[LeetCode] 307. Range Sum Query - Mutable

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.

Thought process:
If we continue to use prefix sum, update() will take O(n). To reduce the time complexity, use binary indexed tree or segment tree instead.

 Solution 1 (Binary indexed tree):

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

    public NumArray(int[] nums) {
        int len = nums.length;
        this.nums = new int[len];
        tree = new int[len + 1];
        
        for (int i = 0; i < len; i++) {
            update(i, nums[i]);
        }
    }
    
    public void update(int i, int val) {
        int diff = val - nums[i];
        nums[i] = val;
        
        for (int j = i + 1; j < tree.length; j += (j & -j)) {
            tree[j] += diff;
        }
    }
    
    public int sumRange(int i, int j) {
        return sum(j) - sum(i - 1);
    }
    
    private int sum(int i) {
        int sum = 0;
        for (int j = i + 1; j > 0; j -= (j & -j)) {
            sum += tree[j];
        }
        return sum;
    }
}

/**
 * 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);
 */

Solution 2 (Segment tree - recursive):
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class NumArray {
    private int[] tree;
    private int len;
    
    public NumArray(int[] nums) {
        len = nums.length;
        tree = new int[(int) Math.pow(2, Math.ceil(Math.log(len) / Math.log(2)) + 1)];
        if (len == 0) {
            return;
        }
        buildTree(nums, 1, 0, len - 1);
    }
    
    public void update(int i, int val) {
        update(i, val, 1, 0, len - 1);
    }
    
    public int sumRange(int i, int j) {
        return sumRange(i, j, 1, 0, len - 1);
    }
    
    private void buildTree(int[] nums, int index, int left, int right) {
        System.out.println(index + ", " + left + ", " + right);
        if (left == right) {
            tree[index] = nums[left];
            return;
        }
        
        int mid = left + (right - left) / 2;
        buildTree(nums, index * 2, left, mid);
        buildTree(nums, index * 2 + 1, mid + 1, right);
        tree[index] = tree[index * 2] + tree[index * 2 + 1];
    }
    
    private int sumRange(int i, int j, int index, int left, int right) {
        if (i > right || j < left) {
            return 0;
        }
        if (i <= left && j >= right) {
            return tree[index];
        }
        
        int mid = left + (right - left) / 2;
        return sumRange(i, j, index * 2, left, mid) + sumRange(i, j, index * 2 + 1, mid + 1, right);
    }
    
    private void update(int i, int val, int index, int left, int right) {
        if (left == right) {
            tree[index] = val;
            return;
        }
        
        int mid = left + (right - left) / 2;
        if (i <= mid) {
            update(i, val, index * 2, left, mid);
        } else {
            update(i, val, index * 2 + 1, mid + 1, right);
        }
        tree[index] = tree[index * 2] + tree[index * 2 + 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);
 */

Solution 3 (Segment tree - iterative):
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class NumArray {
    private int[] tree;
    private int len;
    
    public NumArray(int[] nums) {
        len = nums.length;
        if (len == 0) {
            return;
        }
        tree = new int[len * 2];
        buildTree(nums);
    }
    
    public void update(int i, int val) {
        i += len;
        tree[i] = val;
        
        while (i > 0) {
            int left = i;
            int right = i;
            if (i % 2 == 0) {
                right = i + 1;
            } else {
                left = i - 1;
            }
            tree[i / 2] = tree[left] + tree[right];
            i /= 2;
        }
    }
    
    public int sumRange(int i, int j) {
        i += len;
        j += len;
        int sum = 0;
        
        while (i <= j) {
            if (i % 2 == 1) {
                sum += tree[i];
                i++;
            }
            if (j % 2 == 0) {
                sum += tree[j];
                j--;
            }
            i /= 2;
            j /= 2;
        }
        return sum;
    }
    
    private void buildTree(int[] nums) {
        for (int i = len, j = 0; i < tree.length; i++, j++) {
            tree[i] = nums[j];
        }
        for (int i = len - 1; i > 0; i--) {
            tree[i] = tree[i * 2] + tree[i * 2 + 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);
 */

Time complexity:
  • Constructor: O(n).
  • update: O(logn).
  • sumRange: O(logn).
Location: Philadelphia, PA, USA

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