Assume you are an awesome parent and want to give your children some cookies. But, you should give each child at most one cookie.
Each child i has a greed factor g[i], which is the minimum size of a cookie that the child will be content with; and each cookie j has a size s[j]. If s[j] >= g[i], we can assign the cookie j to the child i, and the child i will be content. Your goal is to maximize the number of your content children and output the maximum number.
Example 1:
Input: g = [1,2,3], s = [1,1] Output: 1 Explanation: You have 3 children and 2 cookies. The greed factors of 3 children are 1, 2, 3. And even though you have 2 cookies, since their size is both 1, you could only make the child whose greed factor is 1 content. You need to output 1.
Example 2:
Input: g = [1,2], s = [1,2,3] Output: 2 Explanation: You have 2 children and 3 cookies. The greed factors of 2 children are 1, 2. You have 3 cookies and their sizes are big enough to gratify all of the children, You need to output 2.
Constraints:
1 <= g.length <= 3 * 1040 <= s.length <= 3 * 1041 <= g[i], s[j] <= 231 - 1
Note: This question is the same as 2410: Maximum Matching of Players With Trainers.
This approach involves sorting the greed factors and cookie sizes. By sorting, the goal is to try to satisfy the least greedy child first with the smallest satisfying cookie. By continuing this way, the solution can maximize the number of content children.
The solution uses two pointers, one for the greed list (g) and one for the cookie size list (s). It increments the pointer for the children only when a matching cookie is found.
This C solution sorts both arrays and uses a two-pointer technique. It keeps a pointer on both the greed factors array and the cookie sizes array. By incrementing both pointers when a child is satisfied, it ensures that all possible cookies are used optimally.
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Time Complexity: O(n log n + m log m), where n is the number of children and m is the number of cookies (due to sorting).
Space Complexity: O(1), as it uses a constant amount of extra space apart from the input arrays.
This involves using binary search to attempt to find the proper index in the sorted list `s` where a given greed factor `g[i]` meets the condition.
For each child in the sorted greed list, perform binary search over the sorted cookie sizes to find the smallest suitable cookie. We'll mark the cookie as used by logically removing it from the pool (using an increment of the index pointer).
This C solution follows the Binary Search technique. It leverages sorting both arrays, then searching for the smallest valid cookie for each child using binary search. It updates counters and marks cookies to avoid reuse improperly.
C++
Java
Python
C#
JavaScript
Time Complexity: O(n log n + n log m), where n is the number of the greed array, m is the number of cookie size array, originating from sorting and binary searching through the cookies.
Space Complexity: O(1) when not considering input arrays.
| Approach | Complexity |
|---|---|
| Greedy Approach using Sorting | Time Complexity: O(n log n + m log m), where n is the number of children and m is the number of cookies (due to sorting). Space Complexity: O(1), as it uses a constant amount of extra space apart from the input arrays. |
| Greedy Approach with Binary Search | Time Complexity: O(n log n + n log m), where n is the number of the greed array, m is the number of cookie size array, originating from sorting and binary searching through the cookies. Space Complexity: O(1) when not considering input arrays. |
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