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Problem · Math

Card Packets

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Problem statement

An e-commerce company specializes in cards with sports figures on them. Each sport has different categories of cards. For instance, there might be more desirable cards with the most popular sports personalities, others with small pieces of a player's jersey attached, and so on. They have a number of each category of card and want to make some number of packets greater than 1 that each contain equal numbers of each type of card. To do this, they will add more cards of each type until each type can be divided equally among some number of packets. Determine the minimum number of additional cards needed to create a number of packets with equal type distribution.

Function

cardPackets(cardTypes: int[]) → int

Complete the function cardPackets in the editor.

cardPackets has the following parameter(s):

  1. int cardTypes[n]: the quantity available of card type

Returns

int: the minimum number of additional cards to add

Examples

Example 1

cardTypes = [4, 7, 5, 11, 15]return = 4

In order to make 2 matching packets, the following numbers of additional cards must be added: [0, 1, 1, 1, 1]. This sums to 4 additional cards. The numbers of cards are [4, 8, 6, 12, 16] and they can be divided evenly among 2 packets. If 3 packets are created, an additional [2, 2, 1, 1, 0] cards are needed, sum = 6 items. This yields quantities [6, 9, 6, 12, 15]. Any number of packets ≥ 2 can be created, but creating 2 packets requires the minimum number of additional cards.

Example 2

cardTypes = [3, 8, 7, 6, 4]return = 2

For 2 packets add: [1, 0, 1, 0, 0] (2 cards) to get [4, 8, 8, 6, 4]. For 3 add [0, 1, 2, 0, 2] (5 cards) to get [3, 9, 9, 6, 6]. Any number of packets ≥ 2 can be created, but making 2 packets requires the minimum number of additional cards.

Constraints

  • 1 ≤ n ≤ 10^5
  • 1 ≤ cardTypes[i] ≤ 500

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public int cardPackets(int[] cardTypes) {
  // write your code here
}
cardTypes[4, 7, 5, 11, 15]
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