Leetcode 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:

Input: nums = [1,3], n = 6
Output: 1
Explanation:
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:

Input: nums = [1,5,10], n = 20
Output: 2
Explanation: The two patches can be [2, 4].

Example 3:

Input: nums = [1,2,2], n = 5
Output: 0

Problem Analysis:

Suppose k is the smallest number missed in nums, [1, …, k) is covered, so add the number k we can cover [1, …, 2*k), if existing nums[i] that k≤nums[i]<2*k, then we can update covering range to [1, …, 2*k+nums[i]).

Iterating the procedure and update until reaching n, we can find the minimum number of patches.

Solution:

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

return count;
}
};

Time Complexity: O(n)

Space Complexity: O(1)