Assign Cookies

class Solution {
public:
    int satisfyChildren(std::vector<int>& children, std::vector<int>& cookies) {
        std::sort(children.begin(), children.end());
        std::sort(cookies.begin(), cookies.end());
        int satisfied = 0;
        int index = 0;
        while (index < cookies.size() && satisfied < children.size()) {
            if (cookies[index] >= children[satisfied]) {
                satisfied++;
            }
            index++;
        }
        return satisfied;
    }
};

The solution provided addresses the problem of assigning cookies to children in a way that maximizes the number of satisfied children. Each child has a minimum size of cookie they need in order to be satisfied. The approach taken here involves sorting both the list of children and cookies by size, which allows for a more efficient way of satisfying the maximum number of children with the available cookies.

In the given C++ code, you'll find a function named satisfyChildren that accepts two vectors of integers: one representing the greed factors of the children (children) and the other representing the sizes of the cookies (cookies). Both vectors are sorted in ascending order to facilitate comparison.

The solution uses a simple while loop to iterate through the cookies, attempting to satisfy each child in sequence. The variable satisfied counts the number of children that have been successfully given a cookie that meets or exceeds their greed factor. The index is used to iterate over the cookies array.

The function returns the total number of satisfied children once all possible comparisons are exhausted. The key to the efficiency of this algorithm lies in the sorting step, which ensures that the smallest available cookie that can satisfy a child is always tried first, minimizing the waste of larger cookies on children with smaller requirements. This greedy algorithm is effective for this type of matching problem and helps achieve an optimal solution under the constraints given.

class Solution {
    public int distributeCookies(int[] children, int[] cookies) {
        Arrays.sort(children);
        Arrays.sort(cookies);
        int satisfiedChildren = 0;
        int index = 0;
        while (index < cookies.length && satisfiedChildren < children.length) {
            if (cookies[index] >= children[satisfiedChildren]) {
                satisfiedChildren++;
            }
            index++;
        }
        return satisfiedChildren;
    }

}

In the given Java solution, the goal is to determine how many children can be satisfied with the given cookies based on size preferences. Each child can be satisfied with a single cookie that meets or exceeds their size preference. Below is a summary of how the solution works:

• Start by sorting both the children and cookies arrays to facilitate the greedy allocation where each child gets the smallest available cookie that meets their need.
• Initialize variables to keep track of the number of satisfied children (satisfiedChildren) and the current index in the cookies array (index).
• Utilize a loop that continues as long as there are cookies left and not all children are satisfied. Within the loop:
  • Compare the current cookie with the current child's size preference.
  • If the size of the cookie satisfies the child's preference, increment the count of satisfied children and move to the next child.
  • Always increment the cookie index to move to the next cookie after each check.
• Return the count of satisfied children as the result of the function.

This approach ensures that the maximum number of children are satisfied using the minimum necessary cookies through efficient comparison facilitated by sorting.

class Solution:
    def countSatisfiedChildren(self, greed: List[int], cookies: List[int]) -> int:
        greed.sort()
        cookies.sort()
        satisfied_count = 0
        cookie_idx = 0
        while cookie_idx < len(cookies) and satisfied_count < len(greed):
            if cookies[cookie_idx] >= greed[satisfied_count]:
                satisfied_count += 1
            cookie_idx += 1
        return satisfied_count

This solution tackles the problem of assigning cookies to children based on their greed factor. The objective is to maximize the number of satisfied children given arrays of greed factors and cookie sizes.

Here's how the code works:

• First, sort the lists for greed and cookies to streamline the comparison process.
• Initialize a counter satisfied_count to keep track of how many children have been satisfied with a cookie.
• Use a while loop to traverse the list of cookies and attempt to satisfy each child in order of their greed. The loop continues as long as there are cookies available and there are still unsatisfied children.
• For each cookie, if it meets or exceeds the current child’s need (greed factor), increment the satisfied_count and move to the next child.
• Return the total count of satisfied children.

This approach efficiently matches cookies to children with minimal waste, ensuring each child only receives a cookie if it satisfies their minimum requirement.