Leetcode no. 330

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本文介绍了一种算法，用于确定在给定的已排序正整数数组中，最少需要添加多少个元素以确保数组可以表示从1到n的所有整数。通过逐步分析数组中的元素和其覆盖的范围，我们最终得出结论，只需添加少量补丁即可实现目标。

330. Patching Array

Given a sorted positive integer array nums and an integer n, add/patch elements to the array such that any number in range [1, n] inclusive can be formed by the sum of some elements in the array. Return the minimum number of patches required.

Example 1:
nums = [1, 3], n = 6
Return 1.

Combinations of nums are [1], [3], [1,3], which form possible sums of: 1, 3, 4.
Now if we add/patch 2 to nums, the combinations are: [1], [2], [3], [1,3], [2,3], [1,2,3].
Possible sums are 1, 2, 3, 4, 5, 6, which now covers the range [1, 6].
So we only need 1 patch.

Example 2:
nums = [1, 5, 10], n = 20
Return 2.
The two patches can be [2, 4].

Example 3:
nums = [1, 2, 2], n = 5
Return 0.

public class Solution {
    public int minPatches(int[] nums, int n) {
        long cover=1; 
        int count=0, i=0;
        while (cover<= n){
            if (i< nums.length && cover>= nums[i])
                cover+= nums[i++];
            else {
                count++;
                cover+= cover;
            }
        }
        return count;
    }
}