LeetCode 35. Search Insert Position

class Solution {
public:
    int searchInsert(vector<int>& nums, int target) {
        int pos;
        int length =nums.size();
        pos = binarySearch(nums,0,length-1,target);

        for(;pos<length;pos++){
            if(nums[pos]>=target)break;
        }
            return pos;
    }

    int binarySearch(vector<int>& nums, int first,int last, int target) {
        int mid = (first+last)/2;
        if(nums[mid]==target||first==mid) return mid;
        else if(nums[mid]<target){
            return binarySearch(nums,mid+1,last,target);
        }
        else{
            return binarySearch(nums,first,mid-1,target);
        }
    }
};

class Solution {
public:
    int searchInsert(vector<int>& nums, int target) {
        int low = 0, high = nums.size()-1;

        // Invariant: the desired index is between [low, high+1]
        while (low <= high) {
            int mid = low + (high-low)/2;

            if (nums[mid] < target)
                low = mid+1;
            else
                high = mid-1;
        }

        // (1) At this point, low > high. That is, low >= high+1
        // (2) From the invariant, we know that the index is between [low, high+1], so low <= high+1. Follwing from (1), now we know low == high+1.
        // (3) Following from (2), the index is between [low, high+1] = [low, low], which means that low is the desired index
        //     Therefore, we return low as the answer. You can also return high+1 as the result, since low == high+1
        return low;
    }
};