330. Patching Array

Hard

Given a sorted integer array nums and an integer n, add/patch elements to the array such that any number in the 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

Constraints:

• 1 <= nums.length <= 1000
• 1 <= nums[i] <= 104
• nums is sorted in ascending order.
• 1 <= n <= 231 - 1

Solution:

class Solution {

    /**
     * @param Integer[] $nums
     * @param Integer $n
     * @return Integer
     */
    function minPatches($nums, $n) {
        $ans = 0;
        $i = 0;
        $miss = 1;
         while ($miss <= $n) {
            if ($i < count($nums) && $nums[$i] <= $miss) {
                $miss += $nums[$i++];
            } else {
                $miss += $miss;
                ++$ans;
            }
        }
        return $ans;
    }
}

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