[算法] 找到最相邻的3元组

问题如下：

You are given with three sorted arrays ( in ascending order), you are required to find a triplet ( one element from each array) such that distance is minimum.

Distance is defined like this : If a[i], b[j] and c[k] are three elements then distance=max(abs(a[i]-b[j]),abs(a[i]-c[k]),abs(b[j]-c[k]))

Please give a solution in O(n) time complexity

这个算法有很强的实用性，比如找到3组用户里面最相似的3元组，这里可以把abs替换为一个similarity函数即可。

下面的代码给出了一个最简单的Bruce force算法和一个优化算法。

package com.autofei.algorithm; import java.util.Arrays; public class GoogleMinimumDistance { static void NavieMin(int[] a, int[] b, int[] c) { int min = Integer.MAX_VALUE; String triplet = ""; int[] tripletArray = new int[3]; for (int i = 0; i < a.length; i++) { for (int j = 0; j < b.length; j++) { for (int k = 0; k < c.length; k++) { tripletArray[0] = Math.abs(a[i] - b[j]); tripletArray[1] = Math.abs(a[i] - c[k]); tripletArray[2] = Math.abs(b[j] - c[k]); Arrays.sort(tripletArray); int distance = tripletArray[2]; if (distance < min) { min = distance; triplet = a[i] + "|" + b[j] + "|" + c[k]; } } } } System.out.println(triplet + " => " + min); } static void SmartMin(int[] a, int[] b, int[] c) { int min = Integer.MAX_VALUE; String tripletString = ""; int[] tripletArray = new int[3]; int i = 0; int j = 0; int k = 0; while (i < a.length && j < b.length && k < c.length) { tripletArray[0] = a[i]; tripletArray[1] = b[j]; tripletArray[2] = c[k]; Arrays.sort(tripletArray); int tripletMax = tripletArray[2]; int tripletMin = tripletArray[0]; int distance = tripletMax - tripletMin; if (distance < min) { min = distance; tripletString = a[i] + "|" + b[j] + "|" + c[k]; } if (a[i] == tripletMin) { i++; } else if (b[j] == tripletMin) { j++; } else if (c[k] == tripletMin) { k++; } } System.out.println(tripletString + " => " + min); } public static void main(String[] args) { int[] a = { 4, 10, 15, 28 }; int[] b = { 1, 3, 29 }; int[] c = { 5, 13, 28 }; GoogleMinimumDistance.NavieMin(a, b, c); GoogleMinimumDistance.SmartMin(a, b, c); } }