Is there a specific search paradigm for finding pairs in a set?
$begingroup$
I'm dealing with a very common problem in computer programming that involves, for example 4 people to be divided into 2 pairs. Mathematically, this is just a permutations problem, and the number of possibilities would be 4!/(2! * 2^2) = 3.
In computer programming, when searching for these specific solutions, a programmer would just recurse through the possible solutions. For example --
int solve(void) {
int i, count = 0;
for (i = 0; i < n; i++) {
if (partners[i] == -1) {
break;
}
}
// if all the pairs are matched with each other
if (i == n) {
return check() ? 1 : 0;
}
for (int j = i + 1; j < n; j++) {
if (partners[j] == -1) {
partners[i] = j;
partners[j] = i;
// recurse back through to find all possible sets of pairs with this configuration
count += solve();
partners[i] = partners[j] = -1;
}
}
return count;
}
Now, what I found interesting was that when you draw a permutation tree diagram, you see that the unique solutions for this problem arise naturally in this pattern:
Permutation Tree. This pattern goes on as the number of people increases. Taking all that into account, my question is, is this simple recursive function a unique search paradigm (like BFS or DFS) that models the behavior/pattern seen in the tree? If not, could an algorithm be designed that models that pattern?
I'm a high school student, and I'm comfortable with basic and intermediate algorithm design concepts, but I'm still learning, so if you could, please explain your answer in more depth than usual.
permutations algorithms computer-science trees recursive-algorithms
asked Jan 3 at 20:22
user2300851user2300851
1
$endgroup$
add a comment |
$begingroup$
I'm dealing with a very common problem in computer programming that involves, for example 4 people to be divided into 2 pairs. Mathematically, this is just a permutations problem, and the number of possibilities would be 4!/(2! * 2^2) = 3.
In computer programming, when searching for these specific solutions, a programmer would just recurse through the possible solutions. For example --
int solve(void) {
int i, count = 0;
for (i = 0; i < n; i++) {
if (partners[i] == -1) {
break;
}
}
// if all the pairs are matched with each other
if (i == n) {
return check() ? 1 : 0;
}
for (int j = i + 1; j < n; j++) {
if (partners[j] == -1) {
partners[i] = j;
partners[j] = i;
// recurse back through to find all possible sets of pairs with this configuration
count += solve();
partners[i] = partners[j] = -1;
}
}
return count;
}
Now, what I found interesting was that when you draw a permutation tree diagram, you see that the unique solutions for this problem arise naturally in this pattern:
Permutation Tree. This pattern goes on as the number of people increases. Taking all that into account, my question is, is this simple recursive function a unique search paradigm (like BFS or DFS) that models the behavior/pattern seen in the tree? If not, could an algorithm be designed that models that pattern?
I'm a high school student, and I'm comfortable with basic and intermediate algorithm design concepts, but I'm still learning, so if you could, please explain your answer in more depth than usual.
permutations algorithms computer-science trees recursive-algorithms
asked Jan 3 at 20:22
user2300851user2300851
1
$endgroup$
$begingroup$
Why is this a permutation problem? What ischeck()?
$endgroup$
– Somos
Jan 3 at 22:10
$begingroup$
check() is not relevant to the problem, it's just another part of the program I'm writing. The function above finds the different possibilities of perfect matchings, and I'm visualizing the complete graph as the entire set of permutations, and the perfect matchings as certain permutations obtained by the search function.
$endgroup$
– user2300851
Jan 3 at 22:23
add a comment |
$begingroup$
I'm dealing with a very common problem in computer programming that involves, for example 4 people to be divided into 2 pairs. Mathematically, this is just a permutations problem, and the number of possibilities would be 4!/(2! * 2^2) = 3.
In computer programming, when searching for these specific solutions, a programmer would just recurse through the possible solutions. For example --
int solve(void) {
int i, count = 0;
for (i = 0; i < n; i++) {
if (partners[i] == -1) {
break;
}
}
// if all the pairs are matched with each other
if (i == n) {
return check() ? 1 : 0;
}
for (int j = i + 1; j < n; j++) {
if (partners[j] == -1) {
partners[i] = j;
partners[j] = i;
// recurse back through to find all possible sets of pairs with this configuration
count += solve();
partners[i] = partners[j] = -1;
}
}
return count;
}
Now, what I found interesting was that when you draw a permutation tree diagram, you see that the unique solutions for this problem arise naturally in this pattern:
Permutation Tree. This pattern goes on as the number of people increases. Taking all that into account, my question is, is this simple recursive function a unique search paradigm (like BFS or DFS) that models the behavior/pattern seen in the tree? If not, could an algorithm be designed that models that pattern?
I'm a high school student, and I'm comfortable with basic and intermediate algorithm design concepts, but I'm still learning, so if you could, please explain your answer in more depth than usual.
permutations algorithms computer-science trees recursive-algorithms
asked Jan 3 at 20:22
user2300851user2300851
1
$endgroup$
I'm dealing with a very common problem in computer programming that involves, for example 4 people to be divided into 2 pairs. Mathematically, this is just a permutations problem, and the number of possibilities would be 4!/(2! * 2^2) = 3.
In computer programming, when searching for these specific solutions, a programmer would just recurse through the possible solutions. For example --
int solve(void) {
int i, count = 0;
for (i = 0; i < n; i++) {
if (partners[i] == -1) {
break;
}
}
// if all the pairs are matched with each other
if (i == n) {
return check() ? 1 : 0;
}
for (int j = i + 1; j < n; j++) {
if (partners[j] == -1) {
partners[i] = j;
partners[j] = i;
// recurse back through to find all possible sets of pairs with this configuration
count += solve();
partners[i] = partners[j] = -1;
}
}
return count;
}
Now, what I found interesting was that when you draw a permutation tree diagram, you see that the unique solutions for this problem arise naturally in this pattern:
Permutation Tree. This pattern goes on as the number of people increases. Taking all that into account, my question is, is this simple recursive function a unique search paradigm (like BFS or DFS) that models the behavior/pattern seen in the tree? If not, could an algorithm be designed that models that pattern?
I'm a high school student, and I'm comfortable with basic and intermediate algorithm design concepts, but I'm still learning, so if you could, please explain your answer in more depth than usual.
permutations algorithms computer-science trees recursive-algorithms
permutations algorithms computer-science trees recursive-algorithms
asked Jan 3 at 20:22
user2300851user2300851
1
asked Jan 3 at 20:22
user2300851user2300851
1
asked Jan 3 at 20:22
user2300851user2300851
1
asked Jan 3 at 20:22
user2300851user2300851
1
asked Jan 3 at 20:22
user2300851user2300851
1
1
$begingroup$
Why is this a permutation problem? What ischeck()?
$endgroup$
– Somos
Jan 3 at 22:10
$begingroup$
check() is not relevant to the problem, it's just another part of the program I'm writing. The function above finds the different possibilities of perfect matchings, and I'm visualizing the complete graph as the entire set of permutations, and the perfect matchings as certain permutations obtained by the search function.
$endgroup$
– user2300851
Jan 3 at 22:23
add a comment |
$begingroup$
Why is this a permutation problem? What ischeck()?
$endgroup$
– Somos
Jan 3 at 22:10
$begingroup$
check() is not relevant to the problem, it's just another part of the program I'm writing. The function above finds the different possibilities of perfect matchings, and I'm visualizing the complete graph as the entire set of permutations, and the perfect matchings as certain permutations obtained by the search function.
$endgroup$
– user2300851
Jan 3 at 22:23
$begingroup$
Why is this a permutation problem? What is
check()?$endgroup$
– Somos
Jan 3 at 22:10
$begingroup$
Why is this a permutation problem? What is
check()?$endgroup$
– Somos
Jan 3 at 22:10
$begingroup$
check() is not relevant to the problem, it's just another part of the program I'm writing. The function above finds the different possibilities of perfect matchings, and I'm visualizing the complete graph as the entire set of permutations, and the perfect matchings as certain permutations obtained by the search function.
$endgroup$
– user2300851
Jan 3 at 22:23
$begingroup$
check() is not relevant to the problem, it's just another part of the program I'm writing. The function above finds the different possibilities of perfect matchings, and I'm visualizing the complete graph as the entire set of permutations, and the perfect matchings as certain permutations obtained by the search function.
$endgroup$
– user2300851
Jan 3 at 22:23
add a comment |
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$begingroup$
Why is this a permutation problem? What is
check()?$endgroup$
– Somos
Jan 3 at 22:10
$begingroup$
check() is not relevant to the problem, it's just another part of the program I'm writing. The function above finds the different possibilities of perfect matchings, and I'm visualizing the complete graph as the entire set of permutations, and the perfect matchings as certain permutations obtained by the search function.
$endgroup$
– user2300851
Jan 3 at 22:23