Rokua P1755 attack on Mars

Title Description

A group of aliens will attack Mars.

The map of Mars is an n-point graph without a direction. The aliens will invade as follows, with an attack level of 0 (equivalent to removing it), then a 1 point, and so on, until the n-1 point.

All the point statistics are dynamic statistics. (When a point is deleted, the point of the point connected to it will be-1). An alien attack is an attack at the same time as a certain number of points.

You need to design the side of the diagram to make the most of the points that are not being attacked.

Input/output format Input Format:

The input file contains one line of integer n.

output Format:

An integer line that represents the most last point that was not attacked.

Input/Output sample Input Sample # #:

3

Sample # # of output:

1

Description

"Sample Interpretation"

①-②-③, so first delete the degree of 1 ① and ③, at this time ② degrees of 0, will not be deleted.

"Data Range"

For 20% of data 1<=n<=10

For 100% of data 1<=n<=50000

"Source of the topic"

Tinylic adaptation

by Tinylic

After finding the law, we can find the answer is n-2.

Here is the proof:

Order D[i] is the degree of I.

Consider the condition that a point I is not deleted, necessarily the point J (which can be multiple) adjacent to the front and I, which is deleted, leading to D[i]

Decrease to less than or equal to d[j].

1) Easy to know ans!=n.

2) Consider whether ans can be n-1, that is, to delete only one point, set this point for I.

Because I is the only point deleted, so d[i] must not be the largest, that is, d[i]<n-1.

The second deletion of I causes the rest of the d[] to change and thus cannot be deleted.

That I and the rest of the points are connected, d[i]=n-1, contradiction.

So ans!=n-1.

3) We can construct the situation of ans=n-2:

Construct complete graph G and delete an edge (I,J). This d[i]=d[j]=n-2, the rest of the d[] are n-1.

First delete the VI,VJ, so that the remaining points are less than two sides, d[] all become n-3, do not have to be deleted.

This n-2 is a legal solution and the largest solution, so the answer is n-2.

1 /*by Silvern*/2#include <iostream>3#include <cstdio>4 using namespacestd;5 intMain () {6     intN;7scanf"%d",&n);8printf"%d\n", Max (0, N-2));9     return 0;Ten}

Rokua P1755 attack on Mars