2910. Minimum Number of Groups to Create a Valid Assignment

Description

You are given a 0-indexed integer array nums of length n.

We want to group the indices so for each index i in the range [0, n - 1], it is assigned to exactly one group.

A group assignment is valid if the following conditions hold:

For every group g, all indices i assigned to group g have the same value in nums.
For any two groups g₁ and g₂, the difference between the number of indices assigned to g₁ and g₂ should not exceed 1.

Return an integer denoting the minimum number of groups needed to create a valid group assignment.

Example 1:

Input: nums = [3,2,3,2,3]
Output: 2
Explanation: One way the indices can be assigned to 2 groups is as follows, where the values in square brackets are indices:
group 1 -> [0,2,4]
group 2 -> [1,3]
All indices are assigned to one group.
In group 1, nums[0] == nums[2] == nums[4], so all indices have the same value.
In group 2, nums[1] == nums[3], so all indices have the same value.
The number of indices assigned to group 1 is 3, and the number of indices assigned to group 2 is 2.
Their difference doesn't exceed 1.
It is not possible to use fewer than 2 groups because, in order to use just 1 group, all indices assigned to that group must have the same value.
Hence, the answer is 2.

Example 2:

Input: nums = [10,10,10,3,1,1]
Output: 4
Explanation: One way the indices can be assigned to 4 groups is as follows, where the values in square brackets are indices:
group 1 -> [0]
group 2 -> [1,2]
group 3 -> [3]
group 4 -> [4,5]
The group assignment above satisfies both conditions.
It can be shown that it is not possible to create a valid assignment using fewer than 4 groups.
Hence, the answer is 4.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁹

Solutions

Solution 1: Hash Table + Enumeration

We use a hash table $cnt$ to count the number of occurrences of each number in the array $nums$. Let $k$ be the minimum value of the number of occurrences, and then we can enumerate the size of the groups in the range $[k,..1]$. Since the difference in size between each group is not more than $1$, the group size can be either $k$ or $k+1$.

For the current group size $k$ being enumerated, we traverse each occurrence $v$ in the hash table. If $\lfloor \frac{v}{k} \rfloor < v \bmod k$, it means that we cannot divide the occurrence $v$ into $k$ or $k+1$ groups with the same value, so we can skip this group size $k$ directly. Otherwise, it means that we can form groups, and we only need to form as many groups of size $k+1$ as possible to ensure the minimum number of groups. Therefore, we can divide $v$ numbers into $\lceil \frac{v}{k+1} \rceil$ groups and add them to the current enumerated answer. Since we enumerate $k$ from large to small, as long as we find a valid grouping scheme, it must be optimal.

The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $nums$.

class Solution {
    public int minGroupsForValidAssignment(int[] nums) {
        Map<Integer, Integer> cnt = new HashMap<>();
        for (int x : nums) {
            cnt.merge(x, 1, Integer::sum);
        }
        int k = nums.length;
        for (int v : cnt.values()) {
            k = Math.min(k, v);
        }
        for (;; --k) {
            int ans = 0;
            for (int v : cnt.values()) {
                if (v / k < v % k) {
                    ans = 0;
                    break;
                }
                ans += (v + k) / (k + 1);
            }
            if (ans > 0) {
                return ans;
            }
        }
    }
}

class Solution {
public:
    int minGroupsForValidAssignment(vector<int>& nums) {
        unordered_map<int, int> cnt;
        for (int x : nums) {
            cnt[x]++;
        }
        int k = 1e9;
        for (auto& [_, v] : cnt) {
            ans = min(ans, v);
        }
        for (;; --k) {
            int ans = 0;
            for (auto& [_, v] : cnt) {
                if (v / k < v % k) {
                    ans = 0;
                    break;
                }
                ans += (v + k) / (k + 1);
            }
            if (ans) {
                return ans;
            }
        }
    }
};

class Solution:
    def minGroupsForValidAssignment(self, nums: List[int]) -> int:
        cnt = Counter(nums)
        for k in range(min(cnt.values()), 0, -1):
            ans = 0
            for v in cnt.values():
                if v // k < v % k:
                    ans = 0
                    break
                ans += (v + k) // (k + 1)
            if ans:
                return ans

func minGroupsForValidAssignment(nums []int) int {
	cnt := map[int]int{}
	for _, x := range nums {
		cnt[x]++
	}
	k := len(nums)
	for _, v := range cnt {
		k = min(k, v)
	}
	for ; ; k-- {
		ans := 0
		for _, v := range cnt {
			if v/k < v%k {
				ans = 0
				break
			}
			ans += (v + k) / (k + 1)
		}
		if ans > 0 {
			return ans
		}
	}
}

function minGroupsForValidAssignment(nums: number[]): number {
    const cnt: Map<number, number> = new Map();
    for (const x of nums) {
        cnt.set(x, (cnt.get(x) || 0) + 1);
    }
    for (let k = Math.min(...cnt.values()); ; --k) {
        let ans = 0;
        for (const [_, v] of cnt) {
            if (((v / k) | 0) < v % k) {
                ans = 0;
                break;
            }
            ans += Math.ceil(v / (k + 1));
        }
        if (ans) {
            return ans;
        }
    }
}

use std::collections::HashMap;

impl Solution {
    pub fn min_groups_for_valid_assignment(nums: Vec<i32>) -> i32 {
        let mut cnt: HashMap<i32, i32> = HashMap::new();

        for x in nums.iter() {
            let count = cnt.entry(*x).or_insert(0);
            *count += 1;
        }

        let mut k = i32::MAX;

        for &v in cnt.values() {
            k = k.min(v);
        }

        for k in (1..=k).rev() {
            let mut ans = 0;

            for &v in cnt.values() {
                if v / k < v % k {
                    ans = 0;
                    break;
                }

                ans += (v + k) / (k + 1);
            }

            if ans > 0 {
                return ans;
            }
        }

        0
    }
}

2910 - Minimum Number of Groups to Create a Valid Assignment

2910. Minimum Number of Groups to Create a Valid Assignment

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2910. Minimum Number of Groups to Create a Valid Assignment

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All Problems

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