How to use Binary Indexed tree to count the number of elements that is smaller than the value at index?

问题

The problem is to count the number of of values less than the value after index. Here is the code, but I can't understand how binary indexed tree has been used to do this?

#include <iostream>
#include <vector>
#include <algorithm>
#define LL long long
#define MOD 1000000007
#define MAXN 10
using namespace std;
typedef pair<int, int> ii;
int BIT[MAXN+1];
int a[MAXN+1];
vector< ii > temp;
int countSmallerRight[MAXN+1];
int read(int idx) {
    int sum = 0;
    while (idx > 0) {
    sum += BIT[idx];
    idx -= (idx & -idx);
    }
    return sum;
}
void update(int idx, int val) {
    while (idx <= MAXN) {
    BIT[idx] += val;
    idx += (idx & -idx);
    }
}
int main(int argc, const char * argv[])
{
int N;

scanf("%d", &N);

 for (int i = 1; i <= N; i++) {
    scanf("%d", &a[i]);
    temp.push_back(ii(a[i], i));
    }

sort(temp.begin(), temp.end());
countSmallerRight[temp[0].second] = 0;
update(1, 1);
update(temp[0].second, -1);

for (int i = 1; i < N; i++) {
    countSmallerRight[temp[i].second] = read(temp[i].second);
    update(1, 1);
    update(temp[i].second, -1);
}
for (int i = 1; i <= N; i++) {
    printf("%d,", countSmallerRight[i]);
}


putchar('\n');


return 0;


}

It would be helpful if someone could explain the working principal of the code.

回答1:

to understand BIT this is one of the best links .
TC gives the full explaination of functions you used , but rest part is logic on how to use it .
For basic understanding :

ques: there are n heaps and in each heap initially there are 1 stones then we add stones from u to v…find how much stone are there in given heap.

the solution , with answer at each iteration is http://pastebin.com/9QJ589VR. After you understand it , try to implement your question .

来源：https://stackoverflow.com/questions/21234399/how-to-use-binary-indexed-tree-to-count-the-number-of-elements-that-is-smaller-t

标签

c++

algorithm

fenwick-tree