LeetCode 167. 两数之和II-输入有序数组 Two Sum II - Input Array is Sorted

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3-6 对撞指针 Two Sum II - Input Array is Sorted

双索引技术（Two Points）

1. 对撞指针
2. 滑动窗口

题目: LeetCode 167. 两数之和II-输入有序数组

给定一个已按照升序排列 的有序数组，找到两个数使得它们相加之和等于目标数。

函数应该返回这两个下标值 index1 和 index2，其中 index1 必须小于 index2。

说明:

返回的下标值（index1 和 index2）不是从零开始的。
你可以假设每个输入只对应唯一的答案，而且你不可以重复使用相同的元素。
示例:

输入: numbers = [2, 7, 11, 15], target = 9
输出: [1,2]
解释: 2 与 7 之和等于目标数 9 。因此 index1 = 1, index2 = 2 。

// 167. Two Sum II - Input array is sorted
// https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/description/
//
// 暴力枚举法
// 时间复杂度: O(n^2)
// 空间复杂度: O(1)
public class Solution1 {

    public int[] twoSum(int[] numbers, int target) {

        if(numbers.length < 2 /*|| !isSorted(numbers)*/)
            throw new IllegalArgumentException("Illegal argument numbers");

        for(int i = 0 ; i < numbers.length ; i ++)
            for(int j = i+1 ; j < numbers.length ; j ++)
                if(numbers[i] + numbers[j] == target){
                    int[] res = {i+1, j+1};
                    return res;
                }

        throw new IllegalStateException("The input has no solution");
    }

    private boolean isSorted(int[] numbers){
        for(int i = 1 ; i < numbers.length ; i ++)
            if(numbers[i] < numbers[i-1])
                return false;
        return true;
    }

    private static void printArr(int[] nums){
        for(int num: nums)
            System.out.print(num + " ");
        System.out.println();
    }

    public static void main(String[] args) {

        int[] nums = {2, 7, 11, 15};
        int target = 9;
        printArr((new Solution1()).twoSum(nums, target));
    }
}

// 167. Two Sum II - Input array is sorted
// https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/description/
//
// 二分搜索法
// 时间复杂度: O(nlogn)
// 空间复杂度: O(1)
public class Solution2 {

    public int[] twoSum(int[] numbers, int target) {

        if(numbers.length < 2 /*|| !isSorted(numbers)*/)
            throw new IllegalArgumentException("Illegal argument numbers");

        for(int i = 0 ; i < numbers.length - 1 ; i ++){
            int j = binarySearch(numbers, i+1, numbers.length-1, target - numbers[i]);
            if(j != -1){
                int[] res = {i+1, j+1};
                return res;
            }
        }

        throw new IllegalStateException("The input has no solution");
    }

    private int binarySearch(int[] nums, int l, int r, int target){

        if(l < 0 || l > nums.length)
            throw new IllegalArgumentException("l is out of bound");

        if(r < 0 || r > nums.length)
            throw new IllegalArgumentException("r is out of bound");

        while(l <= r){
            int mid = l + (r - l)/2;
            if(nums[mid] == target)
                return mid;
            if(target > nums[mid])
                l = mid + 1;
            else
                r = mid - 1;
        }

        return -1;
    }

    private boolean isSorted(int[] numbers){
        for(int i = 1 ; i < numbers.length ; i ++)
            if(numbers[i] < numbers[i-1])
                return false;
        return true;
    }

    private static void printArr(int[] nums){
        for(int num: nums)
            System.out.print(num + " ");
        System.out.println();
    }

    public static void main(String[] args) {

        int[] nums = {2, 7, 11, 15};
        int target = 9;
        printArr((new Solution2()).twoSum(nums, target));
    }
}

// 167. Two Sum II - Input array is sorted
// https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/description/
//
// 对撞指针
// 时间复杂度: O(n)
// 空间复杂度: O(1)
public class Solution3 {

    public int[] twoSum(int[] numbers, int target) {

        if(numbers.length < 2 /*|| !isSorted(numbers)*/)
            throw new IllegalArgumentException("Illegal argument numbers");

        int l = 0, r = numbers.length - 1;
        while(l < r){

            if(numbers[l] + numbers[r] == target){
                int[] res = {l+1, r+1};
                return res;
            }
            else if(numbers[l] + numbers[r] < target)
                l ++;
            else // numbers[l] + numbers[r] > target
                r --;
        }

        throw new IllegalStateException("The input has no solution");
    }

    private boolean isSorted(int[] numbers){
        for(int i = 1 ; i < numbers.length ; i ++)
            if(numbers[i] < numbers[i-1])
                return false;
        return true;
    }

    private static void printArr(int[] nums){
        for(int num: nums)
            System.out.print(num + " ");
        System.out.println();
    }

    public static void main(String[] args) {

        int[] nums = {2, 7, 11, 15};
        int target = 9;
        printArr((new Solution3()).twoSum(nums, target));
    }
}