Luo Gu P2789 straight cross points [number theory, recursion]

　　Topic Portal

Title Description

There N of straight lines on the plane, three lines and no common points, then these straight lines can have a different number of intersection points?

Input Format

A positive integer N

Output Format

An integer that represents the total program

Sample input and output

Input # 1

　4

Output # 1

　5

Description / Tips

N<=25

---

　　analysis:

　　Given n-you $ $ straight lines, which if $ i $ parallel strips, not parallel to the other, then the number of intersections is $ (i * (ni)) $ + (Ni $ $ intersection points of the straight lines). Then we can find $ n $ recursive straight line all the possible scenarios (as $ n $ is small), then record the number of programs on the line.

　　In fact, it is equivalent to this $ $ n-divided into a number of parallel straight lines of the line group, and then add the number of intersections of a group of a group.

　　Code：

 

//It is made by HolseLee on 16th Aug 2019
//Luogu.org P2789
#include<bits/stdc++.h>
using namespace std;

int n,ans;
bool vis[50005];

void dfs(int now,int num)
{
    if( now==0 ) { 
        if( !vis[num] ) ans++; 
        vis[num]=1; return;
    }
    for(int i=now; i>=1; --i) dfs(now-i,i*(now-i)+num);
}

int main () 
{ 
    cin >> n; dfs (n, 0 ); cout << years; return  0 ; 
}