Cutpoints Search Algorithm
The Cutpoints Search Algorithm is an optimization technique used in the field of machine learning and pattern recognition for determining the optimal cutpoints in a dataset. It is particularly useful for problems involving classification and decision-making, where the goal is to identify the best thresholds or cutpoints that can effectively separate a dataset into groups or classes based on specific criteria. The algorithm works by exhaustively examining all possible cutpoints and evaluating their performance, typically using an objective function that measures the quality of the resulting partition. This process can be computationally expensive, especially for large datasets, but it ensures that the best possible cutpoints are identified.
There are several variations of the Cutpoints Search Algorithm, including those that rely on recursive partitioning, dynamic programming, and greedy search strategies. These methods can help to reduce the computational complexity of the search process and improve the efficiency of the algorithm. Some of these approaches may not guarantee the optimal solution but provide a good approximation in a more reasonable timeframe. Depending on the problem context and the specific objectives, the Cutpoints Search Algorithm can be applied to various domains such as medical diagnosis, image segmentation, and financial risk assessment, where it helps to improve the accuracy and interpretability of the classification models.
/**************************************************************************************
Algorithm for finding all cutpoints in the graph (vertices, after removal of
which graph divides into several components). O(M)
Based on problem D from here: http://codeforces.ru/gym/100083
**************************************************************************************/
#include <iostream>
#include <fstream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <cassert>
#include <utility>
#include <iomanip>
using namespace std;
const int MAXN = 105000;
int n, m;
vector <int> g[MAXN];
int tin[MAXN], mn[MAXN];
bool used[MAXN];
vector <int> cutVertices;
int timer;
void dfs(int v, int par = -1) {
used[v] = true;
timer++;
tin[v] = timer;
mn[v] = tin[v];
int childNum = 0;
bool isCutVertex = false;
for (int i = 0; i < (int) g[v].size(); i++) {
int to = g[v][i];
if (!used[to]) {
childNum++;
dfs(to, v);
if (par != -1 && mn[to] >= tin[v] && !isCutVertex) {
isCutVertex = true;
cutVertices.push_back(v);
}
mn[v] = min(mn[v], mn[to]);
}
else if (to != par) {
mn[v] = min(mn[v], tin[to]);
}
}
if (par == -1 && childNum > 1)
cutVertices.push_back(v);
}
int main() {
assert(freopen("points.in","r",stdin));
assert(freopen("points.out","w",stdout));
scanf("%d %d", &n, &m);
for (int i = 1; i <= m; i++) {
int from, to;
scanf("%d %d", &from, &to);
g[from].push_back(to);
g[to].push_back(from);
}
for (int i = 1; i <= n; i++)
if (!used[i])
dfs(i);
sort(cutVertices.begin(), cutVertices.end());
printf("%d\n", (int) cutVertices.size());
for (int i = 0; i < (int) cutVertices.size(); i++)
printf("%d\n", cutVertices[i]);
return 0;
}
