Optimal Merge Pattern algorithm

OptimalMergePattern.java

import java.util.*;

public class OptimalMergePattern {
    public static void main(String[] args) {
        System.out.println(getLeastMergingCost(new int[]{20, 30, 10, 5, 30}));
    }

    private static int getLeastMergingCost(int[] list) {
        Arrays.sort(list);
        int maxCost = list[0];
        int minMergingCost = maxCost;
        int n = list.length;

        int i = 0;
        while (i < n) {
            if (i == 0) {
                if ((i + 1) < n) {
                    maxCost += list[i + 1];
                    i += 2;
                } else {
                    break;
                }
            } else {
                if ((i + 1) < n) {
                    if ((maxCost + list[i]) > (list[i] + list[i + 1])) {
                        minMergingCost += list[i] + list[i + 1];
                        maxCost += list[i] + list[i + 1];
                        i += 2;
                    } else {
                        maxCost += list[i];
                        i++;
                    }
                } else {
                    maxCost += list[i];
                    i++;
                }
            }

            minMergingCost += maxCost;
        }

        return minMergingCost;
    }
}