307. Range Sum Query

Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.

The update(i, val) function modifies nums by updating the element at index i to val.

Example:

Given nums = [1, 3, 5]

sumRange(0, 2) -> 9
update(1, 2)
sumRange(0, 2) -> 8

Note:

1. The array is only modifiable by the update function.
2. You may assume the number of calls to update and sumRange function is distributed evenly.

本题主要考查的是两种数据结构，一种是二分索引树，另一种是线段树。

先说线段树，用于解决连续区间的动态查询问题，实现起来不是很复杂，代码如下：

public class NumArray {
    class SegmentTreeNode{
        int start;
        int end;
        int sum;
        SegmentTreeNode left,right;
        public SegmentTreeNode(int start,int end){
            this.start = start;
            this.end = end;
            this.left = null;
            this.right = null;
            this.sum = 0;
        }
    }
    SegmentTreeNode root = null;
    public NumArray(int[] nums) {
        root=buildtree(nums,0,nums.length-1);
    }
    public SegmentTreeNode buildtree(int[] nums,int start,int end){
        if(start>end){
            return null;
        }else{
            SegmentTreeNode node = new SegmentTreeNode(start,end);
            if(start==end){
                node.sum = nums[start];
            }else{
                int mid = start+(end-start)/2;
                node.left = buildtree(nums,start,mid);
                node.right = buildtree(nums,mid+1,end);
                node.sum = node.left.sum+node.right.sum;
            }
            return node;
        }
    }
    
    public void update(int i, int val) {
        update(root,i,val);
    }
    public void update(SegmentTreeNode root,int pos,int val){
        if(root.start==root.end){
            root.sum = val;
        }else{
            int mid = root.start+(root.end-root.start)/2;
            if(pos<=mid){
                update(root.left,pos,val);
            }else{
                update(root.right,pos,val);
            }
            root.sum = root.left.sum+root.right.sum;
        }
    }
    public int sumRange(int i, int j) {
        return sumRange(root,i,j);
    }
    public int sumRange(SegmentTreeNode root,int start,int end){
        if(root.start==start&&root.end==end) return root.sum;
        else{
            int mid = root.start+(root.end-root.start)/2;
            if(start>mid){
                return sumRange(root.right,start,end);
            }else if(end<=mid){
                return sumRange(root.left,start,end);
            }else{
                return sumRange(root.left,start,mid)+sumRange(root.right,mid+1,end);
            }
        }
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * obj.update(i,val);
 * int param_2 = obj.sumRange(i,j);
 */

下面是二分索引树，该树要注意一点，就是下标从1开始的，代码如下：

public class NumArray {
    int[] BIT;
    int[] nums;
    int len;
    public NumArray(int[] nums) {
        len = nums.length;
        BIT = new int[len+1];
        this.nums = nums;
        for(int i=0;i<len;i++){
            init(i,nums[i]);
        }
    }
    public void init(int i,int val){
        i++;
        while(i<=len){
            BIT[i] += val;
            i+=(i&-i);
        }
    }
    
    public void update(int i, int val) {
        int diff = val-nums[i];
        nums[i] = val;
        init(i,diff);
    }
    public int getSum(int i){
        int sum = 0;
        i++;
        while(i>0){
            sum += BIT[i];
            i-=(i&-i);
        }
        return sum;
    }
    
    public int sumRange(int i, int j) {
        return getSum(j)-getSum(i-1);
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * obj.update(i,val);
 * int param_2 = obj.sumRange(i,j);
 */