描述

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.

樣例

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.

dalao思路： https://www.cnblogs.com/grandyang/p/5165821.html

另外做這道題的時候沒想通一個問題，如果n個數的和為m，那麼這n個數的組合可以構成1-m的任何數

  public int minPatches2(int[] nums, int n) {
        //
        long miss = 1;
        int res = 0;
        int i = 0;
        while (miss <= n) {
            if (i < nums.length && nums[i] <= miss) {
                miss += nums[i++];
            } else {
                miss += miss;
                ++res;
            }
        }
        return res;
}
 

summary：用一個變量表示範圍內最符合/不符合條件的數，並以此作為邊界，一步步處理