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To maximize the like-time coefficient, we can sort the satisfaction levels in non-descending order and calculate the possible like-time coefficients by considering prefixes from the end of the sorted array. This allows us to selectively choose higher satisfaction dishes to maximize the total like-time coefficient.
Time Complexity: O(n log n) due to sorting.
Space Complexity: O(1) for using a constant amount of extra space.
1import java.util.Arrays;
2
3public class ReducingDishes {
4 public static int maxSatisfaction(int[] satisfaction) {
5 Arrays.sort(satisfaction);
6 int total = 0, sum = 0;
7 for (int i = satisfaction.length - 1; i >= 0; i--) {
8 sum += satisfaction[i];
9 if (sum > 0) {
10 total += sum;
11 } else {
12 break;
13 }
14 }
15 return total;
16 }
17
18 public static void main(String[] args) {
19 int[] satisfaction = {-1, -8, 0, 5, -9};
20 System.out.println(maxSatisfaction(satisfaction));
21 }
22}This Java solution sorts the satisfaction array in ascending order, then effectively handles calculations from the end of the array to maximize the like-time coefficient.
An alternative approach involves using dynamic programming to maximize the like-time coefficient. We maintain a DP table where `dp[i]` represents the maximum like-time coefficient attainable using the first `i` dishes. This approach computes overlap coefficients dynamically using state transitions calculated for each dish considered.
Time Complexity: O(n^2)
Space Complexity: O(n)
1using System;
class Program {
static int MaxSatisfaction(int[] satisfaction) {
Array.Sort(satisfaction);
int n = satisfaction.Length;
int[] dp = new int[n + 1];
for (int i = n - 1; i >= 0; i--) {
for (int t = 0; t <= i; t++) {
dp[t] = Math.Max(dp[t], dp[t + 1] + satisfaction[i] * (t + 1));
}
}
return dp[0];
}
static void Main() {
int[] satisfaction = {4, 3, 2};
Console.WriteLine(MaxSatisfaction(satisfaction));
}
}The C# program adopts dynamic programming to make state transitions represent time indices for prepared dishes, updating choices dynamically to achieve the maximum like-time coefficient.