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Range Sum Query - Immutable

Easy Arrays & Hashing Prefix Sum Strategy Original on LeetCode

Range Sum Query - Immutable is a easy arrays & hashing problem solved with the prefix sum strategy pattern. The best approach, optimal (prefix sums), runs in O(n) build, O(1) per query time and O(n) space. Below are 2 approaches in Java, from brute force up.

Problem

Design a class that takes an integer array once and then answers many queries sumRange(left, right): the sum of the elements between indices left and right, inclusive. The array never changes.

Examples

Example 1

Input
NumArray([3, -1, 4, 2]); sumRange(0, 2); sumRange(1, 3)
Output
6, 5
Why
3 + -1 + 4 = 6 and -1 + 4 + 2 = 5.

Constraints

  • 1 <= nums.length <= 10^4
  • At most 10^4 calls to sumRange.
  • The array never changes.

Animated walkthrough

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Solutions

Try it yourself first. Then compare: each approach lists its idea, the steps, its time and space, and the Java code.

ApproachTimeSpace
Brute forceO(n) per queryO(1)
Optimal (prefix sums)O(n) build, O(1) per queryO(n)

1Brute force

TimeO(n) per query
SpaceO(1)

Store the array and loop from left to right on every query.

  1. sumRange adds nums[left..right].
Java
class NumArray {
    private final int[] nums;

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

    public int sumRange(int left, int right) {
        int sum = 0;
        for (int i = left; i <= right; i++) sum += nums[i];
        return sum;
    }
}

2Optimal (prefix sums)

TimeO(n) build, O(1) per query
SpaceO(n)

Build pre where pre[i] is the sum of the first i elements, with pre[0] = 0. Then the sum of left..right is pre[right + 1] - pre[left].

  1. pre[i + 1] = pre[i] + nums[i].
  2. sumRange returns pre[right + 1] - pre[left].
Java
class NumArray {
    private final int[] pre;

    public NumArray(int[] nums) {
        pre = new int[nums.length + 1];
        for (int i = 0; i < nums.length; i++) pre[i + 1] = pre[i] + nums[i];
    }

    public int sumRange(int left, int right) {
        return pre[right + 1] - pre[left];
    }
}

Edge cases to test

  • left == right
  • left == 0 (why the prefix array has an extra leading 0)

Hints

Hint 1

If you store prefix sums once, any range sum is a single subtraction.

FAQ

What is the best time complexity for Range Sum Query - Immutable?

Optimal (prefix sums) runs in O(n) build, O(1) per query time and O(n) extra space.

Which pattern does Range Sum Query - Immutable use?

It is a arrays & hashing problem that uses the prefix sum strategy pattern. Other problems with the same pattern: Subarray Sum Equals K, Subarray with given XOR.

Is there a brute force solution for Range Sum Query - Immutable?

Yes. Brute force takes O(n) per query time and O(1) space. Store the array and loop from left to right on every query.

Which edge cases should I test for Range Sum Query - Immutable?

left == right; left == 0 (why the prefix array has an extra leading 0).