JavaScript: K^th smallest number in a multiplication table

Last update on April 13 2024 13:27:37 (UTC/GMT +8 hours)

JavaScript Math: Exercise-111 with Solution

Write a JavaScript program that creates a multiplication table of size m x n using integers where 1 <= k <= m * n. Return the kth smallest element in the said multiplication table.

In mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system.
The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 x 9.
The illustration below shows a table up to 12 x 12, which is a size commonly used nowadays in English-world schools.

x	1	2	3	4	5	6	7	8	9	10	11	12
0	0	0	0	0	0	0	0	0	0	0	0	0
1	1	2	3	4	5	6	7	8	9	10	11	12
2	2	4	6	8	10	12	14	16	18	20	22	24
3	3	6	9	12	15	18	21	24	27	30	33	36
4	4	8	12	16	20	24	28	32	36	40	44	48
5	5	10	15	20	25	30	35	40	45	50	55	60
6	6	12	18	24	30	36	42	48	54	60	66	72
7	7	14	21	28	35	42	49	56	63	70	77	84
8	8	16	24	32	40	48	56	64	72	80	88	96
9	9	18	27	36	45	54	63	72	81	90	99	108
10	10	20	30	40	50	60	70	80	90	100	110	120
11	11	22	33	44	55	66	77	88	99	110	121	132
12	12	24	36	48	60	72	84	96	108	120	132	144

Test Data:
(3,3,8) -> 6
(2,3,4) -> 3

Sample Solution:

JavaScript Code:

/**
 * Function to find the kth smallest element in the multiplication table of dimensions m x n.
 * @param {number} m - The number of rows in the multiplication table.
 * @param {number} n - The number of columns in the multiplication table.
 * @param {number} k - The kth smallest element to find.
 * @returns {number|boolean} - The kth smallest element if found, otherwise false.
 */
function test(m, n, k) {
    // If k is less than 1 or greater than the total number of elements in the multiplication table, return false
    if (k < 1 || k > m * n) return false;
    var s = 1, p = n * m;
    // Binary search to find the kth smallest element
    while (s <= p) {
        var mid = s + Math.floor((p - s) / 2);
        var t = 0;
        // Calculate the number of elements less than or equal to mid in the multiplication table
        for (i = 1; i <= m; i++) {
            t += Math.min(Math.floor(mid / i), n);
        }
        // Adjust the search range based on the value of t
        if (t >= k) {
            p = mid - 1;
        } else {
            s = mid + 1;
        }
    }
    // Return the lower bound of the search range
    return s;
}

// Test cases
m = 3;
n = 3;
k = 8;
console.log("m = " + m + " : n = " + n + ", k = " + k);
console.log("kth smallest element in m x n multiplication table: " + test(m, n, k));
m = 2;
n = 3;
k = 4;
console.log("m = " + m + " : n = " + n + ", k = " + k);
console.log("kth smallest element in m x n multiplication table: " + test(m, n, k));

Output:

m = 3 : n = 3, k = 8
kth smallest element in m x n multiplication table: 6
m = 2 : n = 3, k = 4
kth smallest element in m x n multiplication table: 3

Flowchart:

$JavaScript: Kth smallest number in a multiplication table.$

Live Demo:

See the Pen javascript-math-exercise-111 by w3resource (@w3resource) on CodePen.

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