interval-sum.cpp

// Time:  ctor:   O(n),
//        query:  O(logn)
// Space: O(n)

/**
 * Definition of Interval:
 * classs Interval {
 *     int start, end;
 *     Interval(int start, int end) {
 *         this->start = start;
 *         this->end = end;
 *     }
 */

// Segment Tree solution.
class SegmentTreeSumNode {
public:
    int start, end;
    long long sum;
    SegmentTreeSumNode *left, *right;
    SegmentTreeSumNode(int start, int end, long long sum) {
        this->start = start;
        this->end = end;
        this->sum = sum;
        this->left = this->right = NULL;
    }
};

class Solution {
public:
    /**
     *@param A, queries: Given an integer array and an query list
     *@return: The result list
     */
    vector<long long> intervalSum(vector<int> &A, vector<Interval> &queries) {
        vector<long long> res;

        // Build segment tree.
        SegmentTreeSumNode *root = build(A, 0, A.size() - 1);

        // Do each query.
        for (const auto& q : queries) {
            res.emplace_back(query(root, q.start, q.end));
        }

        return res;
    }


    // Build segment tree.
    SegmentTreeSumNode *build(vector<int> &A, int start, int end) {
        if (start > end) {
            return nullptr;
        }

        // The root's start and end is given by build method.
        SegmentTreeSumNode *root = new SegmentTreeSumNode(start, end, 0);

        // If start equals to end, there will be no children for this node.
        if (start == end) {
            root->sum = A[start];
            return root;
        }

        // Left child: start=A.left, end=(A.left + A.right) / 2.
        root->left = build(A, start, (start + end) / 2);

        // Right child: start=(A.left + A.right) / 2 + 1, end=A.right.
        root->right = build(A, (start + end) / 2 + 1, end);

        long long left_sum = root->left != nullptr? root->left->sum : 0;
        long long right_sum = root->right != nullptr? root->right->sum : 0;

        // Update sum.
        root->sum = left_sum + right_sum;
        return root;
    }


    // Query sum in given range.
    long long query(SegmentTreeSumNode *root, int start, int end) {
        // Out of range.
        if (root == nullptr || root->start > end || root->end <  start) {
            return 0;
        }

        // Current segment is totally within range [start, end]
        if (root->start >= start && root->end <= end) {
            return root->sum;
        }

        long long left = query(root->left, start, end);
        long long right = query(root->right, start, end);

        // Find sum in the children.
        return left + right;
    }
};

// Time:  ctor:   O(n),
//        query:  O(logn)
// Space: O(n)
// Binary Indexed Tree (BIT) solution.
class Solution2 { 
public:
    /**
     *@param A, queries: Given an integer array and an query list
     *@return: The result list
     */
    vector<long long> intervalSum(vector<int> &A, vector<Interval> &queries) {
        nums_ = A;

        vector<long long> res;

        bit_ = vector<long long>(nums_.size() + 1);
        for (int i = 1; i < bit_.size(); ++i) {
            bit_[i] = A[i - 1] + bit_[i - 1];
        }
        for (int i = bit_.size() - 1; i >= 1; --i) {
            int last_i = i - lower_bit(i);
            bit_[i] -= bit_[last_i];
        }

        for (const auto& q : queries) {
            res.emplace_back(query(q.start, q.end));
        }

        return res;
    }

private:
    vector<int> nums_;
    vector<long long> bit_;

    long long query(int start, int end) {
        long long sum = sumRegion_bit(end);
        if (start > 0) {
            sum -= sumRegion_bit(start - 1);
        }
        return sum;
    }

    long long sumRegion_bit(long long i) {
        ++i;
        long long sum = 0;
        for (; i > 0; i -= lower_bit(i)) {
            sum += bit_[i];
        }
        return sum;
    }

    void add(int i, int val) {
        ++i;
        for (; i <= nums_.size(); i += lower_bit(i)) {
            bit_[i] += val;
        }
    }

    int lower_bit(int i) {
        return i & -i;
    }
};