# Smallest Difference (POJ 2718)

This is a hard problem. To run it within time limits, we have to take some manners to improve the time efficiency. At first, the minimum difference occurs when two numbers have near or same number of digits. When difference of two integers' numbers of digits is too large, it won't contribute to the smallest difference. So we first iterate all subset of and then we permute all permutations of this subset and its complemental subset and calculate the difference. In this procedure, we need to skip cases that the number starts with zero.

We you binary bits way to iterate all subset of size and we need to implement next permutation function correctly. The next permutation should return true if there is a next permutation and return false if it is already the lexicographic largest permutation. Before return false, it must reverse the sequence to restore it to the lexicographic smallest permuation.

import java.io.*;
import java.util.*;

public class SmallestDifference {
private static boolean nextPermuation(int[] nums) {
if (nums.length == 0) return false;
int i = nums.length - 1;
while (i > 0) {
if (nums[i - 1] < nums[i]) break;
i--;
}
if (i <= 0) {
for (int j = 0; j < nums.length / 2; j++) {
int t = nums[j];
nums[j] = nums[nums.length - j - 1];
nums[nums.length - j - 1] = t;
}
return false;
}
int j = nums.length - 1;
while (nums[j] <= nums[i - 1] && j >= i) j--;
int t = nums[j];
nums[j] = nums[i - 1];
nums[i - 1] = t;
Arrays.sort(nums, i, nums.length);
return true;
}
private static int nextSubset(int comb) {
int x = comb & -comb, y = comb + x;
return ((comb & ~y) / x >> 1) | y;
}
private static long getNumber(int[] nums) {
long num = 0;
for (int n : nums) {
num = num * 10 + n;
}
return num;
}
private static void solve(int[] ints) {
int N = ints.length;

int k = N / 2;
int comb = (1 << k) - 1;
int[] a = new int[k];
int[] b = new int[N - k];
long min = Long.MAX_VALUE;
while (comb < (1 << N)) {
int l = 0, r = 0;
for (int i = 0; i < N; i++) {
if (((comb >> i) & 1) == 1) {
a[l++] = ints[i];
} else {
b[r++] = ints[i];
}
}

if (a == 0 && a.length > 1) {
comb = nextSubset(comb);
continue;
}

do {
long anum = getNumber(a);
do {
if (b == 0 && b.length > 1) continue;
long bnum = getNumber(b);
min = Math.min(min, Math.abs(anum - bnum));
} while (nextPermuation(b));
} while (nextPermuation(a));
comb = nextSubset(comb);
}
System.out.println(min);
}
public static void main(String[] args) throws IOException {