Question

2321. Maximum Score Of Spliced Array

中文文档

Description

You are given two 0-indexed integer arrays nums1 and nums2, both of length n.

You can choose two integers left and right where 0 <= left <= right < n and swap the subarray nums1[left...right] with the subarray nums2[left...right].

• For example, if nums1 = [1,2,3,4,5] and nums2 = [11,12,13,14,15] and you choose left = 1 and right = 2, nums1 becomes [1,12,13,4,5] and nums2 becomes [11,2,3,14,15].

You may choose to apply the mentioned operation once or not do anything.

The score of the arrays is the maximum of sum(nums1) and sum(nums2), where sum(arr) is the sum of all the elements in the array arr.

Return _the maximum possible score_.

A subarray is a contiguous sequence of elements within an array. arr[left...right] denotes the subarray that contains the elements of nums between indices left and right (inclusive).

 

Example 1:

Input: nums1 = [60,60,60], nums2 = [10,90,10]
Output: 210
Explanation: Choosing left = 1 and right = 1, we have nums1 = [60,90,60] and nums2 = [10,60,10].
The score is max(sum(nums1), sum(nums2)) = max(210, 80) = 210.

Example 2:

Input: nums1 = [20,40,20,70,30], nums2 = [50,20,50,40,20]
Output: 220
Explanation: Choosing left = 3, right = 4, we have nums1 = [20,40,20,40,20] and nums2 = [50,20,50,70,30].
The score is max(sum(nums1), sum(nums2)) = max(140, 220) = 220.

Example 3:

Input: nums1 = [7,11,13], nums2 = [1,1,1]
Output: 31
Explanation: We choose not to swap any subarray.
The score is max(sum(nums1), sum(nums2)) = max(31, 3) = 31.

 

Constraints:

• n == nums1.length == nums2.length
• 1 <= n <= 105
• 1 <= nums1[i], nums2[i] <= 104

Solutions

Solution 1

class Solution:
  def maximumsSplicedArray(self, nums1: List[int], nums2: List[int]) -> int:
    def f(nums1, nums2):
      d = [a - b for a, b in zip(nums1, nums2)]
      t = mx = d[0]
      for v in d[1:]:
        if t > 0:
          t += v
        else:
          t = v
        mx = max(mx, t)
      return mx

    s1, s2 = sum(nums1), sum(nums2)
    return max(s2 + f(nums1, nums2), s1 + f(nums2, nums1))

class Solution {
  public int maximumsSplicedArray(int[] nums1, int[] nums2) {
    int s1 = 0, s2 = 0, n = nums1.length;
    for (int i = 0; i < n; ++i) {
      s1 += nums1[i];
      s2 += nums2[i];
    }
    return Math.max(s2 + f(nums1, nums2), s1 + f(nums2, nums1));
  }

  private int f(int[] nums1, int[] nums2) {
    int t = nums1[0] - nums2[0];
    int mx = t;
    for (int i = 1; i < nums1.length; ++i) {
      int v = nums1[i] - nums2[i];
      if (t > 0) {
        t += v;
      } else {
        t = v;
      }
      mx = Math.max(mx, t);
    }
    return mx;
  }
}

class Solution {
public:
  int maximumsSplicedArray(vector<int>& nums1, vector<int>& nums2) {
    int s1 = 0, s2 = 0, n = nums1.size();
    for (int i = 0; i < n; ++i) {
      s1 += nums1[i];
      s2 += nums2[i];
    }
    return max(s2 + f(nums1, nums2), s1 + f(nums2, nums1));
  }

  int f(vector<int>& nums1, vector<int>& nums2) {
    int t = nums1[0] - nums2[0];
    int mx = t;
    for (int i = 1; i < nums1.size(); ++i) {
      int v = nums1[i] - nums2[i];
      if (t > 0)
        t += v;
      else
        t = v;
      mx = max(mx, t);
    }
    return mx;
  }
};

func maximumsSplicedArray(nums1 []int, nums2 []int) int {
  s1, s2 := 0, 0
  n := len(nums1)
  for i, v := range nums1 {
    s1 += v
    s2 += nums2[i]
  }
  f := func(nums1, nums2 []int) int {
    t := nums1[0] - nums2[0]
    mx := t
    for i := 1; i < n; i++ {
      v := nums1[i] - nums2[i]
      if t > 0 {
        t += v
      } else {
        t = v
      }
      mx = max(mx, t)
    }
    return mx
  }
  return max(s2+f(nums1, nums2), s1+f(nums2, nums1))
}