Range Sum Query - Mutable

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先补知识：

Segment Tree 线段树

Binary Indexed Tree 树状数组

明天再补充

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

Note:

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

题意很好理解。返回部分和可以修改某个数同时返回的部分和会更新

代码参照 YRB 总结的很好，而且是用java写的，一个题会用好几种方法做赞最近好多都是看它的博客

http://www.cnblogs.com/yrbbest/p/5056739.html

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

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