Algorithm

[LeetCode 330] Patching Array [Java] [Runtime : 1MS]

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2017-07-12

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07/12

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

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;
}

6.Test

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));
    }
}

Greedy

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