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3354. Make Array Elements Equal to Zero

Approach 1: $O(n)$ space

  • Time: $O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  int countValidSelections(vector<int>& nums) {
    const int n = nums.size();
    int ans = 0;
    vector<int> prefix(n);  // sum(nums[0..i - 1])
    vector<int> suffix(n);  // sum(nums[i + 1..n - 1])

    for (int i = 1; i < n; ++i)
      prefix[i] = prefix[i - 1] + nums[i - 1];

    for (int i = n - 2; i >= 0; --i)
      suffix[i] = suffix[i + 1] + nums[i + 1];

    for (int i = 0; i < n; ++i) {
      if (nums[i] > 0)
        continue;
      if (prefix[i] == suffix[i])
        ans += 2;  // Go to either direction.
      if (abs(prefix[i] - suffix[i]) == 1)
        ans += 1;  // Go to the direction with the larger sum.
    }

    return ans;
  }
};

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class Solution {
  public int countValidSelections(int[] nums) {
    final int n = nums.length;
    int ans = 0;
    int[] prefix = new int[n]; // sum(nums[0..i - 1])
    int[] suffix = new int[n]; // sum(nums[i + 1..n - 1])

    for (int i = 1; i < n; ++i)
      prefix[i] = prefix[i - 1] + nums[i - 1];

    for (int i = n - 2; i >= 0; --i)
      suffix[i] = suffix[i + 1] + nums[i + 1];

    for (int i = 0; i < n; ++i) {
      if (nums[i] > 0)
        continue;
      if (prefix[i] == suffix[i])
        ans += 2; // Go to either direction.
      if (Math.abs(prefix[i] - suffix[i]) == 1)
        ans += 1; // Go to the direction with the larger sum.
    }

    return ans;
  }
}

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class Solution:
  def countValidSelections(self, nums: list[int]) -> int:
    ans = 0
    prefix = list(itertools.accumulate(nums))
    suffix = list(itertools.accumulate(nums[::-1]))[::-1]

    for i, num in enumerate(nums):
      if num > 0:
        continue
      if prefix[i] == suffix[i]:
        ans += 2  # Go to either direction.
      if abs(prefix[i] - suffix[i]) == 1:
        ans += 1  # Go to the direction with the larger sum.

    return ans

Approach 2: $O(1)$ space

  • Time: $O(n)$
  • Space: $O(1)$
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class Solution {
 public:
  int countValidSelections(vector<int>& nums) {
    int ans = 0;
    int prefix = 0;
    int suffix = accumulate(nums.begin(), nums.end(), 0);

    for (int i = 0; i < nums.size(); ++i) {
      suffix -= nums[i];
      prefix += nums[i];
      if (nums[i] > 0)
        continue;
      if (prefix == suffix)
        ans += 2;  // Go to either direction.
      if (abs(prefix - suffix) == 1)
        ans += 1;  // Go to the direction with the larger sum.
    }

    return ans;
  }
};

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class Solution {
  public int countValidSelections(int[] nums) {
    int ans = 0;
    int prefix = 0;
    int suffix = Arrays.stream(nums).sum();

    for (int i = 0; i < nums.length; ++i) {
      suffix -= nums[i];
      prefix += nums[i];
      if (nums[i] > 0)
        continue;
      if (prefix == suffix)
        ans += 2; // Go to either direction.
      if (Math.abs(prefix - suffix) == 1)
        ans += 1; // Go to the direction with the larger sum.
    }

    return ans;
  }
}

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class Solution:
  def countValidSelections(self, nums: list[int]) -> int:
    ans = 0
    prefix = 0
    suffix = sum(nums)

    for i, num in enumerate(nums):
      suffix -= num
      prefix += num
      if num > 0:
        continue
      if prefix == suffix:
        ans += 2  # Go to either direction.
      if abs(prefix - suffix) == 1:
        ans += 1  # Go to the direction with the larger sum.

    return ans