Patching Array

07/18/2016 Greedy

Question

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:

nums = [1, 3], n = 6

Return 1.

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:

nums = [1, 5, 10], n = 20

Return 2.

The two patches can be [2, 4].

Example 3:

nums = [1, 2, 2], n = 5

Return 0.

Solution

Result: Accepted Time: 4 ms

Here should be some explanations.

    int minPatches(int* nums, int numsSize, int n)
{
int ret = 0,ptr = 0;
unsigned int range = 0,limit = n;
while(range < limit)
{
if(ptr == numsSize || range + 1 < nums[ptr])
++ret,range = (range << 1) | 1;
else
range += nums[ptr++];
}
return ret;
}
// if you can reach [1,n] ,then you patch n+1 ,you get [1,2n+1].


Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$