Question

1887. Reduction Operations to Make the Array Elements Equal

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Description

Given an integer array nums, your goal is to make all elements in nums equal. To complete one operation, follow these steps:

1. Find the largest value in nums. Let its index be i (0-indexed) and its value be largest. If there are multiple elements with the largest value, pick the smallest i.
2. Find the next largest value in nums strictly smaller than largest. Let its value be nextLargest.
3. Reduce nums[i] to nextLargest.

Return _the number of operations to make all elements in _nums_ equal_.

 

Example 1:

Input: nums = [5,1,3]
Output: 3
Explanation: It takes 3 operations to make all elements in nums equal:
1. largest = 5 at index 0. nextLargest = 3. Reduce nums[0] to 3. nums = [3,1,3].
2. largest = 3 at index 0. nextLargest = 1. Reduce nums[0] to 1. nums = [1,1,3].
3. largest = 3 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1,1].

Example 2:

Input: nums = [1,1,1]
Output: 0
Explanation: All elements in nums are already equal.

Example 3:

Input: nums = [1,1,2,2,3]
Output: 4
Explanation: It takes 4 operations to make all elements in nums equal:
1. largest = 3 at index 4. nextLargest = 2. Reduce nums[4] to 2. nums = [1,1,2,2,2].
2. largest = 2 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1,1,2,2].
3. largest = 2 at index 3. nextLargest = 1. Reduce nums[3] to 1. nums = [1,1,1,1,2].
4. largest = 2 at index 4. nextLargest = 1. Reduce nums[4] to 1. nums = [1,1,1,1,1].

 

Constraints:

• 1 <= nums.length <= 5 * 104
• 1 <= nums[i] <= 5 * 104

Solutions

Solution 1

class Solution:
  def reductionOperations(self, nums: List[int]) -> int:
    nums.sort()
    ans = cnt = 0
    for i, v in enumerate(nums[1:]):
      if v != nums[i]:
        cnt += 1
      ans += cnt
    return ans

class Solution {
  public int reductionOperations(int[] nums) {
    Arrays.sort(nums);
    int ans = 0, cnt = 0;
    for (int i = 1; i < nums.length; ++i) {
      if (nums[i] != nums[i - 1]) {
        ++cnt;
      }
      ans += cnt;
    }
    return ans;
  }
}

class Solution {
public:
  int reductionOperations(vector<int>& nums) {
    sort(nums.begin(), nums.end());
    int ans = 0, cnt = 0;
    for (int i = 1; i < nums.size(); ++i) {
      cnt += nums[i] != nums[i - 1];
      ans += cnt;
    }
    return ans;
  }
};

func reductionOperations(nums []int) int {
  sort.Ints(nums)
  ans, cnt := 0, 0
  for i, v := range nums[1:] {
    if v != nums[i] {
      cnt++
    }
    ans += cnt
  }
  return ans
}

function reductionOperations(nums: number[]): number {
  nums.sort((a, b) => a - b);
  let ans = 0;
  let cnt = 0;
  for (let i = 1; i < nums.length; ++i) {
    if (nums[i] != nums[i - 1]) {
      ++cnt;
    }
    ans += cnt;
  }
  return ans;
}

public class Solution {
  public int ReductionOperations(int[] nums) {
    Array.Sort(nums);
    int ans = 0, up = 0;
    for (int i = 1; i < nums.Length; i++) {
      if (nums[i] != nums[i - 1]) {
        up++;
      }
      ans += up;
    }
    return ans;
  }
}

Solution 2

class Solution:
  def reductionOperations(self, nums: List[int]) -> int:
    ans = cnt = 0
    for _, v in sorted(Counter(nums).items()):
      ans += cnt * v
      cnt += 1
    return ans

class Solution {
  public int reductionOperations(int[] nums) {
    Map<Integer, Integer> tm = new TreeMap<>();
    for (int v : nums) {
      tm.put(v, tm.getOrDefault(v, 0) + 1);
    }
    int ans = 0, cnt = 0;
    for (int v : tm.values()) {
      ans += cnt * v;
      ++cnt;
    }
    return ans;
  }
}

class Solution {
public:
  int reductionOperations(vector<int>& nums) {
    map<int, int> m;
    for (int v : nums) ++m[v];
    int ans = 0, cnt = 0;
    for (auto [_, v] : m) {
      ans += cnt * v;
      ++cnt;
    }
    return ans;
  }
};