338CountingBits

从1开始，【0】、【1】、【1、2】、【1、2、 2、3】...【2^root, .. 2^root+2^(root-1),.. ,.2^(root+1)】

其中【2^root, .. 2^root+2^(root-1)】重复前面一个区间的序列，【2^root+2^(root-1),.. ,.2^(root+1)】是前面的序列的对应的每个值加1；

余下不足的一个完整区间长度的部分，分为前半部分和后半部分考虑。

public class Solution {
public int[] countBits(int num) {
if(num < 0) return null;
switch(num){
case 0: return new int[]{0};
case 1: return new int[]{0, 1};
case 2: return new int[]{0, 1, 1};
case 3: return new int[]{0, 1, 1, 2};  //数组赋值与初始化方法
default :
int res[] = new int[num+1]; //0~num 总共num+1个元素
res[0] = 0;
res[1] = 1;
res[2] = 1;
res[3] = 2;
int i, cur = 3, count;
int root = (int)Math.floor(Math.log(num+1)/Math.log(2)); // 2^root <= num < 2^(root+1)
while(cur <= root){ //one range
count = (int)Math.pow(2, cur-1); //eles in the range
for(i = count; i < count + count/2; i++){
res[i] = res[i- count/2];
res[i+count/2] = res[i] + 1;
}
cur++;
}
cur = (int)Math.pow(2, root);
count = num - cur + 1;
if(count <= cur/2){
for(i = cur; count > 0; i++, count--){
res[i] = res[i - cur/2];
}
}
else{
//System.out.println(" " + root);
int rem = cur;
for(i = rem, cur = 0 ; cur < rem/2; i++, cur++){
res[i] = res[i - rem/2];
}
// System.out.println(i +" " + cur);
while(count - cur > 0){
res[i] = res[i - rem/2] + 1;
i++;
count--;
}
}
return res;
}
}
}