When working with large bitsets in C++, it can be time-consuming to count the number of set bits (1s) in the bitset. One efficient way of counting the number of set bits in a bitset is by using a lookup table.

Why use a lookup table?

A lookup table is a pre-calculated array that maps each possible input to the desired output. In this case, we can use a lookup table to store the number of set bits for all possible 8-bit values (0-255). By using the lookup table, we save computational time by avoiding the need for bit manipulation operations.

Creating the lookup table

To create the lookup table, we can use an array of 256 integers. Each index in the array corresponds to an 8-bit value, and the value stored at that index represents the number of set bits in that particular value.

std::array<int, 256> lookupTable;

void createLookupTable() {
   for (int i = 0; i < 256; ++i) {
      lookupTable[i] = std::bitset<8>(i).count();
   }
}

In the createLookupTable function, we iterate over all possible 8-bit values (from 0 to 255) and use the std::bitset class to initialize a bitset with the current value. We then use the count method of the bitset to count the number of set bits in that value and store it in the lookup table.

Counting set bits using the lookup table

After creating the lookup table, we can use it to count the number of set bits in a given bitset. Let’s assume we have a bitset named myBitset:

std::bitset<32> myBitset;

To count the set bits in myBitset, we can iterate over each 8-bit chunk and use the lookup table to look up the count of set bits for each chunk:

int countSetBits(const std::bitset<32>& bitset) {
   int count = 0;
   for (int i = 0; i < bitset.size() / 8; ++i) {
      count += lookupTable[bitset.to_ulong() >> (i * 8) & 0xFF];
   }
   return count;
}

In the countSetBits function, we divide the size of the bitset by 8 to determine the number of 8-bit chunks. We then iterate over each chunk and calculate the value of the chunk by shifting the bitset by i * 8 and masking it with 0xFF to get the 8 least significant bits. We use this value to look up the count of set bits in the lookup table and add it to the running count.

Conclusion

Using a lookup table is an efficient way to count the number of set bits in a large bitset. By pre-calculating and storing the counts for all possible 8-bit values, we can avoid expensive bit manipulation operations and significantly improve the performance of our code.

#cplusplus #bitmanipulation