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330. Patching Array

Description

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

Solutions

• Java
• C++
• Python
• Go
• TypeScript

• class Solution {
      public int minPatches(int[] nums, int n) {
          long x = 1;
          int ans = 0;
          for (int i = 0; x <= n;) {
              if (i < nums.length && nums[i] <= x) {
                  x += nums[i++];
              } else {
                  ++ans;
                  x <<= 1;
              }
          }
          return ans;
      }
  }
  

• class Solution {
  public:
      int minPatches(vector<int>& nums, int n) {
          long long x = 1;
          int ans = 0;
          for (int i = 0; x <= n;) {
              if (i < nums.size() && nums[i] <= x) {
                  x += nums[i++];
              } else {
                  ++ans;
                  x <<= 1;
              }
          }
          return ans;
      }
  };
  

• class Solution:
      def minPatches(self, nums: List[int], n: int) -> int:
          x = 1
          ans = i = 0
          while x <= n:
              if i < len(nums) and nums[i] <= x:
                  x += nums[i]
                  i += 1
              else:
                  ans += 1
                  x <<= 1
          return ans
  
  

• func minPatches(nums []int, n int) (ans int) {
  	x := 1
  	for i := 0; x <= n; {
  		if i < len(nums) && nums[i] <= x {
  			x += nums[i]
  			i++
  		} else {
  			ans++
  			x <<= 1
  		}
  	}
  	return
  }
  

• function minPatches(nums: number[], n: number): number {
      let x = 1;
      let ans = 0;
      for (let i = 0; x <= n; ) {
          if (i < nums.length && nums[i] <= x) {
              x += nums[i++];
          } else {
              ++ans;
              x *= 2;
          }
      }
      return ans;
  }
  
  

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