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;
     }
 }