leetcode 4 - binary search

博客指出处理nums1和nums2时,要保证nums1长度比nums2小,否则vector指针会越界。当分割线在首或尾时,需用INT_MIN和INT_MAX代替。思路转载自相关博客。

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注意:

1)需要保证nums1 的长度比 nums2 的长度小;(否则vector指针会越界)

2)  当分割线(partition)在首或尾时,用INT_MIN 和 INT_MAX 代替。

思路:

 

class Solution {
public:
    double static findMedianSortedArrays(vector<int>& nums1, vector<int>& nums2) {

        int x = nums1.size();
        int y = nums2.size();
        
        if(x>y)
            return findMedianSortedArrays(nums2, nums1);
        
        int l = x + y;
        int length = (x + y + 1) / 2;
        double median = 0;
        //vector x 中:
        int start = 0;
        int end = x;

        while (start <= end) {
            //cout << start << endl << end << endl;
            int p_x = (start + end) / 2;
            int p_y = length - p_x;

            //if p_x is 0 it means nothing is there on left side, use -INF for maxLeftX
            //if p_x is length of input then there is nothing on right side, use +INF for minRightX
            double maxLeftX = (p_x == 0) ? INT_MIN : nums1[p_x - 1];
            double minRightX = (p_x == x) ? INT_MAX : nums1[p_x];

            double maxLeftY = (p_y == 0) ? INT_MIN : nums2[p_y - 1];
            double minRightY = (p_y == y) ? INT_MAX : nums2[p_y];

            if (maxLeftX <= minRightY && maxLeftY <= minRightX)
            {
                if (l % 2 == 0)
                    //长度为偶数
                    {
                        median = (max(maxLeftX, maxLeftY)+ min(minRightX, minRightY)) / 2.0;
                        //cout << max(maxLeftX, maxLeftY) << endl << min(minRightX, minRightY) << endl;
                    }
                else
                    median = max(maxLeftX, maxLeftY);
                return median;
            }
            else if (maxLeftX > minRightY)
                end = p_x - 1;       //nums1的分割线左移
            else if (maxLeftY > minRightX)
                start = p_x + 1;   //nums1的分割线右移
        }
        return -1;
    }
};

 

转载于:https://www.cnblogs.com/Bella2017/p/10546961.html

### LeetCode 475 Heaters Problem Solution and Explanation In this problem, one needs to find the minimum radius of heaters so that all houses can be warmed. Given positions of `houses` and `heaters`, both represented as integer arrays, the task is to determine the smallest maximum distance from any house to its nearest heater[^1]. To solve this issue efficiently: #### Binary Search Approach A binary search on answer approach works well here because increasing the radius monotonically increases the number of covered houses. Start by sorting the list of heaters' locations which allows using binary search for finding closest heater distances quickly. ```python def findRadius(houses, heaters): import bisect houses.sort() heaters.sort() max_distance = 0 for house in houses: pos = bisect.bisect_left(heaters, house) dist_to_right_heater = abs(heaters[pos] - house) if pos < len(heaters) else float('inf') dist_to_left_heater = abs(heaters[pos-1] - house) if pos > 0 else float('inf') min_dist_for_house = min(dist_to_right_heater, dist_to_left_heater) max_distance = max(max_distance, min_dist_for_house) return max_distance ``` This code snippet sorts the lists of houses and heaters first. For each house, it finds the nearest heater either directly or indirectly (to the left side). It calculates the minimal distance between these two options and updates the global maximal value accordingly[^3]. The constraints specify that numbers of houses and heaters do not exceed 25000 while their positions range up to \(10^9\)[^2], making efficient algorithms like binary search necessary due to large input sizes involved.
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