棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=2085
棰樼洰鎻忚堪:
Problem Description
鏌愭牳鍙嶅簲鍫嗘湁涓ょ被浜嬩歡鍙戠敓錛?br>楂樿兘璐ㄧ偣紕板嚮鏍稿瓙鏃訛紝璐ㄧ偣琚惛鏀訛紝鏀懼嚭3涓珮鑳借川鐐瑰拰1涓綆鑳借川鐐癸紱
浣庤兘璐ㄧ偣紕板嚮鏍稿瓙鏃訛紝璐ㄧ偣琚惛鏀訛紝鏀懼嚭2涓珮鑳借川鐐瑰拰1涓綆鑳借川鐐廣?br>鍋囧畾寮濮嬬殑鏃跺欙紙0寰錛夊彧鏈変竴涓珮鑳借川鐐瑰皠鍏ユ牳鍙嶅簲鍫嗭紝姣忎竴寰寮曡搗涓涓簨浠跺彂鐢?瀵逛簬涓涓簨浠訛紝褰撳墠瀛樺湪鐨勬墍鏈夎川鐐歸兘浼氭挒鍑繪牳瀛?錛岃瘯紜畾n寰鏃墮珮鑳借川鐐瑰拰浣庤兘璐ㄧ偣鐨勬暟鐩?br>
Input
杈撳叆鍚湁涓浜涙暣鏁皀(0≤n≤33)錛屼互寰涓哄崟浣嶏紝鑻涓?/span>-1琛ㄧず澶勭悊緇撴潫銆?br>
Output
鍒嗗埆杈撳嚭n寰鏃跺埢楂樿兘璐ㄧ偣鍜屼綆鑳借川鐐圭殑鏁伴噺錛岄珮鑳借川鐐逛笌浣庤兘璐ㄧ偣鏁伴噺涔嬮棿浠ラ楀彿絀烘牸鍒嗛殧銆傛瘡涓緭鍑哄崰涓琛屻?br>
Sample Input
5 2
-1
Sample Output
571, 209
11, 4
鏌愭牳鍙嶅簲鍫嗘湁涓ょ被浜嬩歡鍙戠敓錛?br>楂樿兘璐ㄧ偣紕板嚮鏍稿瓙鏃訛紝璐ㄧ偣琚惛鏀訛紝鏀懼嚭3涓珮鑳借川鐐瑰拰1涓綆鑳借川鐐癸紱
浣庤兘璐ㄧ偣紕板嚮鏍稿瓙鏃訛紝璐ㄧ偣琚惛鏀訛紝鏀懼嚭2涓珮鑳借川鐐瑰拰1涓綆鑳借川鐐廣?br>鍋囧畾寮濮嬬殑鏃跺欙紙0寰錛夊彧鏈変竴涓珮鑳借川鐐瑰皠鍏ユ牳鍙嶅簲鍫嗭紝姣忎竴寰寮曡搗涓涓簨浠跺彂鐢?瀵逛簬涓涓簨浠訛紝褰撳墠瀛樺湪鐨勬墍鏈夎川鐐歸兘浼氭挒鍑繪牳瀛?錛岃瘯紜畾n寰鏃墮珮鑳借川鐐瑰拰浣庤兘璐ㄧ偣鐨勬暟鐩?br>
Input
杈撳叆鍚湁涓浜涙暣鏁皀(0≤n≤33)錛屼互寰涓哄崟浣嶏紝鑻涓?/span>-1琛ㄧず澶勭悊緇撴潫銆?br>
Output
鍒嗗埆杈撳嚭n寰鏃跺埢楂樿兘璐ㄧ偣鍜屼綆鑳借川鐐圭殑鏁伴噺錛岄珮鑳借川鐐逛笌浣庤兘璐ㄧ偣鏁伴噺涔嬮棿浠ラ楀彿絀烘牸鍒嗛殧銆傛瘡涓緭鍑哄崰涓琛屻?br>
Sample Input
5 2
-1
Sample Output
571, 209
11, 4
涓涓緢綆鍗曠殑閫掓帹棰?:
H[i] = 3 * H[i-1] + 2 * L[i-1]; //楂樿兘
L[i] = H[i-1] + L[i-1]; // 浣庤兘
L[i] = H[i-1] + L[i-1]; // 浣庤兘
鏈変竴鐐硅娉ㄦ剰 , 闇瑕?64浣嶆暣褰繚瀛樼粨鏋? 鍚﹀垯浼氭孩鍑?
浠ｇ爜濡備笅:
MiYu鍘熷垱, 杞笘璇鋒敞鏄?: 杞澆鑷?______________鐧界櫧銇眿
#include <iostream>
using namespace std;
int main ()
{
long long H[34] = { 1 , 3 },L[34] = { 0 , 1 };
for ( int i = 2; i != 34; ++ i )
{
H[i] = 3 * H[i-1] + 2 * L[i-1];
L[i] = H[i-1] + L[i-1];
}
int N;
while ( cin >> N , N + 1 )
{
cout << H[N] << ", " << L[N] << endl;
}
return 0;
}
#include <iostream>
using namespace std;
int main ()
{
long long H[34] = { 1 , 3 },L[34] = { 0 , 1 };
for ( int i = 2; i != 34; ++ i )
{
H[i] = 3 * H[i-1] + 2 * L[i-1];
L[i] = H[i-1] + L[i-1];
}
int N;
while ( cin >> N , N + 1 )
{
cout << H[N] << ", " << L[N] << endl;
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=2064
棰樼洰鎻忚堪:
姹夎濉擨II
綰?9涓栫邯鏈紝鍦ㄦ宸炵殑鍟嗗簵涓嚭鍞竴縐嶆櫤鍔涚帺鍏鳳紝鍦ㄤ竴鍧楅摐鏉夸笂鏈変笁鏍規潌錛屾渶宸﹁竟鐨勬潌涓婅嚜涓婅屼笅銆佺敱灝忓埌澶ч『搴忎覆鐫鐢?4涓渾鐩樻瀯鎴愮殑濉斻傜洰鐨勬槸灝嗘渶宸﹁竟鏉嗕笂鐨勭洏鍏ㄩ儴縐誨埌鍙寵竟鐨勬潌涓婏紝鏉′歡鏄竴嬈″彧鑳界Щ鍔ㄤ竴涓洏錛屼笖涓嶅厑璁稿ぇ鐩樻斁鍦ㄥ皬鐩樼殑涓婇潰銆?br>鐜板湪鎴戜滑鏀瑰彉娓告垙鐨勭帺娉曪紝涓嶅厑璁哥洿鎺ヤ粠鏈宸?鍙?杈圭Щ鍒版渶鍙?宸?杈?姣忔縐誨姩涓瀹氭槸縐誨埌涓棿鏉嗘垨浠庝腑闂寸Щ鍑?錛屼篃涓嶅厑璁稿ぇ鐩樻斁鍒頒笅鐩樼殑涓婇潰銆?br>Daisy宸茬粡鍋氳繃鍘熸潵鐨勬眽璇哄闂鍜屾眽璇哄II錛屼絾紕板埌榪欎釜闂鏃訛紝濂規兂浜嗗緢涔呴兘涓嶈兘瑙ｅ喅錛岀幇鍦ㄨ浣犲府鍔╁ス銆傜幇鍦ㄦ湁N涓渾鐩橈紝濂硅嚦灝戝灝戞縐誨姩鎵嶈兘鎶婅繖浜涘渾鐩樹粠鏈宸﹁竟縐誨埌鏈鍙寵竟錛?/span>
姹夎濉?font color=#000000 size=2>鏄釜寰堢粡鍏哥殑閫掓帹瀹炰緥, 濡傛灉瑙勫垯娌¤繖涔堝彉鎬侊紝鍏佽鐩存帴浠?璺ㄨ秺鍒?錛岄偅n涓洏鏈灝戦渶瑕?n - 1嬈°?br>
鑰岃繖閲屽鍔犱簡涓浜涙柊鐨勮鍒? 鎴戜滑鍙互濡備笅鍒嗘瀽, 鎬庢牱鎶?span style="COLOR: red">n涓洏浠?span style="COLOR: #ff0000">1鎼埌3 :
絎?姝?鍒濆鐘舵?
絎?姝?鎶婁笂闈㈢殑n-1涓洏縐誨埌絎?鍙鋒潌涓?
絎?姝?鎶婄n涓洏浠?縐誨埌2:
絎?姝?鎶婂墠n-1涓粠3縐誨埌1錛岀粰絎釜鐩樿璺?
絎?姝?鎶婄n涓洏浠?縐誨埌3:
絎?姝?鎶婂墠n-1涓粠縐誨埌3錛屽畬鎴愮Щ鍔?
鎴戜滑璁緁(n)涓烘妸n涓洏浠?縐誨埌3鎵闇瑕佺殑姝ユ暟錛屽綋鐒朵篃絳変簬浠?縐誨埌1鐨勬鏁般?br>
鐢變笂闈㈢殑鍥炬垜浠彲浠ョ湅鍒?瑕佹兂鎶婄n涓洏浠?縐誨埌3錛岄渶瑕?涓楠?:
1.) 鎶婂墠n-1涓粠1縐誨姩3 .
2.) 絎琻涓洏瑕佷粠1->2->3緇忓巻2姝?
3.) 鑰屽墠n-1涓洏闇瑕佸厛 3->1 ( 榪欐槸涓轟簡緇?絎琻涓洏璁╄礬 ), 鏈鍚庡啀 1->3銆?br>
∴f(n) = 3 × f(n-1) + 2;
f(1) = 2;
f(n) = 3 × f(n-1) + 2
f(1) = 2
=>
f(n) + 1 = 3 × [f(n-1) + 1]
f(1) + 1 = 2 + 1 = 3
=>
f(n) + 1 = 3n
=>
f(n) = 3n - 1
鏈鍚庤創涓婁唬鐮?:
//MiYu鍘熷垱, 杞笘璇鋒敞鏄?: 杞澆鑷?______________鐧界櫧銇眿
#include <iostream>
#include <cmath>
using namespace std;
long long myPow ( int n , int e )
{
long long mlt = 1;
for ( int i = 1; i <= e ; ++ i )
{
mlt *= n;
}
return mlt;
}
int main ()
{
int N;
while ( cin >> N )
{
cout << myPow ( 3, N ) - 1 << endl;
}
return 0;
}
]]>