LeetCode1 Two Sum

LeetCode1

Given an array of integers, find two numbers such that they add up to a specific target number.

The function twoSum should return indices of the two numbers such that they add up to the target, where index1 must be less than index2. Please note that your returned answers (both index1 and index2) are not zero-based.

You may assume that each input would have exactly one solution.

Input: numbers={2, 7, 11, 15}, target=9
Output: index1=1, index2=2

O(n2) runtime, O(1) space – Brute force:

The brute force approach is simple. Loop through each element x and find if there is another value that equals to target – x. As finding another value requires looping through the rest of array, its runtime complexity is O(n2).

public int[] twoSum(int[] nums, int target) {
        int[] result = new int[2];
        for (int i = 0; i < nums.length; i++) {
            for (int j = i+1; j < nums.length; j++) {
                if (nums[i]+nums[j] == target){
                    result[0] = i + 1;
                    result[1] = j + 1;
                }
            }
        }
        return result;
}

O(n) runtime, O(n) space – Hash table:

We could reduce the runtime complexity of looking up a value to O(1) using a hash map that maps a value to its index.

public int[] twoSum(int[] nums, int target) {
        int[] result = new int[2];
        Map<Integer, Integer> map = new HashMap<Integer, Integer>();
        for (int i = 0; i < nums.length; i++) {
            int temp = target - nums[i];
            if (map.containsKey(temp)){
                result[0] = map.get(temp);
                result[1] = i+1;
            }else{
                map.put(nums[i], i+1);
            }
        }
        return result;
}

总结

第一种采用暴力求解，可以轻松解决问题，且空间复杂度低
第二种方法采用hashmap方法实现了空间换时间。