你能给我解释一下这段按位运算符的代码吗？ [复制]

Question

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What does the statement if (counter & (1<<j)) mean and how does it work? (2 answers)

Closed 11 months ago .

void printPowerSet(char *set, int set_size) {

  unsigned int pow_set_size = pow(2, set_size);
  int counter, j;

  for (counter = 0; counter < pow_set_size; counter++) {
    for (j = 0; j < set_size; j++) {

      if (counter & (1 << j))
        cout << set[j];
    }
    cout << endl;
  }
}

I am not able to understand the if (counter & (1 << j)) part here. How can this code give subsets of a set {a,b,c} ?

Answer 1

The main loop is iterating from 0 to (2^set_size)-1. For example if there are three elements in the set it will iterate from 0 to 7 ((2^3)-1). If you represent it in binary it will be: 000, 001, 010, 011, 100, 101, 110, 111. These are all subsets of a three-element set (1 - we take the element, 0 - we don't take it). Now you only need to iterate and check if we take j-th element (if the j-th bit is equal to 1). The easiest way to do it is to check if (i & (2^j)) is equal to a non-zero value (& is a bitwise operation that for every position in the numbers returns 1 if in both numbers have on this position a lit bit and 0 in any other case). The if operation treats 0 as false and positive values as true, so if the j-th bit is lit the operation will return 2^j and it will be a true value, so this element will be taken to this subset, otherwise if the bit isn't lit the operation will return 0, so this element isn't in this subset.