Java Tape Equilibrium
public class Solution {
    public static int tapeEquilibrium(int[] a) {
        long firstPart = 0;
        long secondPart = 0;
        for (int v : a) {
            secondPart += v;
        }

        long min = Long.MAX_VALUE;
        for (int i = 0; i < a.length - 1; i++) {
            firstPart += i;
            secondPart -= i;
            long difference = Math.abs(firstPart - secondPart);
            min = Math.min(min, difference);
        }

        return (int) min;
    }
}

This keeps left and right running sums and updates the smallest difference at each split point.

Java Triangle
import java.util.Arrays;

public class Solution {
    public static int triangle(int[] a) {
        int[] sorted = a.clone();
        Arrays.sort(sorted);
        int c = sorted.length;
        if (c < 3) {
            return 0;
        }

        for (int i = 0; i < c - 2; i++) {
            if (sorted[i] > 0 && sorted[i] > (long) sorted[i + 2] - sorted[i + 1]) {
                return 1;
            }
        }

        return 0;
    }
}

This sorts the values and checks nearby triples, because a valid triangle only needs one local match after sorting.