Range sum query using Sparse Table in JavaScript Array

In this article we will learn about Range sum query using Sparse Table in JavaScript Array, The Sparse Table is a data structure that efficiently solves static range query problems. In the context of the range sum queries, Sparse Table precomputes and stores the sum of the ranges of elements in an array. This allows for fast retrieval of the sum of any range within the array.

These are the following approaches by using these we can Range sum query using a Sparse Table in JavaScript Array:

Precompute and Query (Naive)

• In the naive approach of implementing a Sparse Table for the range sum queries.
• We follow a straightforward process of precomputing the table and querying the sum for the given range.

Example: In this example, we are implementing the above-explained approach.

Javascript

class GFG {
    constructor(arr) {
        this.arr = arr;
        this.n = arr.length;
        this.table = Array.from({ length: this.n },
            () => Array(Math.ceil(Math.log2(this.n)) + 1).fill(0));
        this.buildSparseTable(arr);
    }
    buildSparseTable(arr) {
        // Initialize table with the array elements
        for (let i = 0; i < this.n; i++) {
            this.table[i][0] = arr[i];
        }
        // Build sparse table using the dynamic programming
        for (let j = 1; (1 << j) <= this.n; j++) {
            for (let i = 0; i + (1 << j) - 1 < this.n; i++) {
                this.table[i][j] = this.table[i][j - 1]
                    + this.table[i + (1 << (j - 1))][j - 1];
            }
        }
    }
    queryNaive(left, right) {
        let result = 0;
        // Naively sum elements in the range
        for (let i = left; i <= right; i++) {
            result += this.arr[i];
        }
        return result;
    }
}

// Example Usage
const arr = [1, 2, 3, 4, 5, 6, 7, 8];
const sparseTable = new GFG(arr);

// Query using Naive approach
const sumNaive = sparseTable.queryNaive(2, 5);
console.log("Sum using Naive approach:", sumNaive);

Output

Sum using Naive approach: 18

Precompute and Query with Optimized Loop

• In this approach, we optimize the loop within query method to achieve the faster range sum queries.
• The optimization involves iterating through the sparse table in a more efficient way.
• Reducing the time complexity of range sum queries.

Example: In this example, we are implementing the above-explained approach.

Javascript

class GFG {
    constructor(arr) {
        this.table = this.buildSparseTable(arr);
    }
    // Build Sparse Table
    buildSparseTable(arr) {
        const n = arr.length;
        const table = new Array(n).fill()
            .map(() => new Array(Math.ceil(Math.log2(n)) + 1).fill(0));

        // Fill the first column with the array values
        for (let i = 0; i < n; i++) {
            table[i][0] = arr[i];
        }

        // Build the sparse table using the dynamic programming
        for (let j = 1; (1 << j) <= n; j++) {
            for (let i = 0; i + (1 << j) <= n; i++) {

                // Compute the minimum value in current range
                table[i][j] = table[i][j - 1] + table[i + (1 << (j - 1))][j - 1];
            }
        }
        return table;
    }

    // Optimized Query method
    queryOptimized(left, right) {
        let result = 0;

        // Iterate through powers of 2 in descending order
        for (let j = Math.floor(Math.log2(right - left + 1));
            j >= 0; j--) {
            // Check if the current power of 2 is within the range
            if ((1 << j) <= right - left + 1) {
                // Update the result and move to
                // next non-overlapping range
                result += this.table[left][j];
                left += 1 << j;
            }
        }

        return result;
    }
}
// Example Usage
const arr = [1, 2, 3, 4, 5, 6, 7, 8];
const sparseTable = new GFG(arr);
// Query using Optimized approach
const sumOptimized = sparseTable.queryOptimized(0, 0);
console.log("Sum using Optimized approach:", sumOptimized);

Output

Sum using Optimized approach: 1