Candy

描述

There are N children standing in a line. Each child is assigned a rating value.

You are giving candies to these children subjected to the following requirements:

  • Each child must have at least one candy.
  • Children with a higher rating get more candies than their neighbors.
    What is the minimum candies you must give?

分析

无

迭代版

  1. // Candy
  2. // 时间复杂度O(n)，空间复杂度O(n)
  3. public class Solution {
  4.     public int candy(int[] ratings) {
  5.         final int n = ratings.length;
  6.         final int[] increment = new int[n];
  8.         // 左右各扫描一遍
  9.         for (int i = 1, inc = 1; i < n; i++) {
  10.             if (ratings[i] > ratings[i - 1])
  11.                 increment[i] = Math.max(inc++, increment[i]);
  12.             else
  13.                 inc = 1;
  14.         }
  16.         for (int i = n - 2, inc = 1; i >= 0; i--) {
  17.             if (ratings[i] > ratings[i + 1])
  18.                 increment[i] = Math.max(inc++, increment[i]);
  19.             else
  20.                 inc = 1;
  21.         }
  22.         // 初始值为n，因为每个小朋友至少一颗糖
  23.         int sum = n;
  24.         for (int i : increment) sum += i;
  25.         return sum;
  26.     }
  27. };

递归版

  1. // Candy
  2. // 备忘录法，时间复杂度O(n)，空间复杂度O(n)
  3. // java.lang.StackOverflowError
  4. public class Solution {
  5.     public int candy(int[] ratings) {
  6.         final int[] f = new int[ratings.length];
  7.         int sum = 0;
  8.         for (int i = 0; i < ratings.length; ++i)
  9.             sum += solve(ratings, f, i);
  10.         return sum;
  11.     }
  12.     int solve(int[] ratings, int[] f, int i) {
  13.         if (f[i] == 0) {
  14.             f[i] = 1;
  15.             if (i > 0 && ratings[i] > ratings[i - 1])
  16.                 f[i] = Math.max(f[i], solve(ratings, f, i - 1) + 1);
  17.             if (i < ratings.length - 1 && ratings[i] > ratings[i + 1])
  18.                 f[i] = Math.max(f[i], solve(ratings, f, i + 1) + 1);
  19.         }
  20.         return f[i];
  21.     }
  22. }

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/java/linear-list/array/candy.html