Question

2155. All Divisions With the Highest Score of a Binary Array

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Description

You are given a 0-indexed binary array nums of length n. nums can be divided at index i (where 0 <= i <= n) into two arrays (possibly empty) numsleft and numsright:

• numsleft has all the elements of nums between index 0 and i - 1 (inclusive), while numsright has all the elements of nums between index i and n - 1 (inclusive).
• If i == 0, numsleft is empty, while numsright has all the elements of nums.
• If i == n, numsleft has all the elements of nums, while numsright is empty.

The division score of an index i is the sum of the number of 0's in numsleft and the number of 1's in numsright.

Return _all distinct indices that have the highest possible division score_. You may return the answer in any order.

 

Example 1:

Input: nums = [0,0,1,0]
Output: [2,4]
Explanation: Division at index
- 0: numsleft is []. numsright is [0,0,1,0]. The score is 0 + 1 = 1.
- 1: numsleft is [0]. numsright is [0,1,0]. The score is 1 + 1 = 2.
- 2: numsleft is [0,0]. numsright is [1,0]. The score is 2 + 1 = 3.
- 3: numsleft is [0,0,1]. numsright is [0]. The score is 2 + 0 = 2.
- 4: numsleft is [0,0,1,0]. numsright is []. The score is 3 + 0 = 3.
Indices 2 and 4 both have the highest possible division score 3.
Note the answer [4,2] would also be accepted.

Example 2:

Input: nums = [0,0,0]
Output: [3]
Explanation: Division at index
- 0: numsleft is []. numsright is [0,0,0]. The score is 0 + 0 = 0.
- 1: numsleft is [0]. numsright is [0,0]. The score is 1 + 0 = 1.
- 2: numsleft is [0,0]. numsright is [0]. The score is 2 + 0 = 2.
- 3: numsleft is [0,0,0]. numsright is []. The score is 3 + 0 = 3.
Only index 3 has the highest possible division score 3.

Example 3:

Input: nums = [1,1]
Output: [0]
Explanation: Division at index
- 0: numsleft is []. numsright is [1,1]. The score is 0 + 2 = 2.
- 1: numsleft is [1]. numsright is [1]. The score is 0 + 1 = 1.
- 2: numsleft is [1,1]. numsright is []. The score is 0 + 0 = 0.
Only index 0 has the highest possible division score 2.

 

Constraints:

• n == nums.length
• 1 <= n <= 105
• nums[i] is either 0 or 1.

Solutions

Solution 1

class Solution:
  def maxScoreIndices(self, nums: List[int]) -> List[int]:
    left, right = 0, sum(nums)
    mx = right
    ans = [0]
    for i, num in enumerate(nums):
      if num == 0:
        left += 1
      else:
        right -= 1
      t = left + right
      if mx == t:
        ans.append(i + 1)
      elif mx < t:
        mx = t
        ans = [i + 1]
    return ans

class Solution {

  public List<Integer> maxScoreIndices(int[] nums) {
    int left = 0, right = sum(nums);
    int mx = right;
    List<Integer> ans = new ArrayList<>();
    ans.add(0);
    for (int i = 0; i < nums.length; ++i) {
      if (nums[i] == 0) {
        ++left;
      } else {
        --right;
      }
      int t = left + right;
      if (mx == t) {
        ans.add(i + 1);
      } else if (mx < t) {
        mx = t;
        ans.clear();
        ans.add(i + 1);
      }
    }
    return ans;
  }

  private int sum(int[] nums) {
    int s = 0;
    for (int num : nums) {
      s += num;
    }
    return s;
  }
}

class Solution {
public:
  vector<int> maxScoreIndices(vector<int>& nums) {
    int left = 0, right = accumulate(nums.begin(), nums.end(), 0);
    int mx = right;
    vector<int> ans;
    ans.push_back(0);
    for (int i = 0; i < nums.size(); ++i) {
      if (nums[i] == 0)
        ++left;
      else
        --right;
      int t = left + right;
      if (mx == t)
        ans.push_back(i + 1);
      else if (mx < t) {
        mx = t;
        ans.clear();
        ans.push_back(i + 1);
      }
    }
    return ans;
  }
};

func maxScoreIndices(nums []int) []int {
  left, right := 0, 0
  for _, num := range nums {
    right += num
  }
  mx := right
  ans := []int{0}
  for i, num := range nums {
    if num == 0 {
      left++
    } else {
      right--
    }
    t := left + right
    if mx == t {
      ans = append(ans, i+1)
    } else if mx < t {
      mx = t
      ans = []int{i + 1}
    }
  }
  return ans
}

function maxScoreIndices(nums: number[]): number[] {
  const n = nums.length;
  const total = nums.reduce((a, c) => a + c, 0);
  let left = 0,
    right = total;
  let record: Array<number> = [total];
  for (const num of nums) {
    if (num == 0) {
      left++;
    } else {
      right--;
    }
    record.push(left + right);
  }
  const max = Math.max(...record);
  let ans: Array<number> = [];
  for (let i = 0; i <= n; i++) {
    if (record[i] == max) {
      ans.push(i);
    }
  }
  return ans;
}