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public class Solution {
    public int minPatches(int[] nums, int n) {
        long end = 0; // [1,2,31,33] 2147483647 => 28
        int i = 0;
        int count = 0;
        while (i < nums.length) {
            if (end >= n) {
                return count;
            }
            if (nums[i] <= end + 1) {
                end += nums[i++];
            } else {
                count++;
                end += end + 1;
            }
        }
        while (end < n) { // [] 7 => 3
            end += end + 1;
            count++;
        }
        return count;
    }
}

public class Solution {
    public int minPatches(int[] nums, int n) {
        long range = 1;//the max val that can get in the current nums in the array.
		int add = 0;
		int i = 0;
		while(range <= n){
			if(i < nums.length && nums[i] <= range){
				range += nums[i++];
			}
			else{
				add++;
				range *= 2;
			}
		}
		return add;    
    }
}