【LeetCode】455. Assign Cookies(分配饼干)

题目

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 gi, which is the minimum size of a cookie that the child will be content with; and each cookie j has a size sj. If sj >= gi, 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.

Note:
You may assume the greed factor is always positive.
You cannot assign more than one cookie to one child.

Example 1:
Input: [1,2,3], [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: [1,2], [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.

题目描述:每个孩子都有一个满足度,每个饼干都有一个大小,只有饼干的大小大于一个孩子的满足度,该孩子才会获得满足。求解最多可以获得满足的孩子数量。

因为最小的孩子最容易得到满足,因此先满足最小孩子。给一个孩子的饼干应当尽量小又能满足该孩子,这样大饼干就能拿来给满足度比较大的孩子。

证明:假设在某次选择中,贪心策略选择给第 i 个孩子分配第 m 个饼干,并且第 i 个孩子满足度最小,第 m 个饼干为可以满足第 i 个孩子的最小饼干,利用贪心策略最终可以满足 k 个孩子。假设最优策略在这次选择中给 i 个孩子分配第 n 个饼干,并且这个饼干大于第 m 个饼干。我们发现使用第 m 个饼干去替代第 n 个饼干完全不影响后续的结果,因此不存在比贪心策略更优的策略,即贪心策略就是最优策略。

public int findContentChildren(int[] g, int[] s) {
    Arrays.sort(g);
    Arrays.sort(s);
    int i = 0, j = 0;
    while(i < g.length && j < s.length){
        if(g[i] <= s[j]) i++;
        j++;
    }
    return i;
}
最后修改:2018 年 03 月 21 日 08 : 35 PM
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