2300. Successful Pairs of Spells and Potions

Description

You are given two positive integer arrays spells and potions, of length n and m respectively, where spells[i] represents the strength of the ith spell and potions[j] represents the strength of the jth potion.

You are also given an integer success. A spell and potion pair is considered successful if the product of their strengths is at least success.

Return an integer array pairs of length n where pairs[i] is the number of potions that will form a successful pair with the ith spell.

 

Example 1:

Input: spells = [5,1,3], potions = [1,2,3,4,5], success = 7
Output: [4,0,3]
Explanation:
- 0th spell: 5 * [1,2,3,4,5] = [5,10,15,20,25]. 4 pairs are successful.
- 1st spell: 1 * [1,2,3,4,5] = [1,2,3,4,5]. 0 pairs are successful.
- 2nd spell: 3 * [1,2,3,4,5] = [3,6,9,12,15]. 3 pairs are successful.
Thus, [4,0,3] is returned.

Example 2:

Input: spells = [3,1,2], potions = [8,5,8], success = 16
Output: [2,0,2]
Explanation:
- 0th spell: 3 * [8,5,8] = [24,15,24]. 2 pairs are successful.
- 1st spell: 1 * [8,5,8] = [8,5,8]. 0 pairs are successful. 
- 2nd spell: 2 * [8,5,8] = [16,10,16]. 2 pairs are successful. 
Thus, [2,0,2] is returned.

 

Constraints:

• n == spells.length
• m == potions.length
• 1 <= n, m <= 105
• 1 <= spells[i], potions[i] <= 105
• 1 <= success <= 1010

 

Solutions

Solution: Binary Search

• Time complexity: O(nlogm)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number[]} spells
 * @param {number[]} potions
 * @param {number} success
 * @return {number[]}
 */
const successfulPairs = function (spells, potions, success) {
  const m = potions.length;

  potions.sort((a, b) => a - b);

  const findGreaterEqual = spell => {
    let left = 0;
    let right = m - 1;

    while (left <= right) {
      const mid = Math.floor((left + right) / 2);
      const product = spell * potions[mid];

      product >= success ? (right = mid - 1) : (left = mid + 1);
    }

    return left;
  };

  return spells.map(spell => {
    const index = findGreaterEqual(spell);

    return m - index;
  });
};