LeetCode Patching Array
Tags: Algorithm, LeetCodeGiven 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.
Java Solution
The following algorithm is from https://discuss.leetcode.com/topic/35494/solution-explanation
We define miss to be the smallest number that will miss, which means, given an input {1…m}, we can build all sums in [0, miss). For the next number x in the array, if x <= miss, then we can build sums in the range [0, miss + x), thus there is no need to add a number.
If the array is empty, or the next number x in the array is larger than miss, we have to add a number to get miss. The best strategy is to add miss itself. Then our next range is [0, miss + miss).
I also used an example below to describe how this method works.
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 |
public class Solution { public int minPatches(int[] nums, int n) { // [1,2,5,9] //set miss = 1 // 1 ==> {1} [1, miss <= miss + 1 == 2) // since 2 <= miss, {1} + 2 ==> {1, 2, 3} === [1, miss + 2 == 4) // since 5 is larger than 4, we have to add 4 // with 4, we can build {1, 2, 3} + 4 ==> {1, 2, 3, 4, 5, 6, 7} == [1, 4 + 4 == 8) // 9 > 8, so we have to add 8: {1, 2, 3, ... 7} + {8} ==> {1, .... 8 + 7} == [1, 8 + 8 == 16) //{1}, 1 >> 0 //{1, 2}, 3 >> 0 //{1, 2}, 4 >> 1 long miss = 1; int cnt = 0; int i = 0; while(miss <= n){ if(i < nums.length && nums[i] <= miss) { miss += nums[i]; i++; } else { miss += miss; // add miss to the array cnt++; } } return cnt; } } |
