Candy

https://leetcode.com/problems/candy/

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?

解题思路：

开始没看清题意，以为相邻的相同rating，获得candy数量也必须一样。实际上这点没要求。

所以用了下面的方法，从左到右和从右到左分别找出连续最大长度的递增子数列，再将这两者比较，这样就可以确定那个拿到最多candy的顶点了。然后从这个顶点分别向左右扩展，遇到大的+1，相等的不变，小的-1，直到遇到数组两头。但因为题意理解错误，也就无法验证正确性了。

public class Solution {

    public int candy(int[] ratings) {

        if(ratings.length == 0){

            return 0;

        }

        if(ratings.length == 1){

            return 1;

        }

        int longestPeakIndexUp = 0, longestPeakIndexDown = 0;

        int longestLengthUp = 1, maxLengthUp = 1, longestLengthDown = 1, maxLengthDown = 1;

        for(int i = 1; i < ratings.length; i++){

            if(ratings[i] > ratings[i - 1]){

                longestLengthUp++;

                if(i == ratings.length - 1){

                    if(longestLengthUp > maxLengthUp){

                        maxLengthUp = longestLengthUp;

                        longestPeakIndexUp = i;

                    }

                }

            }else{

                if(longestLengthUp > maxLengthUp){

                    maxLengthUp = longestLengthUp;

                    longestPeakIndexUp = i - 1;

                }

                longestLengthUp = 1;

            }

        }

        

        for(int i = ratings.length - 2; i >= 0; i--){

            if(ratings[i] > ratings[i + 1]){

                longestLengthDown++;

                if(i == 0){

                    if(longestLengthDown > maxLengthDown){

                        maxLengthDown = longestLengthDown;

                        longestPeakIndexDown = i;

                    }

                }

            }else{

                if(longestLengthDown > maxLengthDown){

                    maxLengthDown = longestLengthDown;

                    longestPeakIndexDown = i + 1;

                }

                longestLengthDown = 1;

            }

        }

        

        int maxLength = maxLengthUp;

        int longestPeakIndex = longestPeakIndexUp;

        if(maxLengthUp < maxLengthDown){

            maxLength = maxLengthDown;

            longestPeakIndex = longestPeakIndexDown;

        }

        

        int candyNumbers = maxLength, thisNumber = maxLength;

        for(int i = longestPeakIndex + 1; i < ratings.length; i++){

            if(ratings[i] > ratings[i - 1]){

                thisNumber++;

            }else if(ratings[i] < ratings[i - 1]){

                thisNumber--;

            }

            candyNumbers += thisNumber;

        }

        thisNumber = maxLength;

        for(int i = longestPeakIndex - 1; i >= 0; i--){

            if(ratings[i] > ratings[i + 1]){

                thisNumber++;

            }else if(ratings[i] < ratings[i + 1]){

                thisNumber--;

            }

            candyNumbers += thisNumber;

        }

        return candyNumbers;

    }

}

发现了错误后，意味着有两个变化。第一，12333321这样的数列，中间的3完全可以全是1。第二，42341这样的数列，num就是21231。注意倒数第二个数字4，它的num来自于左侧较长的递增数列。

理解了题意，代码倒是简单了。首先将默认的num都置为1。然后从左到右递增就+1，不变就置为1。从右到左递增+1，但是如果前面已经赋值了，而且此时的值不如以前大，比如上面的4位置，就不能更新值，否则会打破从左到右的递增。这样的值基本上是左右都是递增的peak。

public class Solution {

    public int candy(int[] ratings) {

        int[] num = new int[ratings.length];

        if(ratings.length == 0 || ratings.length == 1){

            return ratings.length;

        }

        for(int i = 0; i < num.length; i++){

            num[i] = 1;

        }

        //从左到右更新

        for(int i = 1; i < ratings.length; i++){

            if(ratings[i] > ratings[i - 1]){

                num[i] = num[i - 1] + 1;

            }else if(ratings[i] == ratings[i - 1]){

                num[i] = 1;

            }

        }

        //从右到左更新

        for(int i = ratings.length - 2; i >= 0; i--){

            if(ratings[i] > ratings[i + 1]){

                int temp = num[i + 1] + 1;

                if(temp >= num[i]){

                    num[i] = temp;

                }

            }

        }

        int total = 0;

        for(int i = 0; i < num.length; i++){

            total += num[i];

        }

        return total;

    }

}