Partition of a set of integer into 3 subsets of approximately equal sum
Let $x_i,\ i=1\ldots,n$, be the list of nutritional values of the $n$ fruits, which I assume are nonnegative integers.

You want to partition $\{1,\ldots,n\}$ into three sets $A,B,C$ to maximize the minimum of $x_A = \sum_{i\in A} x_i$, $x_B = \sum_{i \in B} x_i$, $x_C = \sum_{i \in C} x_i$.  This is a variant of the set-partitioning problem.  It is NP-complete.

However, there is a dynamic programming algorithm that is pseudo-polynomial (i.e. polynomial in $n$ and $S = \sum_{i=1}^n x_i$). Namely, for $1 \le m \le n$, $u, v \ge 0$ with $u+v \le \sum_{i=1}^m x_i$, let 
$T(m,u,v) = 1$ if there are disjoint subsets $A(m,u,v), B(m,u,v)$ of $\{1,\ldots,m\}$ 
such that $\sum_{i \in A(m,u,v)} x_i = u$ and $\sum_{i \in B(m,u,v)} x_i = v$, $T(m,u,v) = 0$ otherwise.
Thus 
$$T(1,0,0) = T(1,0,x_1) = 1,\ T(1,u,v) = 0 \text{ otherwise.}$$
For $m &gt; 1$,
$$T(m,u,v) = 1 \Longleftrightarrow T(m-1,u,v) + T(m-1,u-x_m,v) + T(m-1,u,v-x_m) \ge 1.$$

After computing all $T(m,u,v)$ using this recursion, you want to find the $(u,v)$ with $u$ as large as possible subject to $T(m,u,v) = 1$ and $u \le v \le S - u - v$.