Range Sum Query - Mutable
<p>Given an integer array <code>nums</code>, handle multiple queries of the following types:</p>

<ol>
	<li><strong>Update</strong> the value of an element in <code>nums</code>.</li>
	<li>Calculate the <strong>sum</strong> of the elements of <code>nums</code> between indices <code>left</code> and <code>right</code> <strong>inclusive</strong> where <code>left &lt;= right</code>.</li>
</ol>

<p>Implement the <code>NumArray</code> class:</p>

<ul>
	<li><code>NumArray(int[] nums)</code> Initializes the object with the integer array <code>nums</code>.</li>
	<li><code>void update(int index, int val)</code> <strong>Updates</strong> the value of <code>nums[index]</code> to be <code>val</code>.</li>
	<li><code>int sumRange(int left, int right)</code> Returns the <strong>sum</strong> of the elements of <code>nums</code> between indices <code>left</code> and <code>right</code> <strong>inclusive</strong> (i.e. <code>nums[left] + nums[left + 1] + ... + nums[right]</code>).</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;NumArray&quot;, &quot;sumRange&quot;, &quot;update&quot;, &quot;sumRange&quot;]
[[[1, 3, 5]], [0, 2], [1, 2], [0, 2]]
<strong>Output</strong>
[null, 9, null, 8]

<strong>Explanation</strong>
NumArray numArray = new NumArray([1, 3, 5]);
numArray.sumRange(0, 2); // return 1 + 3 + 5 = 9
numArray.update(1, 2);   // nums = [1, 2, 5]
numArray.sumRange(0, 2); // return 1 + 2 + 5 = 8
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>-100 &lt;= nums[i] &lt;= 100</code></li>
	<li><code>0 &lt;= index &lt; nums.length</code></li>
	<li><code>-100 &lt;= val &lt;= 100</code></li>
	<li><code>0 &lt;= left &lt;= right &lt; nums.length</code></li>
	<li>At most <code>3 * 10<sup>4</sup></code> calls will be made to <code>update</code> and <code>sumRange</code>.</li>
</ul>
Design; Binary Indexed Tree; Segment Tree; Array; Divide and Conquer
type BinaryIndexedTree struct {
	n int
	c []int
}

func newBinaryIndexedTree(n int) *BinaryIndexedTree {
	c := make([]int, n+1)
	return &BinaryIndexedTree{n, c}
}

func (t *BinaryIndexedTree) update(x, delta int) {
	for ; x <= t.n; x += x & -x {
		t.c[x] += delta
	}
}

func (t *BinaryIndexedTree) query(x int) (s int) {
	for ; x > 0; x -= x & -x {
		s += t.c[x]
	}
	return s
}

type NumArray struct {
	tree *BinaryIndexedTree
}

func Constructor(nums []int) NumArray {
	tree := newBinaryIndexedTree(len(nums))
	for i, v := range nums {
		tree.update(i+1, v)
	}
	return NumArray{tree}
}

func (t *NumArray) Update(index int, val int) {
	prev := t.SumRange(index, index)
	t.tree.update(index+1, val-prev)
}

func (t *NumArray) SumRange(left int, right int) int {
	return t.tree.query(right+1) - t.tree.query(left)
}

/**
 * Your NumArray object will be instantiated and called as such:
 * obj := Constructor(nums);
 * obj.Update(index,val);
 * param_2 := obj.SumRange(left,right);
 */