#2861
Maximum Number of Alloys
expert · 1020 · lc medium +32 · verified · 40.4% accepted · 302 likes · top 20%
Description
A company produces alloys from n metal types using k machines. Machine i needs composition[i][j] units of metal j per alloy. You start with stock[i] units of metal i, and buying one unit of metal i costs cost[i] coins.
All alloys must be produced by the same machine. Given integers n, k, budget, a 1-indexed 2D array composition, and 1-indexed arrays stock and cost, return the maximum number of alloys producible within the budget.
Example 1:
Input: n = 3, k = 2, budget = 15, composition = [[1,1,1],[1,1,10]], stock = [0,0,0], cost = [1,2,3]
Output: 2
Explanation: It is optimal to use the 1st machine to create alloys.
To create 2 alloys we need to buy the:
- 2 units of metal of the 1st type.
- 2 units of metal of the 2nd type.
- 2 units of metal of the 3rd type.
In total, we need 2 * 1 + 2 * 2 + 2 * 3 = 12 coins, which is smaller than or equal to budget = 15.
Notice that we have 0 units of metal of each type and we have to buy all the required units of metal.
It can be proven that we can create at most 2 alloys.
Example 2:
Input: n = 3, k = 2, budget = 15, composition = [[1,1,1],[1,1,10]], stock = [0,0,100], cost = [1,2,3]
Output: 5
Explanation: It is optimal to use the 2nd machine to create alloys.
To create 5 alloys we need to buy:
- 5 units of metal of the 1st type.
- 5 units of metal of the 2nd type.
- 0 units of metal of the 3rd type.
In total, we need 5 * 1 + 5 * 2 + 0 * 3 = 15 coins, which is smaller than or equal to budget = 15.
It can be proven that we can create at most 5 alloys.
Example 3:
Input: n = 2, k = 3, budget = 10, composition = [[2,1],[1,2],[1,1]], stock = [1,1], cost = [5,5]
Output: 2
Explanation: It is optimal to use the 3rd machine to create alloys.
To create 2 alloys we need to buy the:
- 1 unit of metal of the 1st type.
- 1 unit of metal of the 2nd type.
In total, we need 1 * 5 + 1 * 5 = 10 coins, which is smaller than or equal to budget = 10.
It can be proven that we can create at most 2 alloys.
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