咒語和藥水的成功配對數 Successful Pairs of Spells&Potions_LC 2300 精選75題

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題目敘述

題目會給我們兩個輸入陣列spells咒語、potions藥水，還有一個參數success。

當咒語和藥水相乘的值 >= success就是一個成功配對。

請問每個咒語能夠形成的成功配對數有多少?

以陣列的形式輸出返回答案。

題目的原文敘述

測試範例

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.

約束條件

Constraints:

• n == spells.length

咒語陣列的長度為n。

• m == potions.length

藥水陣列的長度為m。

• 1 <= n, m <= 10^5

輸入陣列的長度都介於1~十萬。

• 1 <= spells[i], potions[i] <= 10^5

輸入陣列的元素值都介於1~十萬。

• 1 <= success <= 10^10

參數success介於1~一百億。

演算法 排序 +二分搜尋

除了傳統的暴力搜索配對之外，還有一個比較高效率的排序+二分搜尋演算法。

先把potion藥水陣列從小到大排序，
這是為了後續的二分搜尋鋪路，滿足已排序的性質。