# Range Sum Query - Mutable

`Segment Tree`, `Binary Indexed Tree`

Medium

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.

## Solution

### Segment Tree

\~100 lines of code; 58 ms, faster than 100.00%; 45.9 MB, less than 93.37%

```java
class SegmentTreeNode {
    int start;
    int end;
    int sum;
    SegmentTreeNode left;
    SegmentTreeNode right;

    public SegmentTreeNode (int start, int end, int sum) {
        this.start = start;
        this.end = end;
        this.sum = sum;
        this.left = null;
        this.right = null;
    }
}

class SegmentTree {
    SegmentTreeNode root;

    public SegmentTree (int[] nums) {
        root = build(0, nums.length - 1, nums);
    }

    public SegmentTreeNode build(int start, int end, int[] nums) {
        if (start > end) {
            return null;
        }

        SegmentTreeNode root = new SegmentTreeNode(start, end, 0);

        if (start == end) {
            root.sum = nums[start];
        } else {
            int mid = start + (end - start) / 2;
            root.left = build(start, mid, nums);
            root.right = build(mid + 1, end, nums);
            root.sum = root.left.sum + root.right.sum;
        }
        return root;
    }

    public int query (SegmentTreeNode root, int start, int end) {
        if (root.start == start && root.end == end) {
            return root.sum;
        }

        int mid = root.start + (root.end - root.start) / 2;
        int leftSum = 0, rightSum = 0;

        if (start <= mid) {
            if (mid < end) {
                leftSum = query(root.left, start, mid);
            } else {
                leftSum = query(root.left, start, end);
            }
        }

        if (mid < end) {
            if (start <= mid) {
                rightSum = query(root.right, mid + 1, end);
            } else {
                rightSum = query(root.right, start, end);
            }
        }

        return leftSum + rightSum;
    }

    public void modify(SegmentTreeNode root, int index, int value) {
        if (root.start == index && root.end == index) {
            root.sum = value;
            return;
        }

        int mid = root.start + (root.end - root.start) / 2;
        if (index <= mid && root.start <= mid) {
            modify(root.left, index, value);
        } else if (index > mid && root.end >= mid) {
            modify(root.right, index, value);
        }

        root.sum = root.left.sum + root.right.sum;
    }
}

class NumArray {

    SegmentTree st;

    public NumArray(int[] nums) {
        this.st = new SegmentTree(nums);
    }

    public void update(int i, int val) {
        st.modify(st.root, i, val);
    }

    public int sumRange(int i, int j) {
        return st.query(st.root, i, j);
    }
}

/**
 * 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);
 */
```

### Binary Indexed Tree

```java
/**
* This reference program is provided by @jiuzhang.com
* Copyright is reserved. Please indicate the source for forwarding
*/

public class NumArray {
    private int[] arr, bit;

    /**
     * @return: nothing
     */
    public NumArray(int[] nums) {
        arr = new int[nums.length];
        bit = new int[nums.length + 1];

        for (int i = 0; i < nums.length; i++) {
            update(i, nums[i]);
        }
    }

    public void update(int index, int val) {
        int delta = val - arr[index];
        arr[index] = val;

        for (int i = index + 1; i <= arr.length; i = i + lowbit(i)) {
            bit[i] += delta;
        }
    }

    public int getPrefixSum(int index) {
        int sum = 0;
        for (int i = index + 1; i > 0; i = i - lowbit(i)) {
            sum += bit[i];
        }
        return sum;
    }

    private int lowbit(int x) {
        return x & (-x);
    }

    public int sumRange(int left, int right) {
        return getPrefixSum(right) - getPrefixSum(left - 1);
    }
}
```


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