array A contains all the integers from 0 through n, except for one number which is missing. In this problem, we cannot access an entire integer in A with a single operation. The elements of A are represented in binary, and the only operation we can use to access them is "fetch thejth bit ofAfi]," which takes constant time. Write code to find the missing integer. Can you do it in 0(n) time?

最简单的做法就是累加0到n，用求和公式得到的和减去计算出来的和，得到missing number。复杂度是O(nlgn)。因为n有lgn+1个bit。其实lgn一般也就32，如果n>>32，当然这种算法还是可以的。

所以还是要二分，想到了要按位计数，但是没有想到比较0的个数和1的个数。

在确定了LSBi的值后，需要去掉那些不符合的结果。

5.8 A monochrome screen is stored as a single array of bytes, allowing eight consecutive pixels to be stored in one byte. The screen has width w, where w is divisible by 8 (that is, no byte will be split across rows). The height of the screen, of course, can be derived from the length of the array and the width. Implement a function drawHorizontalLine(byte[] screen, int width, intxl, intx2, inty) which draws a horizontal line from (x 1, y) to (x2, y).

string binary(int n) {
    stringstream s;

    //while (n) { // negative number will always refill 1s for the most significant digit 
    for (int i = 0; i < 32; ++i) {
        s << (char)('0' + (n & 0x01));
        //cout << (char)('0' + (n & 0x01)) << endl;
        //cout << n << endl;
        n = n >> 1;
    }
    string ret = s.str();
    int i = 0, j = ret.length() - 1;
    while (j > i) {
        swap(ret[i], ret[j]);
        i++; j--;
    }
    return ret;
}

// 5.3
int getNextSmallest(int n) {
    int i = 0, c1 = 0;
    for (; i <= 31 && (n & (1 << i)) == 0; ++i); 
    for (; (n & (1 << i)) != 0; ++i, ++c1);
    if (i > 31) return -1; 
    n |= 1 << i; // set i-th bit
    n &= ~0 << i;
    n |= ((1 << (c1 - 1)) - 1);
    return n;
}

int getPrevLargest(int n) {
    // example: 11100111
    int i = 0, c1 = 0;
    for (; (n & (1 << i)) != 0; ++i, ++c1); // ignore 1s, c1=3
    for (; i <= 31 && (n & (1 << i)) == 0; ++i); // find first 1, i=5
    if (i > 31) return -1; // error, 00001111 
    n &= ~0 << (i + 1); // clear i-th bit, n=11000000
    n |= ((1 << (c1 + 1)) - 1) << (i - c1 - 1); //n=11011110
    return n;
}

// 5.5 
int diffBits(int a, int b) {
    int count = 0;
    for (int n = a ^ b; n != 0; n = n & (n - 1)) {
        count++;
    }
    return count;
}

// 5.6
int swapBits(int n) {
    int ret = 0;
    for (int i = 0; i < 32; i += 2)  {
        int tmp = (n >> i) & 0x03;
        switch (tmp) {
            case 1: ret |= (2 << i); break;
            case 2: ret |= (1 << i); break;
            case 3: ret |= (3 << i); break;
        }
    }
    return ret;
}

int swapBits2(int n) {
    return ((n & 0xaaaaaaaa) >> 1) | ((n & 0x55555555) << 1);
}

// 5.8
void drawLine(char* screen, int width, int x1, int x2, int y) {
    int p1 = y * width + x1, p2 = y * width + x2;
    int b1 = p1 >> 3, b2 = p2 >> 3; //bucket
    int s1 = p1 & 0x07, s2 = p1 & 0x07; //shift
    for (int i = b1 + 1; i < b2; ++i) {
        screen[i] = 0xff;
    }
    int m1 = 0xff >> s1, m2 = ~(0xff >> (s2 + 1)); //mask
    if (b1 == b2) {
        screen[b1] |= (m1 & m2);
    } else {
        screen[b1] |= m1;
        screen[b2] |= m2;
    }
}