{ "data": { "question": { "questionId": "3095", "questionFrontendId": "2861", "boundTopicId": null, "title": "Maximum Number of Alloys", "titleSlug": "maximum-number-of-alloys", "content": "
You are the owner of a company that creates alloys using various types of metals. There are n
different types of metals available, and you have access to k
machines that can be used to create alloys. Each machine requires a specific amount of each metal type to create an alloy.
For the ith
machine to create an alloy, it needs composition[i][j]
units of metal of type j
. Initially, you have stock[i]
units of metal type i
, and purchasing one unit of metal type i
costs cost[i]
coins.
Given integers n
, k
, budget
, a 1-indexed 2D array composition
, and 1-indexed arrays stock
and cost
, your goal is to maximize the number of alloys the company can create while staying within the budget of budget
coins.
All alloys must be created with the same machine.
\n\nReturn the maximum number of alloys that the company can create.
\n\n\n
Example 1:
\n\n\nInput: n = 3, k = 2, budget = 15, composition = [[1,1,1],[1,1,10]], stock = [0,0,0], cost = [1,2,3]\nOutput: 2\nExplanation: It is optimal to use the 1st machine to create alloys.\nTo create 2 alloys we need to buy the:\n- 2 units of metal of the 1st type.\n- 2 units of metal of the 2nd type.\n- 2 units of metal of the 3rd type.\nIn total, we need 2 * 1 + 2 * 2 + 2 * 3 = 12 coins, which is smaller than or equal to budget = 15.\nNotice that we have 0 units of metal of each type and we have to buy all the required units of metal.\nIt can be proven that we can create at most 2 alloys.\n\n\n
Example 2:
\n\n\nInput: n = 3, k = 2, budget = 15, composition = [[1,1,1],[1,1,10]], stock = [0,0,100], cost = [1,2,3]\nOutput: 5\nExplanation: It is optimal to use the 2nd machine to create alloys.\nTo create 5 alloys we need to buy:\n- 5 units of metal of the 1st type.\n- 5 units of metal of the 2nd type.\n- 0 units of metal of the 3rd type.\nIn total, we need 5 * 1 + 5 * 2 + 0 * 3 = 15 coins, which is smaller than or equal to budget = 15.\nIt can be proven that we can create at most 5 alloys.\n\n\n
Example 3:
\n\n\nInput: n = 2, k = 3, budget = 10, composition = [[2,1],[1,2],[1,1]], stock = [1,1], cost = [5,5]\nOutput: 2\nExplanation: It is optimal to use the 3rd machine to create alloys.\nTo create 2 alloys we need to buy the:\n- 1 unit of metal of the 1st type.\n- 1 unit of metal of the 2nd type.\nIn total, we need 1 * 5 + 1 * 5 = 10 coins, which is smaller than or equal to budget = 10.\nIt can be proven that we can create at most 2 alloys.\n\n\n
\n
Constraints:
\n\n1 <= n, k <= 100
0 <= budget <= 108
composition.length == k
composition[i].length == n
1 <= composition[i][j] <= 100
stock.length == cost.length == n
0 <= stock[i] <= 108
1 <= cost[i] <= 100
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