Successful Pairs of Spells and Potions

arraytwo pointersbinary search

Problem Statement

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

Examples

Example 1

Input: spells = [5,1,3], potions = [1,2,3,4,5], success = 7
Output: [4,0,3]
- 0 ^th spell: 5 * [1,2,3,4,5] = [5, 10 , 15 , 20 , 25 ]. 4 pairs are successful.
- 1 ^st spell: 1 * [1,2,3,4,5] = [1,2,3,4,5]. 0 pairs are successful.
- 2 ^nd 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]
- 0 ^th spell: 3 * [8,5,8] = [ 24 ,15, 24 ]. 2 pairs are successful.
- 1 ^st spell: 1 * [8,5,8] = [8,5,8]. 0 pairs are successful. 
- 2 ^nd 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 <= 10 ^5

1 <= spells[i], potions[i] <= 10 ^5

1 <= success <= 10 ^10

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicTwo Pointers