vector<int> countSmaller(vector<int>& nums) {
vector<int> result(nums.size(), 0);
bit.resize(nums.size()+1, 0);
//get the ordered-index-array
vector<int> sorted_nums(nums);
vector<int> places(nums.size(), 0);
sort(sorted_nums.begin(), sorted_nums.end());
for (int i = 0; i < nums.size(); ++i) {
places[i] = lower_bound(sorted_nums.begin(), sorted_nums.end(), nums[i]) - sorted_nums.begin();
//cout<<i<<"th places:"<<places[i]<<endl;
}
for(int i=places.size()-1; i>=0; i--){
result[i]=bit_sum(places[i]-1);
bit_add(places[i], 1);
}
return result;
}
void merge(vector<int> & nums, int begin, int mid, int end){
vector<int> sorted_nums(end-begin+1);
int cur_pos = 0;
int left = begin;
int right = mid +1;
while( left <= mid && right <= end){
if( nums[left] < nums[right] ){
sorted_nums[cur_pos ++ ] = nums[left ++];
}else{
sorted_nums[cur_pos ++ ] = nums[right ++];
}
}
while( left <= mid){
sorted_nums[cur_pos ++] = nums[left ++];
}
while( right <= end){
sorted_nums[cur_pos ++] = nums[right ++];
}
for(int i=0; i < cur_pos; i ++ ){
nums[begin +i] = sorted_nums[i];
}
}