Fair Electoral Vote Apportionment

Fair Electoral Vote Apportionment There are 50 states. State i has population population[i]. Allocate a total of E electoral votes subject to the following rules: Every state receives at least one vote. The remaining votes should be allocated as proportionally to population as possible. Define fairness using the largest-remainder (Hamilton) method: Give every state one vote first. Let R = E - 50 be the number of remaining votes. Compute quota[i] = population[i] / sum(population) * R. Each state first receives floor(quota[i]) additional votes. Allocate any unassigned votes in descending order of the fractional parts of quota[i]. Break equal fractional-part ties by smaller state index (states are indexed from 0). Output an array of 50 integers, where element i is the final number of electoral votes allocated to state i. Input Format Line 1: integer E, the total number of electoral votes. Line 2: 50 positive integers representing state populations. Output Format Print 50 space-separated integers representing the allocation. Constraints 50 <= E <= 10^9 1 <= population[i] <= 10^12 The total population is positive. Example Input: 55 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Output: 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Each state first gets one vote. The five remaining votes have equal fractional remainders for every state, so they go to states with indices 0 through 4. Example Input 50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Output 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1