• 455. Assign Cookies(分饼干)(leetcode)


    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等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。

    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。因为最小的孩子最容易得到满足,所以先满足最小的孩子。

    证明:假设在某次选择中,贪心策略选择给当前满足度最小的孩子分配第 m 个饼干,第 m 个饼干为可以满足该孩子的最小饼干。假设存在一种最优策略,给该孩子分配第 n 个饼干,并且 m < n。我们可以发现,经过这一轮分配,贪心策略分配后剩下的饼干一定有一个比最优策略来得大。因此在后续的分配中,贪心策略一定能满足更多的孩子。也就是说不存在比贪心策略更优的策略,即贪心策略就是最优策略。

    方法一:贪心算法

    保证每次操作都是局部最优的,并且最后得到的结果是全局最优的。

    时间复杂度:o(nlogn)

    苟有恒,何必三更眠五更起;最无益,莫过一日暴十日寒。
  • 相关阅读:
    POJ2425 A Chess Game[博弈论 SG函数]
    POJ1740A New Stone Game[组合游戏]
    Vijos P1196吃糖果游戏[组合游戏]
    CF724D. Dense Subsequence[贪心 字典序!]
    CF724B. Batch Sort[枚举]
    CF731C. Socks[DFS 贪心]
    CF733D Kostya the Sculptor[贪心 排序]
    CF733C Epidemic in Monstropolis[模拟 构造 贪心]
    洛谷P1991无线通讯网[kruskal | 二分答案 并查集]
    NOIP2015斗地主[DFS 贪心]
  • 原文地址:https://www.cnblogs.com/shaer/p/10435509.html
Copyright © 2020-2023  润新知