Implementation：Binary Indexed Tree 树状数组

#include <iostream>

#include <cstdlib>



using namespace std;



class BinaryIndexedTree {

private:

    int *mem;

    int capacity;

public:

    BinaryIndexedTree (int n) {

        if (n <= 0) {

            capacity = 0;

            return;

        }

        capacity = n;

        mem = new int[capacity + 1];

        for (int i=0; i<=capacity; i++) mem[i] = 0;

    }

    ~BinaryIndexedTree() {

        delete[] mem;

    }

    int sum(int idx) {

        if (idx++ >= capacity) idx = capacity;

        int s = 0;

        while(idx > 0) {

            s += mem[idx];

            idx -= idx & -idx;

        }

        return s;

    }

    

    void add(int idx, int val) {

        idx++;

        while (idx <= capacity) {

            mem[idx] += val;

            idx += idx & -idx;

        }

    }

};



int main() {

    int nums[] = {5, 3, 7, 9, 6, 4, 1, 2};

    int n = sizeof(nums) / sizeof(int);

    

    BinaryIndexedTree bit(n);

    

    for (int i=0; i<n; i++) {

        bit.add(i, nums[i]);

    }

    

    for (int i=0; i<n; i++) {

        cout<<"["<<0<<", "<<i<<"] :"<<bit.sum(i)<<endl;

    }



    // solve a problem using BIT, calculate how many reverse order pairs

    // in a shuffled array{1, 2, 3...n}; n = array.length

    int array[] = {3,1,2,5,4};

    int size = sizeof(array) / sizeof(int);

    BinaryIndexedTree bt(size);

    int rsum = 0;

    for (int i=0; i<size; i++) {

        rsum += i - bt.sum(array[i]);

        bt.add(array[i], 1);

    }

    cout<<rsum<<endl;

    

    system("pause");

    return 0;

}

 

参考：

　　挑战程序设计竞赛第二版p176