135. 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?

思路：We take ratings array as [5, 6, 2, 2, 4, 8, 9, 5, 4, 0, 5, 1]

In the given problem each student will have at least 1 candy. So distribute 1 candy to each.

ratings:     
[5, 6, 2, 2, 4, 8, 9, 5, 4, 0, 5, 1]
candies:     
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Now traverse the array from left to right. If the rating of (n+1) child is greater than (n) child then set the candy of (n+1) child as one candy more than the (n) child candies.

ratings:     
[5, 6, 2, 2, 4, 8, 9, 5, 4, 0, 5, 1]
candies:     
[1, 2, 1, 1, 2, 3, 4, 1, 1, 1, 2, 1]

Now traverse the array from right to left. If the (n) child rating is more than (n+1) child and (n) child candies is less than one more than (n+1) child candies then update the candies of (n) child as 1+ (n+1) candies.

ratings:     
[5, 6, 2, 2, 4, 8, 9, 5, 4, 0, 5, 1]
candies:     
[1, 2, 1, 1, 2, 3, 4, 3, 2, 1, 2, 1]

Total minimum candies: 23

public class Solution {
    public int candy(int[] ratings) {
        int sum = 0;
        int[] a = new int[ratings.length];
        for (int i=0;i<a.length;i++){
            a[i] = 1;
        }
        for (int i=0;i<ratings.length-1;i++){
            if (ratings[i+1]>ratings[i]){
                a[i+1] = a[i]+1;
            }
        }
        for (int i=ratings.length-1;i>0;i--){
            if (ratings[i-1]>ratings[i]){
                if (a[i-1]<(a[i]+1))
                    a[i-1] = a[i]+1;
            }
        }
        for (int i=0;i<a.length;i++){
            sum += a[i];
        }
        return sum;
    }
}