CreateMaximumNumber.java

package com.fishercoder.solutions;

/**
 * Given two arrays of length m and n with digits 0-9 representing two numbers. Create the maximum number of length k <= m + n from digits of the two. The relative order of the digits from the same array must be preserved. Return an array of the k digits. You should try to optimize your time and space complexity.

 Example 1:
 nums1 = [3, 4, 6, 5]
 nums2 = [9, 1, 2, 5, 8, 3]
 k = 5
 return [9, 8, 6, 5, 3]

 Example 2:
 nums1 = [6, 7]
 nums2 = [6, 0, 4]
 k = 5
 return [6, 7, 6, 0, 4]

 Example 3:
 nums1 = [3, 9]
 nums2 = [8, 9]
 k = 3
 return [9, 8, 9]
 */
public class CreateMaximumNumber {
    public int[] maxNumber(int[] nums1, int[] nums2, int k) {
        int n = nums1.length;
        int m = nums2.length;
        int[] ans = new int[k];
        for(int i = Math.max(0, k-m); i <= k && i <= n; ++i){//what is this and why?
            int[] candidate = merge(maxArray(nums1, i), maxArray(nums2, k-i), k);
            if(greater(candidate, 0, ans, 0)) ans = candidate;
        }
        return ans;
    }

    private boolean greater(int[] nums1, int i, int[] nums2, int j) {
        while(i < nums1.length && j < nums2.length && nums1[i] == nums2[j]){
            i++;
            j++;
        }
        return j == nums2.length || (i < nums1.length && nums1[i] > nums2[j]);
    }

    private int[] merge(int[] nums1, int[] nums2, int k) {
        int[] ans = new int[k];
        for(int i = 0, j = 0, r = 0; r < k; r++){
            ans[r] = greater(nums1, i, nums2, j) ? nums1[i++] : nums2[j++];
        }
        return ans;
    }

    private int[] maxArray(int[] nums, int k) {
        int n = nums.length;
        int[] ans = new int[k];
        for(int i = 0, j = 0; i < n; i++){
            while(n - i + j > k && j > 0 && ans[j-1] < nums[i]) j--;
            if(j < k) ans[j++] = nums[i];
        }
        return ans;
    }
}