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 <= 10001 <= nums[i] <= 104numsis sorted in ascending order.1 <= n <= 231- 1
Approach 01:
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C++
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Python
#include <vector>
class Solution {
public:
int minPatches(std::vector<int>& nums, int n) {
int patches_needed = 0; // Number of patches (numbers) we need to add
int nums_index = 0; // Current index in the nums list
long long current_miss = 1; // The minimum sum in the range [1, n] that we might miss
while (current_miss <= n) {
if (nums_index < nums.size() && nums[nums_index] <= current_miss) {
// If the current number in nums is less than or equal to current_miss,
// add it to the range and move to the next number in nums
current_miss += nums[nums_index];
nums_index += 1;
} else {
// If the current number in nums is greater than current_miss,
// we need to add current_miss itself to the range.
// This action increases the range from [1, current_miss) to [1, 2 * current_miss).
current_miss += current_miss;
patches_needed += 1;
}
}
return patches_needed;
}
};
from typing import List
class Solution:
def minPatches(self, nums: List[int], n: int) -> int:
patches_needed = 0 # Number of patches (numbers) we need to add
nums_index = 0 # Current index in the nums list
current_miss = 1 # The minimum sum in the range [1, n] that we might miss
while current_miss <= n:
if nums_index < len(nums) and nums[nums_index] <= current_miss:
# If the current number in nums is less than or equal to current_miss,
# add it to the range and move to the next number in nums
current_miss += nums[nums_index]
nums_index += 1
else:
# If the current number in nums is greater than current_miss,
# we need to add current_miss itself to the range.
# This action increases the range from [1, current_miss) to [1, 2 * current_miss).
current_miss += current_miss
patches_needed += 1
return patches_needed