algorithm/problem/leetcode/307

307. 区域和检索 - 数组可修改

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给你一个数组 nums ，请你完成两类查询。

1. 其中一类查询要求 更新 数组 nums 下标对应的值
2. 另一类查询要求返回数组 nums 中索引 left 和索引 right 之间（ 包含 ）的nums元素的 和 ，其中 left <= right

实现 NumArray 类：

• NumArray(int[] nums) 用整数数组 nums 初始化对象
• void update(int index, int val) 将 nums[index] 的值 更新 为 val
• int sumRange(int left, int right) 返回数组 nums 中索引 left 和索引 right 之间（ 包含 ）的nums元素的 和 （即，nums[left] + nums[left + 1], ..., nums[right]）

示例 1：

输入：
["NumArray", "sumRange", "update", "sumRange"]
[[[1, 3, 5]], [0, 2], [1, 2], [0, 2]]
输出：
[null, 9, null, 8]

解释：
NumArray numArray = new NumArray([1, 3, 5]);
numArray.sumRange(0, 2); // 返回 1 + 3 + 5 = 9
numArray.update(1, 2);   // nums = [1,2,5]
numArray.sumRange(0, 2); // 返回 1 + 2 + 5 = 8

提示：

• 1 <= nums.length <= 3 * 10^4
• -100 <= nums[i] <= 100
• 0 <= index < nums.length
• -100 <= val <= 100
• 0 <= left <= right < nums.length
• 调用 update 和 sumRange 方法次数不大于 3 * 10^4

树状数组维护前缀和

class FenwickTree {
    int[] tr;  // [1, n]
    public FenwickTree(int[] nums) {  // [0, n-1]
        this.tr = new int[nums.length+1];
        for (int i = 0; i < nums.length; i++) {
            add(i+1, nums[i]);
        }
    }
    public int lowbit(int x) {
        return x & (-x);
    }
    public void add(int i, int val) {
        while (i < tr.length) {
            tr[i] += val;
            i += lowbit(i);
        }
    }
    public int query(int i) {
        int res = 0;
        while (i > 0) {
            res += tr[i];
            i -= lowbit(i);
        }
        return res;
    }
}
class NumArray {
    FenwickTree tree;
    int nums[];
    public NumArray(int[] nums) {
        this.nums = nums;
        tree = new FenwickTree(nums);
    }
    public void update(int index, int val) {
        tree.add(index+1, val-nums[index]);
        nums[index] = val;
    }

    public int sumRange(int left, int right) {
        return tree.query(right+1) - tree.query(left);
    }
}

数组无lazy线段树

class NumArray {
    int[] nums;
    int len;
    int[] tree;

    void upd(int idx, int l, int r, int tl, int tr, int val) {
        if (tl <= l && r <= tr) {
            tree[idx] = val;
            if (l != r) { // 没有用lazy数组的情况，就需要给所有子区间更新，这题单点更新运行不到这里
                int m = l + (r - l) / 2;
                upd(2 * idx, l, m, tl, tr, val);
                upd(2 * idx + 1, m + 1, r, tl, tr, val);
            }
        } else {
            int m = l + (r - l) / 2;
            if (tl <= m)
                upd(2 * idx, l, m, tl, tr, val);
            if (m + 1 <= tr)
                upd(2 * idx + 1, m + 1, r, tl, tr, val);
            tree[idx] = tree[2 * idx] + tree[2 * idx + 1];
        }
    }

    int query(int idx, int l, int r, int tl, int tr) {
        if (tl <= l && r <= tr) {
            return tree[idx];
        } else {
            int m = l + (r - l) / 2, res = 0;
            if (tl <= m)
                res += query(2 * idx, l, m, tl, tr);
            if (m + 1 <= tr)
                res += query(2 * idx + 1, m + 1, r, tl, tr);
            return res;
        }
    }

    void build(int idx, int l, int r) {
        if (l == r) {
            tree[idx] = nums[l];
        } else {
            int m = l + (r - l) / 2;
            build(2 * idx, l, m);
            build(2 * idx + 1, m + 1, r);
            tree[idx] = tree[2 * idx] + tree[2 * idx + 1];
        }
    }

    public NumArray(int[] nums) {
        this.nums = nums;
        this.len = nums.length;
        tree = new int[4 * len];
        build(1, 0, len - 1);
    }

    public void update(int index, int val) {
        upd(1, 0, len - 1, index, index, val);
    }

    public int sumRange(int left, int right) {
        return query(1, 0, len - 1, left, right);
    }
}

/**
 * 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);
 */

套数组无lazy线段树模板

class SegmentTree {
    int[] nums;
    int len;
    int[] tree;
    public SegmentTree(int[] nums) {
        this.nums = nums;
        this.len = nums.length;
        tree = new int[4 * len];
        build(1, 0, len - 1);
    }
    void upd(int idx, int l, int r, int tl, int tr, int val) {
        if (tl <= l && r <= tr) {
            tree[idx] = val;
            if (l != r) { // 没有用lazy数组的情况，就需要给所有子区间更新
                int m = l + (r - l) / 2;
                upd(2 * idx, l, m, tl, tr, val);
                upd(2 * idx + 1, m + 1, r, tl, tr, val);
            }
        } else {
            int m = l + (r - l) / 2;
            if (tl <= m) upd(2 * idx, l, m, tl, tr, val);
            if (m + 1 <= tr) upd(2 * idx + 1, m + 1, r, tl, tr, val);
            tree[idx] = tree[2 * idx] + tree[2 * idx + 1];
        }
    }
    int query(int idx, int l, int r, int tl, int tr) {
        if (tl <= l && r <= tr) {
            return tree[idx];
        } else {
            int m = l + (r - l) / 2, res = 0;
            if (tl <= m) res += query(2 * idx, l, m, tl, tr);
            if (m + 1 <= tr) res += query(2 * idx + 1, m + 1, r, tl, tr);
            return res;
        }
    }
    void build(int idx, int l, int r) {
        if (l == r) {
            tree[idx] = nums[l];
        } else {
            int m = l + (r - l) / 2;
            build(2 * idx, l, m);
            build(2 * idx + 1, m + 1, r);
            tree[idx] = tree[2 * idx] + tree[2 * idx + 1];
        }
    }
}
class NumArray {
    SegmentTree st;
    int len;
    public NumArray(int[] nums) {
        st = new SegmentTree(nums);
        len = nums.length;
    }
    
    public void update(int index, int val) {
        st.upd(1, 0, len - 1, index, index, val);
    }
    
    public int sumRange(int left, int right) {
        return st.query(1, 0, len - 1, left, right);
    }
}

/**
 * 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);
 */

套数组lazy线段树模板

class SegmentTree {
    int[] tree;
    int[] lazy;
    int[] nums;
    int n;
    public SegmentTree(int[] nums) {
        this.nums = nums;
        this.n = nums.length;
        this.tree = new int[4 * n];
        this.lazy = new int[4 * n];
        build(1, 0, n - 1);
    }
    void pushDown(int idx, int l, int r) {
        if (lazy[idx] != 0) {
            int m = l + (r - l) / 2;
            tree[2 * idx] = lazy[idx] * (m - l + 1);
            tree[2 * idx + 1] = lazy[idx] * (r - m);
            lazy[2 * idx] = lazy[idx];
            lazy[2 * idx + 1] = lazy[idx];
            lazy[idx] = 0;
        }
    }
    void pushUp(int idx) {
        tree[idx] = tree[2 * idx] + tree[2 * idx + 1];
    }
    void upd(int idx, int l, int r, int tl, int tr, int val) {
        if (tl <= l && r <= tr) {
            tree[idx] = val * (r - l + 1);
            lazy[idx] = val;
        } else {
            pushDown(idx, l, r);
            int m = l + (r - l) / 2;
            if (tl <= m) upd(2 * idx, l, m, tl, tr, val);
            if (m + 1 <= tr) upd(2 * idx + 1, m + 1, r, tl, tr, val);
            pushUp(idx);
        }
    }
    int query(int idx, int l, int r, int tl, int tr) {
        if (tl <= l && r <= tr) {
            return tree[idx];
        } else {
            pushDown(idx, l, r);
            int m = l + (r - l) / 2;
            int res = 0;
            if (tl <= m) res += query(2 * idx, l, m, tl, tr);
            if (m + 1 <= tr) res += query(2 * idx + 1, m + 1, r, tl, tr);
            return res;
        }
    }
    void build(int idx, int l, int r) {
        if (l == r) {
            tree[idx] = nums[l];
        } else {
            int m = l + (r - l) / 2;
            build(2 * idx, l, m);
            build(2 * idx + 1, m + 1, r);
            pushUp(idx);
        }
    }
}
class NumArray {
    SegmentTree st;
    int len;
    public NumArray(int[] nums) {
        st = new SegmentTree(nums);
        len = nums.length;
    }
    
    public void update(int index, int val) {
        st.upd(1, 0, len - 1, index, index, val);
    }
    
    public int sumRange(int left, int right) {
        return st.query(1, 0, len - 1, left, right);
    }
}

/**
 * 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);
 */