Sparse Table Using JavaScript Array
Last Updated :
10 Oct, 2023
In this article, we are going to learn about Sparse Table using JavaScript array. Sparse Table is a data structure in JavaScript used for efficient range queries (e.g., minimum or maximum) on an array. It precomputes and stores values to answer queries quickly, reducing time complexity.
Example:
Input: arr[] = {7, 2, 3, 0, 5, 10, 3, 12, 18};
query[] = [0, 4], [4, 7], [7, 8]
Output: Minimum of [0, 4] is 0
Minimum of [4, 7] is 3
Minimum of [7, 8] is 12We will explore all the above methods along with their basic implementation with the help of examples.
Approach 1: Using Naive Sparse Table
In this approach, we are using the Naive Sparse Table approach, we create a 2D table to precompute and store minimum values for all subarrays in an input array. This allows efficient querying of minimum values for any subarray.
Example: In this example, we are using the above-explained apporach.
JavaScript
function myFunction(arr) {
const n = arr.length;
const table = new Array(n).fill(0).map(() =>
new Array(n).fill(0));
// Initialize table with the original array
for (let i = 0; i < n; i++) {
table[i][i] = arr[i];
}
// Build the table using a nested loop
for (let len = 2; len <= n; len++) {
for (let i = 0; i + len - 1 < n; i++) {
const j = i + len - 1;
table[i][j] = Math.min(table[i][j - 1],
table[i + 1][j]);
}
}
return table;
}
function sparseTable(table, left, right) {
return table[left][right];
}
const arr = [33, 5, 4, 2, 6];
const result = myFunction(arr);
console.log(sparseTable(result, 1, 4));
Apporach 2: Using Dynamic Programming
In this approach, we build a sparse table for efficient range minimum queries on an array. It precomputes indices of minimum elements, reducing query time. The query function returns the minimum value in a specified range.
Example: In this example, we creates a sparse table for an array to efficiently find minimum values in specific ranges. This technique precomputes data to speed up range query operations.
JavaScript
function buildSparseTable(arr) {
const n = arr.length;
const table = new Array(n);
let j = 0;
for (const value of arr) {
table[j] =
new Array(Math.floor(Math.log2(n)) + 1);
table[j][0] = j;
j++;
}
j = 1;
for (let step = 1; (1 << j) <= n; j++, step = 1 << j) {
for (let i = 0; i + step - 1 < n; i++) {
const x = table[i][j - 1];
const y = table[i + (step >> 1)][j - 1];
table[i][j] = arr[x] < arr[y] ? x : y;
}
}
return {
table, logTable:
new Array(n + 1).fill(0).map((_, i) =>
Math.log2(i))
};
}
function myFunction(sparseTable, left, right) {
const { table, logTable } = sparseTable;
const k = logTable[right - left + 1];
const x = table[left][k];
const y = table[right - (1 << k) + 1][k];
return arr[x];
}
let arr = [33, 5, 4, 2, 6];
let sparseTable = buildSparseTable(arr);
// Query for the minimum value in the range [1, 4]
const result = myFunction(sparseTable, 1, 4);
console.log(result);
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