You are given an integer array nums of 2 * n integers. You need to partition nums into two arrays of length n to minimize the absolute difference of the sums of the arrays. To partition nums, put each element of nums into one of the two arrays.
Return the minimum possible absolute difference.
Example 1:
Input: nums = [3,9,7,3] Output: 2 Explanation: One optimal partition is: [3,9] and [7,3]. The absolute difference between the sums of the arrays is abs((3 + 9) - (7 + 3)) = 2.
Example 2:
Input: nums = [-36,36] Output: 72 Explanation: One optimal partition is: [-36] and [36]. The absolute difference between the sums of the arrays is abs((-36) - (36)) = 72.
Example 3:
Input: nums = [2,-1,0,4,-2,-9] Output: 0 Explanation: One optimal partition is: [2,4,-9] and [-1,0,-2]. The absolute difference between the sums of the arrays is abs((2 + 4 + -9) - (-1 + 0 + -2)) = 0.
Constraints:
1 <= n <= 15nums.length == 2 * n-107 <= nums[i] <= 107
class Solution:
def minimumDifference(self, nums: List[int]) -> int:
n = len(nums) >> 1
f = collections.defaultdict(set)
g = collections.defaultdict(set)
for i in range(1 << n):
s = cnt = 0
s1 = cnt1 = 0
for j in range(n):
if (i & (1 << j)) != 0:
s += nums[j]
cnt += 1
s1 += nums[n + j]
cnt1 += 1
else:
s -= nums[j]
s1 -= nums[n + j]
f[cnt].add(s)
g[cnt1].add(s1)
ans = float('inf')
for i in range(n + 1):
fi, gi = sorted(list(f[i])), sorted(list(g[n - i]))
# min(abs(f[i] + g[n - i]))
for a in fi:
left, right = 0, len(gi) - 1
b = -a
while left < right:
mid = (left + right) >> 1
if gi[mid] >= b:
right = mid
else:
left = mid + 1
ans = min(ans, abs(a + gi[left]))
if left > 0:
ans = min(ans, abs(a + gi[left - 1]))
return ansclass Solution {
public int minimumDifference(int[] nums) {
int n = nums.length >> 1;
Map<Integer, Set<Integer>> f = new HashMap<>();
Map<Integer, Set<Integer>> g = new HashMap<>();
for (int i = 0; i < (1 << n); ++i) {
int s = 0, cnt = 0;
int s1 = 0, cnt1 = 0;
for (int j = 0; j < n; ++j) {
if ((i & (1 << j)) != 0) {
s += nums[j];
++cnt;
s1 += nums[n + j];
++cnt1;
} else {
s -= nums[j];
s1 -= nums[n + j];
}
}
f.computeIfAbsent(cnt, k -> new HashSet<>()).add(s);
g.computeIfAbsent(cnt1, k -> new HashSet<>()).add(s1);
}
int ans = Integer.MAX_VALUE;
for (int i = 0; i <= n; ++i) {
List<Integer> fi = new ArrayList<>(f.get(i));
List<Integer> gi = new ArrayList<>(g.get(n - i));
Collections.sort(fi);
Collections.sort(gi);
for (int a : fi) {
int left = 0, right = gi.size() - 1;
int b = -a;
while (left < right) {
int mid = (left + right) >> 1;
if (gi.get(mid) >= b) {
right = mid;
} else {
left = mid + 1;
}
}
ans = Math.min(ans, Math.abs(a + gi.get(left)));
if (left > 0) {
ans = Math.min(ans, Math.abs(a + gi.get(left - 1)));
}
}
}
return ans;
}
}class Solution {
public:
int minimumDifference(vector<int>& nums) {
int n = nums.size() >> 1;
vector<vector<int>> f(n + 1), g(n + 1);
for (int i = 0; i < (1 << n); ++i)
{
int s = 0, cnt = 0;
int s1 = 0, cnt1 = 0;
for (int j = 0; j < n; ++j)
{
if (i & (1 << j))
{
s += nums[j];
++cnt;
s1 += nums[n + j];
++cnt1;
}
else
{
s -= nums[j];
s1 -= nums[n + j];
}
}
f[cnt].push_back(s);
g[cnt1].push_back(s1);
}
for (int i = 0; i <= n; ++i)
{
sort(f[i].begin(), f[i].end());
sort(g[i].begin(), g[i].end());
}
int ans = INT_MAX;
for (int i = 0; i <= n; ++i)
{
for (int a : f[i])
{
int left = 0, right = g[n - i].size() - 1;
int b = -a;
while (left < right)
{
int mid = (left + right) >> 1;
if (g[n - i][mid] >= b) right = mid;
else left = mid + 1;
}
ans = min(ans, abs(a + g[n - i][left]));
if (left > 0) ans = min(ans, abs(a + g[n - i][left - 1]));
}
}
return ans;
}
};func minimumDifference(nums []int) int {
n := len(nums) >> 1
f := make([][]int, n+1)
g := make([][]int, n+1)
for i := 0; i < (1 << n); i++ {
s, cnt := 0, 0
s1, cnt1 := 0, 0
for j := 0; j < n; j++ {
if (i & (1 << j)) != 0 {
s += nums[j]
cnt++
s1 += nums[n+j]
cnt1++
} else {
s -= nums[j]
s1 -= nums[n+j]
}
}
f[cnt] = append(f[cnt], s)
g[cnt1] = append(g[cnt1], s1)
}
for i := 0; i <= n; i++ {
sort.Ints(f[i])
sort.Ints(g[i])
}
ans := 1 << 30
for i := 0; i <= n; i++ {
for _, a := range f[i] {
left, right := 0, len(g[n-i])-1
b := -a
for left < right {
mid := (left + right) >> 1
if g[n-i][mid] >= b {
right = mid
} else {
left = mid + 1
}
}
ans = min(ans, abs(a+g[n-i][left]))
if left > 0 {
ans = min(ans, abs(a+g[n-i][left-1]))
}
}
}
return ans
}
func min(a, b int) int {
if a < b {
return a
}
return b
}
func abs(x int) int {
if x > 0 {
return x
}
return -x
}