leetcode 307. 区域和检索 - 数组可修改 java

第一次学，码住以后还看

树状数组

让你顿悟树状数组原理与由来 - 此店不售此书的文章 - 知乎
https://zhuanlan.zhihu.com/p/422561589
学习笔记：优美的结构，树状数组 - LinearExpectation的文章 - 知乎
https://zhuanlan.zhihu.com/p/358173145

保留"从低位向高位数，第一个数字1"为运算结果
最低位的 1 所处的位置，对应的就是树从下往上数的层数

class NumArray {
    int[] anums;
    int[] nums;
    int n;
    public NumArray(int[] nums) {
        this.nums=nums;
        n=nums.length;
        anums=new int[n+10];
        for(int i=0;i<n;i++){
            add(i+1,nums[i]);//树状数组从1开始
        }
    }
    
    public void update(int index, int val) {
        int tmp=val-nums[index];
        add(index+1,tmp);//更新树状数组
        nums[index]=val;//更新原数组
    }
    
    public int sumRange(int left, int right) {
        return preSum(right+1)-preSum(left);
    }
    public int lowbit(int x){
        return x&(-x);
    }
    //在index位置加上val
    //需要将index上面的节点也都加上val，维持性质
    public void add(int index,int val){
        for(int x=index;x<=n;x+=lowbit(x)){
            anums[x]+=val;
        }
    }
    public int preSum(int index){
        int res=0;
        for(int x=index;x>0;x-=lowbit(x)){
            res+=anums[x];
        }
        return res;
    }
}

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

线段树

分治

class NumArray {
    int[] trees;
    int n;
    public NumArray(int[] nums) {
        this.n=nums.length;
        this.trees=new int[n*4];
        build(0,0,n-1,nums);
    }
    
    public void update(int index, int val) {
        change(index,val,0,0,n-1);
    }
    
    public int sumRange(int left, int right) {
        return range(left,right,0,0,n-1);
    }

    public void build(int node,int s,int e,int[] nums){
        if(s>e) return;
        if(s==e){
            trees[node]=nums[s];
            return;
        }
        int mid=(e-s)/2+s;
        build(node*2+1,s,mid,nums);
        build(node*2+2,mid+1,e,nums);
        trees[node]=trees[node*2+1]+trees[node*2+2];
    }
    public void change(int index,int val,int node,int s,int e){
        if(s==e){
            trees[node]=val;
            return;
        }
        int mid=(e-s)/2+s;
        if(index<=mid){
            change(index,val,node*2+1,s,mid);
        }
        else{
            change(index,val,node*2+2,mid+1,e);
        }
        trees[node]=trees[node*2+1]+trees[node*2+2];
    }
    public int range(int left,int right,int node,int s,int e){
        if(left==s&&right==e){
            return trees[node];
        }
        int mid=(e-s)/2+s;
        if(mid>=right){
            return range(left,right,node*2+1,s,mid);
        }
        else if(mid<left){
            return range(left,right,node*2+2,mid+1,e);
        }
        else{
            return range(left, mid, node * 2 + 1, s, mid) + range(mid + 1, right, node * 2 + 2, mid + 1, e);
        }
    }
}

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