棰樼洰澶ф剰錛?br> 鏍規(guī)嵁杈撳叆錛屽簭鍒楃殑闀垮害錛屽簭鍒楀拰錛屾眰榪欐牱涓涓插簭鍒?br> 搴忓垪婊¤凍浠ヤ笅鎯呭喌錛?/p>
- for any k, such that 1 <= k < n : |ak - ak+1| = 1 and
- a1 = 0
濡傛灉娌℃湁濡傛搴忓垪鍒欒緭鍑?No"
鎴戜滑鍋囪n-->搴忓垪闀垮害錛孲-->搴忓垪鍜岋紱
S=sigma a[i](1<=i<=n)
浠i=a[i+1]-a[i] (1<=i<n)
b[i]-->-1 or 1
S=sigama (n-i)(b[i]+1)-sigama(n-i)
=2*sigama ((n-i)(b[i]+1)/2) - n*(n-1)/2
d[i]=(b[i]+1)/2-->0 or 1
鏍規(guī)嵁涓婂紡寰楋細(xì)
no-->
1: S+n*(n-1)/2 涓哄鏁?br>2: abs(S)>n*(n-1)/2 //important ....鎴戝氨鏄繖閲屼竴鐩撮敊...緇濆鍊?..娌¤冭檻....
#include<iostream>#include<math.h>int N,S;int main(){ int std,i,d,pre; int T; scanf("%d",&T); for(int j=1;j<=T;j++) { scanf("%d%d",&N,&S); std=(N*(N-1))/2; if((S+std)%2||abs(S)>std) { printf("No\n"); if(j!=T)printf("\n"); continue; } printf("0\n"); for(pre=0,std+=S,std/=2,i=1;i<N;i++) { if(std>=N-i) { d=1; std-=N-i; } else d=0; printf("%d\n",pre=2*d-1+pre); } if(j!=T)printf("\n"); } return 0;}]]>
寮濮嬩竴鐩撮捇鐗涜灝栥傘傜敤鏆村姏鎶婃暟鎹窇浜嗕竴涓嬨傜劧鍚庢壘瑙勫緥銆傘傚彂鐜板ソ鍍忔槸鎵緉鐨勪簰璐ㄧ殑璐ㄥ洜鏁板鏁般傘?br>灝忕殑鏁版嵁鐢ㄦ墜綆楁槸鍙互綆楀嚭鏉ョ殑銆傘備絾鏄笉鐭ラ亾鎬庝箞鐢ㄧ▼搴忔潵綆椼傘?br>
鍚庨潰鍙傝僷c鐨勩傘傘傘傜煡閬撲簡鏄庝箞鍥炰簨銆傘?br>鎴戞兂浠ュ悗濡傛灉鏈夐渶瑕佹眰璐ㄥ洜鏁板鏁扮殑涓暟銆傘傚彲浠ョ敤榪欑鏂規(guī)硶鍙嶈繃鏉ユ眰銆傘?br>
涓嬮潰鏄唬鐮侊細(xì)
#include<iostream>int N;int solve(int N){ int i,ans=1,t; for(i=2;i*i<=N;i++) { t=0; while(!(N%i)) { t++; N/=i; } ans*=2*t+1; } if(ans==1||N!=1)ans*=3; return ans;}int main(){ int T,cas,id; scanf("%d",&T); for(cas=1;cas<=T;cas++) { scanf("%d",&N); id=solve(N); if(N==1)id=1; printf("Scenario #%d:\n%d\n\n",cas,(id+1)/2); } return 0;}]]>
絎竴涓棶棰橈細(xì)
鐢卞鉤闈腑鐨刵鏉＄洿綰跨‘瀹氱殑鏈澶у尯鍩熸暟Ln
Ln=1+n*(n+1)/2;
絎簩涓棶棰橈細(xì)
鏄鉤闈㈢洿綰跨殑鍙樺艦闂錛岀敤寮洸鐨勭嚎鏉ヤ唬鏇跨洿綰匡紝姣忎竴涓集鏇茬嚎鍚湁涓涓?#8220;閿嬌褰㈢殑杞”錛屽悓鏍風(fēng)‘瀹氬鉤闈㈠尯鍩熺殑鏈澶т釜鏁癦n
錛堟垜浠妸涓鏉″集鏇叉姌綰挎娊璞′負(fù)涓ゆ潯錛屼絾鏄悎騫朵簡鏌愪簺鍖哄煙錛?br>Zn=L2n-2*n=2*n*n-n+1;(n>=0);
絎笁涓棶棰橈細(xì)
灝辨槸涓涓嬭繖涓棶棰橈細(xì)
count the regions
鑻ュ綋鍓嶆湁n-1鏉¤竟錛岄偅涔堝湪寰閲岄潰鍔犱竴鏉¤竟錛岃繖鏉℃柊鍔犵殑杈規(guī)渶澶氬拰浠ュ墠鐨勮竟鏈?*(n-1)涓氦鐐癸紝
閭ｄ箞浼?xì)娣诲?9*錛坣-1錛?1涓潰
榪欐潯瑙勫緥瀵逛簬涓婇潰涓ょ涔熸槸鐢紝鍔爔涓偣錛岄偅涔堝氨浼?xì)娣诲姞x+1涓潰
閭ｄ箞鎬葷粨涓嬫潵 Xn=Xn-1+9*(n-1)+1
鍗砐n=(9/2)*n*n-(7/2)*n+1;
浠ヤ笅鏄垜鐨勪唬鐮侊細(xì)
#include<stdio.h>int main(){ long long n; long long ans; while(scanf("%lld",&n)!=EOF){ ans=9*n*n-7*n+2; ans/=2; printf("%lld\n",ans); } return 0;}]]>