{ "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.

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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.

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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.

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All alloys must be created with the same machine.

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Return the maximum number of alloys that the company can create.

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Example 1:

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\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
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Example 2:

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\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
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Example 3:

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\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
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Constraints:

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