。配列のパッチ適用

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.

Returnthe 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 inascending 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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