Formatted question description: https://leetcode.ca/all/1655.html

# 1655. Distribute Repeating Integers

Hard

## Description

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 = 

Output: false

Explanation: The 0th customer cannot be given two different integers.

Example 2:

Input: nums = [1,2,3,3], quantity = 

Output: true

Explanation: The 0th 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 0th customer is given [1,1], and the 1st customer is given [2,2].

Example 4:

Input: nums = [1,1,2,3], quantity = [2,2]

Output: false

Explanation: Although the 0th customer could be given [1,1], the 1st customer cannot be satisfied.

Example 5:

Input: nums = [1,1,1,1,1], quantity = [2,3]

Output: true

Explanation: The 0th customer is given [1,1], and the 1st customer is given [1,1,1].

Constraints:

• n == nums.length
• 1 <= n <= 10^5
• 1 <= nums[i] <= 1000
• m == quantity.length
• 1 <= m <= 10
• 1 <= quantity[i] <= 10^5
• There are at most 50 unique values in nums.

## Solution

First, use a map to store all numbers’ occurrences in nums. Then sort quantity, and do backtrack using the map and quantity, from the last element of quantity.

During the backtrack, if an entry’s value is greater than or equal to the current value of quantity, then try to distribute the integers to a customer, and continue the process for the next customer. If all customers are satisfied, return true. If there is no way to make all customers satisfied, return false.

class Solution {
public boolean canDistribute(int[] nums, int[] quantity) {
int sum = 0;
for (int num : quantity)
sum += num;
if (sum > nums.length)
return false;
Map<Integer, Integer> map = new HashMap<Integer, Integer>();
for (int num : nums) {
int count = map.getOrDefault(num, 0) + 1;
map.put(num, count);
}
Arrays.sort(quantity);
return backtrack(map, quantity, quantity.length - 1);
}

public boolean backtrack(Map<Integer, Integer> map, int[] quantity, int index) {
if (index == -1)
return true;
boolean flag = false;
int curQuantity = quantity[index];
Set<Integer> keySet = map.keySet();
for (int key : keySet) {
int value = map.get(key);
if (value >= curQuantity) {
map.put(key, value - curQuantity);
flag = backtrack(map, quantity, index - 1);
if (flag)
break;
else
map.put(key, value);
}
}
return flag;
}
}