浜插拰鏁幫紝鍏堟毚鍔涚畻鍑烘暟鎹紝鐒跺悗鎵撹〃涔嬨?
B.A New Sequence Problem
鍏圷M涓涓婣C銆傛牴鎹鐩噷鐨勫叕寮忥紝鍏堢敓鎴怉鏁扮粍銆傜畻A[0]闇瑕侀氳繃fibonacci鎵懼驚鐜妭,鎵懼驚鐜妭鐨勬柟娉曞氨鐩存帴鏆村姏鍗沖彲,褰揻[i]=f[1]&&f[i-1]=f[0],i-1蹇呮槸涓涓驚鐜殑闀垮害銆傜畻鍑篈鏁扮粍浠ュ悗錛屽叾瀹炲氨鏄浜庡瓧絎︿覆鐨勬搷浣滀簡銆傛瘮璧涚殑鏃跺欑敤鍚庣紑鏁扮粍綆楀嚭鏉ヤ簡錛屼絾鏄病鎯沖埌O(n)鐨勬搷浣溿傝禌鍚庣湅鍒癆C璇存槸o(n)鐨凞P錛屽潥瀹氬鏉傚害鍚庢兂鍒幫紝鍦ㄧ畻鍑篽eight鏁扮粍鍚庯紝鐢ㄥ綋鍓嶄綅緗〃紺轟負鏈浣庝綅緗紝鐒跺悗鍚戝乏鍚戝彸鎵╁睍鍒扮涓涓瘮褰撳墠浣嶇疆浣庣殑鍦版柟錛屽茍bl[],br[]鏁扮粍璁板綍榪欎釜鏈宸﹀拰鏈鍙籌紝鍑犱箮灝辨槸o(n)鐨勩?/p>
C.Coin Puzzle
緇欏嚭涓涓杈瑰艦鍜屼袱涓渾錛岄棶涓や釜鍦嗚兘涓嶈兘鏀懼湪澶氳竟褰㈤噷錛屽茍涓斾袱鍦嗕笉鐩鎬氦銆?br>姹傚嚭涓や釜鍦嗙殑鍦嗗績鐨勫悎娉曡寖鍥達紝鏄袱涓杈瑰艦錛岀劧鍚庢眰涓や釜澶氳竟褰㈢殑鏈榪滆窛紱?/p>
D.Tree Game
鑳芥瀯鎴愪竴棰楃敓鎴愭爲褰撲笖浠呭綋杈規暟涓嶅皯浜巒-1鏉★紱濡傛灉鑳芥瀯鎴愪竴縐嶇敓鎴愭爲錛岄偅涔堣兘鏋勬垚浠繪剰綾誨瀷鐢熸垚鏍?/p>
E.Swap
鍙戠敓鍦ㄤ袱涓幆闂寸殑浜ゆ崲浼氬皢涓や釜鐜悎騫訛紝鍙戠敓鍦ㄥ悓涓涓幆鐨勪氦鎹細灝嗚繖涓幆鎷嗘垚涓や釜鐜?br>濡傛灉涓嶈冭檻濂囧伓鎬э紝閭ｄ箞姣忎釜鐜箣闂寸浉浜掔嫭绔嬶紝浜掍笉褰卞搷錛岀幇鍦ㄨ嫢涓涓幆閲屽悓濂囧伓鎬э紝渚嬪鍏ㄦ槸濂囨暟錛岄偅浠栬偗瀹氳鍜屽叾浠栫殑鐜彂鐢熸帴瑙︼紝涔熷氨鏄拰鍏朵粬鐜悎騫訛紝榪欓噷閫夋嫨鍏ㄦ槸鍋舵暟鐨勭幆鏄劇劧涓嶄細鏇村樊銆?br>濡傛灉娌℃湁浜嗗伓鏁扮幆錛岄偅灝卞彧鑳介夋嫨鍜屽墿涓嬬殑鏃㈠張濂囧張鏈夊伓鐨勭幆鍚堝茍浜嗐?br>鏈鍚庡彲浠ヨ瘉鏄庝竴涓幆閲屾棦鍙堝鏁板張鏈夊伓鏁版椂錛屾渶蹇皢瀹冨畬鍏ㄦ媶寮闇瑕乶-1姝ャ?/p>
F.JinYueTuan
鐢ㄩ殧鏉挎硶鍙互鐭ラ亾絳旀鏄疌(m+n-1, n) * n!. 浣嗘槸鏁版嵁閲忛潪甯稿ぇ錛岀洿鎺ョ畻涔樼Н瓚呮椂錛屽姞涓婁竴涓壀鏋濈灛闂村嚭瑙ｏ細濡傛灉鍙戠幇鍦ㄨ竟涔樿竟妯＄殑榪囩▼涓瓟妗堝彉涓?錛屽氨鍙互璺沖嚭浜嗐?/p>
G. MiniSum
dp[i][j]琛ㄧず褰撳彧鑰冭檻鍓峣涓墿鍝佹椂錛岃鍑嗗鍔犲叆絎琲+1涓墿鍝佹椂錛孹[i+1]鍓嶉潰鐨勭郴鏁頒負j鏃剁殑鍑芥暟鏈灝忓箋?br>杞Щ灝辨槸dp[i][j] + j * (-Li) --> dp[i+1][j - Li]
dp[i][j] + j * ( Li) --> dp[i+1][j + Li]
鍚戝悗鏇存柊錛屾渶鍚庣瓟妗堝氨鏄痙p[n][?]鍙栦釜鏈澶х殑銆?/p>
H.Urban planning
棰樼洰鍗佸垎璐硅В錛屽彈涓嶄簡浜嗐傘傘?br>姝ｇ‘鐨勭悊瑙ｅ氨鏄粰N涓偣錛屾瘡涓偣鏈変釜鏉冨鹼紝浠ュ強姣忎袱涓偣涔嬮棿鏈夎竟鏉冿紝鍗曞悜鐨勩傛眰鍑轟竴涓寘鍚壒瀹氱偣錛堝亣璁劇紪鍙蜂負1錛夌殑鐐圭殑闆嗗悎婊¤凍錛?br>1銆佽繖涓泦鍚堝厓绱犺灝介噺澶氥?br>2銆侀泦鍚堜腑鐨勫厓绱犱箣闂村樊寮備笉鑳借秴榪嘨銆?br>3銆佸湪姣忎釜闆嗗悎涓夊嚭杈癸紝浣跨壒瀹氱偣鍒板叾浠栫偣閮芥湁璺彲杈撅紝騫朵笖杈規潈涔嬪拰瑕佹渶灝忋?br>4銆佸鏋滀袱涓泦鍚堝厓绱犱釜鏁扮浉鍚岋紝鍙栬緝澶х殑杈規潈銆?br>
棣栧厛錛屽鏋滅粰鍑烘弧瓚蟲潯浠剁殑鐐歸泦錛屾垜浠煡閬撴瘡涓や釜鐐逛箣闂撮兘鏈夎竟錛屽彧瑕佹眰鍑轟竴棰楁渶灝忕敓鎴愭爲灝辮浜嗭紝閴翠簬鏈夊悜錛屾墍浠ユ眰鍑轟粠鐗瑰畾鐐圭殑鏍戝艦鍥懼氨琛屼簡錛堝叧浜庢牴紜畾鐨勬渶灝忔爲褰㈠浘錛屽弬鑰冨垬鏈辯畻娉曪級銆傛墍浠ュ彧瑕佹壘鍒拌繖涓弧瓚蟲潯浠剁殑闆嗗悎灝辮浜嗭紝娉ㄦ剰鍒伴泦鍚堜箣涓殑鍏冪礌鏈澶у樊寮備笉鑳借秴榪嘨錛岃屼笖V涔熷緢灝忥紝鎵浠ュ彲浠ユ灇涓鵑泦鍚堢殑鏉冨煎尯闂碵lo錛宭o+V]錛屾墍鏈夋潈鍊艱惤鍦ㄨ繖涓尯闂翠腑鐨勭偣閮芥弧瓚蟲潯浠訛紝鐢變簬浠諱袱涓偣涔嬮棿閮芥湁杈癸紝鎵浠ヤ竴瀹氬瓨鍦ㄦ爲褰㈠浘錛屾渶鍚庢眰涓嬫渶灝忔爲褰㈠浘錛岀劧鍚庡垽鏂笅灝辮浜嗐傘傘?br>I.Air Strike
紱葷嚎鎿嶄綔錛屾妸鍒犻櫎鍜屾煡璇㈤兘淇濆瓨璧鋒潵銆傛妸鍒犻櫎淇濆瓨鍚庢帓搴忓茍unique錛屾煡璇篃榪涜鎺掑簭錛岀劧鍚庝粠灝忓埌澶ф煡璇紝鐪嬪綋鍓嶆槸鍚﹁鍒犻櫎錛屽垹闄ょ殑璇濊煩榪囧綋鍓嶈繖涓偣寰鍚庣Щ涓涓紝鎯婅浜庢渶鍚庝唬鐮?0琛屼互鍐呫?br>
J.MiniCost
棰樼洰鎰忔濆氨鏄粰鍑轟竴涓嫭鍙峰簭鍒楋紝姣忔鍙互閫夋嫨鏀瑰彉鐗瑰畾鐐逛笂鐨勬嫭鍙鋒柟鍚戯紝騫朵笖鏀瑰彉鏈夋潈鍊箋傛眰鍑烘渶灝忕殑鏀瑰彉鏉冨煎拰錛屼嬌榪欎釜鎷彿搴忓垪鍚堟硶銆?br>鏆傛椂鍙細O錛圢^2錛夌畻娉曘?br>娉ㄦ剰鍒板鏋滀竴涓嫭鍙峰簭鍒楄鏄悎娉曠殑璇濓紝浠繪剰浣嶇疆涓瀹氭槸宸︽嫭鍙鋒暟澶т簬絳変簬鍙蟲嫭鍙鋒暟錛屾墍浠ヤ互姝ゅ畾涔夌姸鎬乨p[i][j]錛岃〃紺哄墠i涓鍙蜂腑錛屽乏鎷彿姣斿彸鎷彿澶歫涓傚彧瑕佹牴鎹綋鍓嶇殑絎﹀彿杞Щ灝辮浜嗐傘?鍒濆鏉′歡dp[0][0] = 0 銆傘傛渶鍚庣瓟妗坉p[N][0] 銆傘傘?