LeetCode 774. Minimize Max Distance to Gas Station

原題鏈接在這里：https://leetcode.com/problems/minimize-max-distance-to-gas-station/description/

題目：

On a horizontal number line, we have gas stations at positions stations[0], stations[1], ..., stations[N-1], where N = stations.length.

Now, we add K more gas stations so that D, the maximum distance between adjacent gas stations, is minimized.

Return the smallest possible value of D.

Example:

Input: stations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], K = 9
Output: 0.500000

Note:

1. stations.length will be an integer in range [10, 2000].
2. stations[i] will be an integer in range [0, 10^8].
3. K will be an integer in range [1, 10^6].
4. Answers within 10^-6 of the true value will be accepted as correct.

題解：

在0到10^8范圍內猜測有這么個distance D.

若是符合要求, 那么每兩個station之間的距離除以這個D取整數就是新加油站的數目.

這些新加的數目和若是<= K, it means that distance is big enough. Think like this, if it is able to add j <= K gas stations to get achieve this distance. Than add K-j more just make the distance even smaller. 

所以可以繼續在較小的一側做 binary search to find a smaller D.

Time Complexity: O(nlogW). n = stations.length. W = 10^14. 從10^8范圍猜到10^-6范圍.

Space: O(1).

AC Java:

class Solution {
    public double minmaxGasDist(int[] stations, int K) {
        double l = 0;
        double r = 1e8;
        while(r - l > 1e-6){
            double m = l + (r-l)/2.0;
            if(possible(stations, K, m)){
                r = m;
            }else{
                l = m;
            }
        }
        
        return l;
    }
    
    private boolean possible(int [] stations, int K, double d){
        int count = 0;
        for(int i = 0; i<stations.length-1; i++){
            count += (int)((stations[i+1] - stations[i])/d);
        }
        
        return count <= K;
    }
}

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