Lintcode: Interval Sum

Given an integer array (index from 0 to n-1, where n is the size of this array), and an query list. Each query has two integers [start, end]. For each query, calculate the sum number between index start and end in the given array, return the result list.

Have you met this question in a real interview? Yes
Example
For array [1,2,7,8,5], and queries [(0,4),(1,2),(2,4)], return [23,9,20]

Note
We suggest you finish problem Segment Tree Build, Segment Tree Query and Segment Tree Modify first.

Challenge
O(logN) time for each query

这道题最简便的方法当然是prefix Sum

/**
 * Definition of Interval:
 * public classs Interval {
 *     int start, end;
 *     Interval(int start, int end) {
 *         this.start = start;
 *         this.end = end;
 *     }
 */
public class Solution {
    /**
     *@param A, queries: Given an integer array and an query list
     *@return: The result list
     */
    public ArrayList<Long> intervalSum(int[] A, 
                                       ArrayList<Interval> queries) {
        // write your code here
        long[] prefixSum = new long[A.length+1];
        for (int i=0; i<A.length; i++) {
            prefixSum[i+1] = prefixSum[i] + A[i];
        }
        ArrayList<Long> res = new ArrayList<Long>();
        for (Interval interval : queries) {
            int start = interval.start;
            int end = interval.end;
            long result = prefixSum[end+1] - prefixSum[start];
            res.add(result);
        }
        return res;
    }
}

用Segment Tree

/**
 * Definition of Interval:
 * public classs Interval {
 *     int start, end;
 *     Interval(int start, int end) {
 *         this.start = start;
 *         this.end = end;
 *     }
 */
public class Solution {
    /**
     *@param A, queries: Given an integer array and an query list
     *@return: The result list
     */
    public class SegmentTreeNode {
        long sum;
        int start;
        int end;
        SegmentTreeNode left;
        SegmentTreeNode right;
        public SegmentTreeNode(int start, int end) {
            this.sum = 0;
            this.start = start;
            this.end = end;
            this.left = null;
            this.right = null;
        }
    }
     
    SegmentTreeNode root;
     
    public ArrayList<Long> intervalSum(int[] A, 
                                       ArrayList<Interval> queries) {
        // write your code here
        ArrayList<Long> res = new ArrayList<Long>();
        root = build(A, 0, A.length-1);
        for (Interval interval : queries) {
            int start = interval.start;
            int end = interval.end;
            res.add(query(root, start, end));
        }
        return res;
    }
    
    public SegmentTreeNode build(int[] A, int start, int end) {
        SegmentTreeNode cur = new SegmentTreeNode(start, end);
        if (start == end) {
            cur.sum = A[start];
        }
        else {
            int mid = (start + end)/2;
            cur.left = build(A, start, mid);
            cur.right = build(A, mid+1, end);
            cur.sum = cur.left.sum + cur.right.sum;
        }
        return cur;
    }
    
    public Long query(SegmentTreeNode cur, int start, int end) {
        if (cur.start==start && cur.end==end) return cur.sum;
        int mid = (cur.start + cur.end)/2;
        if (end <= mid) return query(cur.left, start, end);
        else if (start > mid) return query(cur.right, start, end);
        else return query(cur.left, start, mid) + query(cur.right, mid+1, end);
    }
}