# PAT Advanced 1113 Integer Set Partition

## Overview

PAT Advanced 1113 Integer Set Partition: sort the input, and choose the set A1 to be the first N/2 integers, this is testing gready algorithm and sorting.

## PAT Advenced 1113 Integer Set Partition

Given a set of N (> 1) positive integers, you are supposed to partition them into two disjoint sets A1 and A2 of n1 and n2 numbers, respectively. Let S1 and S2 denote the sums of all the numbers in A1 and A2, respectively. You are supposed to make the partition so that |n1 - n2| is minimized first, and then |S1 - S2| is maximized.

**Input Specification:**

Each input file contains one test case. For each case, the first line gives an integer N (2 <= N <= 105), and then N positive integers follow in the next line, separated by spaces. It is guaranteed that all the integers and their sum are less than 231.

**Output Specification:**

For each case, print in a line two numbers: |n1 - n2| and |S1 - S2|, separated by exactly one space.

**Sample Input 1:**

10 23 8 10 99 46 2333 46 1 666 555

**Sample Output 1:**

0 3611

**Sample Input 2:**

13 110 79 218 69 3721 100 29 135 2 6 13 5188 85

**Sample Output 2:**

1 9359

## PAT Advenced 1113 Integer Set Partition Solution

This is to test greedy algorithm and sorting, the solution is to sort the input, and choose the set A1 to be the first N/2 integers.

The following is the C++ source code that could be accepted by PAT OJ to pass this PAT Advenced 1113 Integer Set Partition:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

#include <vector>
#include <iostream>
#include <algorithm>
#include <numeric>
using std::cin;
using std::cout;
using std::vector;
int main() {
int n;
vector<int> nums;
cin >> n;
nums.resize(n);
for (int i = 0; i < n; ++i) {
cin >> nums[i];
}
std::sort(nums.begin(), nums.end());
int mid = n / 2;
cout << n % 2 << ' ' << std::accumulate(nums.begin() + mid, nums.end(), 0) -
std::accumulate(nums.begin(), nums.begin() + mid, 0);
return 0;
}

## Summary

PAT Advanced 1113 Integer Set Partition: sort the input, and choose the set A1 to be the first N/2 integers, this is testing gready algorithm and sorting.