1. Runtime Distribution

2. Submission Details

3. Description

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.

4. Example

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.

5. Code

[restabs alignment="osc-tabs-right" responsive="true" icon="true" text="More" seltabcolor="#fdfdfd" seltabheadcolor="#000" tabheadcolor="blue"]
[restab title="Java" active="active"]

public int minPatches(int[] nums, int n) {
		int patch = 0; long max = 1;
        for(int i = 0, needPatch = 0; i < nums.length && max <= n; i += needPatch ^ 1){
        	needPatch = nums[i] <= max ? 0 : 1;
        	max += needPatch == 0 ? nums[i] : max;
        	patch += needPatch;
        }
        for(;max <= n;max += max, patch ++);
        return patch;
    }

[/restab]
[/restabs]

6.Test

[restabs alignment="osc-tabs-right" responsive="true" icon="true" text="More" seltabcolor="#fdfdfd" seltabheadcolor="#000" tabheadcolor="blue"]
[restab title="Java" active="active"]

import org.junit.Test;

public class LeetCode0330 {
	
	public int minPatches(int[] nums, int n) {
		int patch = 0; long max = 1;
        for(int i = 0, needPatch = 0; i < nums.length && max <= n; i += needPatch ^ 1){
        	needPatch = nums[i] <= max ? 0 : 1;
        	max += needPatch == 0 ? nums[i] : max;
        	patch += needPatch;
        }
        for(;max <= n;max += max, patch ++);
        return patch;
    }
	
	@Test
	public void test(){
		int[] nums = {1,2,31,33};
		System.out.println(minPatches(nums, 2147483647));
	}
}

[/restab]
[/restabs]