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package g1601_1700.s1655_distribute_repeating_integers;

// #Hard #Array #Dynamic_Programming #Bit_Manipulation #Backtracking #Bitmask
// #2022_04_23_Time_7_ms_(94.23%)_Space_75.4_MB_(73.08%)

import java.util.Arrays;

/**
 * 1655 - Distribute Repeating Integers\.
 *
 * Hard
 *
 * You are given an array of `n` integers, `nums`, where there are at most `50` unique values in the array. You are also given an array of `m` customer order quantities, `quantity`, where `quantity[i]` is the amount of integers the i^th customer ordered. Determine if it is possible to distribute `nums` such that:
 *
 * *   The i^th customer gets **exactly** `quantity[i]` integers,
 * *   The integers the i^th customer gets are **all equal** , and
 * *   Every customer is satisfied.
 *
 * Return `true` _if it is possible to distribute_ `nums` _according to the above conditions_.
 *
 * **Example 1:**
 *
 * **Input:** nums = [1,2,3,4], quantity = [2]
 *
 * **Output:** false
 *
 * **Explanation:** The 0^th customer cannot be given two different integers.
 *
 * **Example 2:**
 *
 * **Input:** nums = [1,2,3,3], quantity = [2]
 *
 * **Output:** true
 *
 * **Explanation:** The 0^th customer is given [3,3]. The integers [1,2] are not used.
 *
 * **Example 3:**
 *
 * **Input:** nums = [1,1,2,2], quantity = [2,2]
 *
 * **Output:** true
 *
 * **Explanation:** The 0^th customer is given [1,1], and the 1st customer is given [2,2].
 *
 * **Constraints:**
 *
 * *   `n == nums.length`
 * *   1 <= n <= 10⁵
 * *   `1 <= nums[i] <= 1000`
 * *   `m == quantity.length`
 * *   `1 <= m <= 10`
 * *   1 <= quantity[i] <= 10⁵
 * *   There are at most `50` unique values in `nums`.
**/
public class Solution {
    public boolean canDistribute(int[] nums, int[] quantity) {
        int[] counter = count(nums);
        Arrays.sort(quantity);
        return dfs(counter, quantity, quantity.length - 1);
    }

    private boolean dfs(int[] counter, int[] quantity, int quantityId) {
        if (quantityId < 0) {
            return true;
        }
        for (int i = 0; i < counter.length; i++) {
            if (i > 0 && counter[i] == counter[i - 1]) {
                continue;
            }
            if (counter[i] >= quantity[quantityId]) {
                counter[i] -= quantity[quantityId];
                if (dfs(counter, quantity, quantityId - 1)) {
                    return true;
                }
                counter[i] += quantity[quantityId];
            }
        }
        return false;
    }

    private int[] count(int[] nums) {
        int[] counter = new int[1001];
        for (int n : nums) {
            counter[n]++;
        }
        Arrays.sort(counter);
        return Arrays.copyOfRange(counter, counter.length - 50, counter.length);
    }
}