# Nuts & Bolts Problem

## Question

Given a set of n nuts of different sizes and n bolts of different sizes. There is a one-one mapping between nuts and bolts. Comparison of a nut to another nut or a bolt to another bolt is not allowed. It means nut can only be compared with bolt and bolt can only be compared with nut to see which one is bigger/smaller.

We will give you a compare function to compare nut with bolt.

Example

Given nuts = ['ab','bc','dd','gg'], bolts = ['AB','GG', 'DD', 'BC'].

Your code should find the matching bolts and nuts.

one of the possible return:

nuts = ['ab','bc','dd','gg'], bolts = ['AB','BC','DD','GG'].

we will tell you the match compare function. If we give you another compare function.

the possible return is the following:

nuts = ['ab','bc','dd','gg'], bolts = ['BC','AA','DD','GG'].

So you must use the compare function that we give to do the sorting.

The order of the nuts or bolts does not matter. You just need to find the matching bolt for each nut.

Tags

Quick Sort Sort

Related Problems

## Solution

Two Pointers Partition

http://www.jiuzhang.com/solutions/nuts-bolts-problem/

``````
public class Solution {
/**
* @param nuts: an array of integers
* @param bolts: an array of integers
* @param compare: a instance of Comparator
* @return: nothing
*/
public void sortNutsAndBolts(String[] nuts, String[] bolts, NBComparator compare) {
if (nuts == null || bolts == null) return;
if (nuts.length != bolts.length) return;

qsort(nuts, bolts, compare, 0, nuts.length - 1);
}

private void qsort(String[] nuts, String[] bolts, NBComparator compare,
int l, int u) {
if (l >= u) return;
// find the partition index for nuts with bolts[l]
int part_inx = partition(nuts, bolts[l], compare, l, u);
// partition bolts with nuts[part_inx]
partition(bolts, nuts[part_inx], compare, l, u);
// qsort recursively
qsort(nuts, bolts, compare, l, part_inx - 1);
qsort(nuts, bolts, compare, part_inx + 1, u);
}

private int partition(String[] str, String pivot, NBComparator compare,
int l, int u) {
for (int i = l; i <= u; i++) {
if (compare.cmp(str[i], pivot) == 0 ||
compare.cmp(pivot, str[i]) == 0) {
swap(str, i, l);
break;
}
}
String now = str[l];
int left = l;
int right = u;
while (left < right) {
while (left < right &&
(compare.cmp(str[right], pivot) == -1 ||
compare.cmp(pivot, str[right]) == 1)) {
right--;
}
str[left] = str[right];

while (left < right &&
(compare.cmp(str[left], pivot) == 1 ||
compare.cmp(pivot, str[left]) == -1)) {
left++;
}
str[right] = str[left];
}
str[left] = now;

return left;
}

private void swap(String[] str, int l, int r) {
String temp = str[l];
str[l] = str[r];
str[r] = temp;
}
}
``````

Another Way of Partition

http://algorithm.yuanbin.me/zh-hans/problem_misc/nuts_and_bolts_problem.html

``````/**
* public class NBCompare {
*     public int cmp(String a, String b);
* }
* You can use compare.cmp(a, b) to compare nuts "a" and bolts "b",
* if "a" is bigger than "b", it will return 1, else if they are equal,
* it will return 0, else if "a" is smaller than "b", it will return -1.
* When "a" is not a nut or "b" is not a bolt, it will return 2, which is not valid.
*/
public class Solution {
/**
* @param nuts: an array of integers
* @param bolts: an array of integers
* @param compare: a instance of Comparator
* @return: nothing
*/
public void sortNutsAndBolts(String[] nuts, String[] bolts, NBComparator compare) {
if (nuts == null || bolts == null) {
return;
}
if (nuts.length != bolts.length) {
return;
}

int totalLength = nuts.length;
qsort(nuts, bolts, 0, totalLength - 1, compare);
}

public void qsort(String[] nuts, String[] bolts, int l, int r, NBComparator compare) {
if (l >= r) {
return;
}
// Find partition index for nuts, with bolts[l]
int partIndex = partition(nuts, bolts[l], l, r, compare);
// Partition bolts, with nuts[partIndex]
partition(bolts, nuts[partIndex], l, r, compare);

// quick sort recursively
qsort(nuts, bolts, l, partIndex - 1, compare);
qsort(nuts, bolts, partIndex + 1, r, compare);
}

public int partition(String[] arr, String pivot, int l, int r, NBComparator compare) {
// pivot is from another array
int m = l;
for (int i = l + 1; i <= r; i++) {
if (compare.cmp(arr[i], pivot) == -1 || compare.cmp(pivot, arr[i]) == 1) {
m++;
swap(arr, i, m);
} else if (compare.cmp(arr[i], pivot) == 0 || compare.cmp(pivot, arr[i]) == 0) {
swap(arr, i, l);
i--;
}
}
swap(arr, m, l);

return m;
}

public void swap(String[] arr, int l, int r) {
String temp = arr[l];
arr[l] = arr[r];
arr[r] = temp;
}
}
``````