Given an integer array nums, handle multiple queries of the following types:
Update the value of an element in nums.
Calculate the sum of the elements of nums between indices left and rightinclusive where left <= right.
Implement the NumArray class:
NumArray(int[] nums) Initializes the object with the integer array nums.
void update(int index, int val)Updates the value of nums[index] to be val.
int sumRange(int left, int right) Returns the sum of the elements of nums between indices left and rightinclusive (i.e. nums[left] + nums[left + 1] + ... + nums[right]).
At most 3 * 104 calls will be made to update and sumRange.
ac1: Binary Indexed Tree
careful: bit.length = nums.length + 1; so need to do i++ in methods
class NumArray {
int[] bit;
int[] nums;
public NumArray(int[] nums) {
this.nums = nums;
bit = new int[nums.length + 1];
for (int i = 0; i < nums.length; i++) {
int val = nums[i];
nums[i] = 0;
update(i, val);
}
}
public void update(int i, int val) {
// index + last '1' bit
int diff = val - nums[i];
nums[i] = val;
i++;
while (i < bit.length) {
bit[i] += diff;
i += i & (-i);
}
}
private int getSum(int i) {
// index - last '1' bit
i++;
int res = 0;
while (i > 0) {
res += bit[i];
i -= i & (-i);
}
return res;
}
public int sumRange(int i, int j) {
return getSum(j) - getSum(i-1);
}
}
/**
* 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);
*/
ac2: Segment Tree
more intuitive, yet more code. Notice: use divide and conquer, no need to care about the mid point unless building the tree.
class NumArray {
class SegTreeNode{
int start, end, sum;
SegTreeNode left, right;
public SegTreeNode(int start, int end){
this.start = start;
this.end = end;
sum = 0;
}
}
SegTreeNode root;
public NumArray(int[] nums) {
root = build(nums, 0, nums.length-1);
}
private SegTreeNode build(int[] nums, int start, int end) {
if (start < 0 || end >= nums.length || start > end) return null;
int mid = start + (end - start) / 2;
SegTreeNode node = new SegTreeNode(start, end);
if (start == end) {
node.sum = nums[start];
} else {
node.left = build(nums, start, mid);
node.right = build(nums, mid+1, end);
node.sum = node.left.sum + node.right.sum;
}
return node;
}
public void update(int i, int val) {
update(root, i, val);
}
private void update(SegTreeNode root, int i, int val) {
if (i < root.start || i > root.end) return; // out of range
if (root.start == root.end) {
root.sum = val; // leaf, sum = nums[i]
return;
}
// divide and conquer
update(root.left, i, val);
update(root.right, i, val);
root.sum = root.left.sum + root.right.sum;
}
public int sumRange(int i, int j) {
return sumRange(root, i, j);
}
private int sumRange(SegTreeNode root, int i, int j) {
if (i > root.end || j < root.start) return 0; // out of range
if (i <= root.start && root.end <= j) return root.sum; // current node within range, return value
// divide and conquer
int res = 0;
res += sumRange(root.left, i, j);
res += sumRange(root.right, i, j);
return res;
}
}
/**
* 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);
*/