LintCode Subarray Sum

　　

For this problem we need to learn a new trick that if your start sum up all elements in an array. When you start from a to b to sum up all elements, if the result is zero, and also the summation of all elements from index a to c ( c<=b ) is zero. Then, we need to think about sub array from index c+1 to index b is a sub array with summation of all elements to zero.

Notice: we need to formalize the summation of index =-1 to 0. Then if there is a sub array start from 0 has summation of 0, we will return the result.

public class Solution {
    /**
     * @param nums: A list of integers
     * @return: A list of integers includes the index of the first number 
     *          and the index of the last number
     */
    public ArrayList<Integer> subarraySum(int[] nums) {
        // write your code here
        ArrayList<Integer> result = new ArrayList<Integer>();
        HashMap<Integer, Integer> map = new HashMap<Integer,Integer>();
        //set index -1 sum to be 0 then when you meet an index with sum equals
        //0 you can return otherwise there is never a 0 stored for the empty
        //list
        map.put(0,-1);
        int sum = 0;
        for (int i = 0; i < nums.length; i++ ) {
            sum += nums[i];
            if (map.containsKey(sum)) {
                result.add(map.get(sum) + 1);
                result.add(i);
                return result;
            }
            map.put(sum,i);
        }
        return result;
    }
}