May LeetCoding Challenge28 之 DP+位运算

4种解法

1.pop count

public class Solution {
    public int[] countBits(int num) {
        int[] ans = new int[num + 1];
        for (int i = 0; i <= num; ++i)
            ans[i] = popcount(i);
        return ans;
    }
    private int popcount(int x) {
        int count;
        for (count = 0; x != 0; ++count)
          x &= x - 1; //zeroing out the least significant nonzero bit
        return count;
    }
}

2.DP + Most Significant Bit

public class Solution {
    public int[] countBits(int num) {
        int[] ans = new int[num + 1];
        int i = 0, b = 1;
        // [0, b) is calculated
        while (b <= num) {
            // generate [b, 2b) or [b, num) from [0, b)
            while(i < b && i + b <= num){
                ans[i + b] = ans[i] + 1;
                ++i;
            }
            i = 0;   // reset i
            b <<= 1; // b = 2b
        }
        return ans;
    }
}

3.DP + Least Significant Bit

public class Solution {
  public int[] countBits(int num) {
      int[] ans = new int[num + 1];
      for (int i = 1; i <= num; ++i)
        ans[i] = ans[i >> 1] + (i & 1); // x / 2 is x >> 1 and x % 2 is x & 1
      return ans;
  }
}

4.DP + Last Set Bit

public class Solution {
  public int[] countBits(int num) {
      int[] ans = new int[num + 1];
      for (int i = 1; i <= num; ++i)
        ans[i] = ans[i & (i - 1)] + 1;
      return ans;
  }
}