Posted 2021-04-18 娣卞叆鍘熺悊

鐐瑰嚮馃憜钃濊壊鈥?nbsp;娣卞叆鍘熺悊鈥濓紝鍏虫敞骞垛€?/span>璁句负鏄熸爣鈥?/span>

鎶€鏈共璐э紝绗竴鏃堕棿鎺ㄩ€?/span>

 

浠婂ぉ锛屾垜涓昏璁插姩鎬佽鍒掔殑涓€浜涚悊璁虹煡璇嗐€傚瀹岃繖鑺傚唴瀹癸紝鍙互甯綘瑙ｅ喅杩欐牱鍑犱釜闂锛氫粈涔堟牱鐨勯棶棰樺彲浠ョ敤鍔ㄦ€佽鍒掕В鍐筹紵瑙ｅ喅鍔ㄦ€佽鍒掗棶棰樼殑涓€鑸€濊€冭繃绋嬫槸浠€涔堟牱鐨勶紵璐績銆佸垎娌汇€佸洖婧€佸姩鎬佽鍒掕繖鍥涚绠楁硶鎬濇兂鍙堟湁浠€涔堝尯鍒拰鑱旂郴锛?/span>

鐞嗚鐨勪笢瑗块兘姣旇緝鎶借薄锛屼笉杩囦綘涓嶇敤鎷呭績锛屾垜浼氱粨鍚堝叿浣撶殑渚嬪瓙鏉ヨ瑙ｏ紝浜夊彇璁╀綘杩欐灏辫兘鐪熸鐞嗚В杩欎簺鐭ヨ瘑鐐癸紝涔熶负鍚庨潰鐨勫簲鐢ㄥ拰瀹炴垬鍋氬ソ鍑嗗銆?/span>

鈥滀竴涓ā鍨嬩笁涓壒寰佲€濈悊璁鸿瑙?/span>

浠€涔堟牱鐨勯棶棰橀€傚悎鐢ㄥ姩鎬佽鍒掓潵瑙ｅ喅鍛紵鎹㈠彞璇濊锛屽姩鎬佽鍒掕兘瑙ｅ喅鐨勯棶棰樻湁浠€涔堣寰嬪彲寰憿锛熷疄闄呬笂锛屽姩鎬佽鍒掍綔涓轰竴涓潪甯告垚鐔熺殑绠楁硶鎬濇兂锛屽緢澶氫汉瀵规宸茬粡鍋氫簡闈炲父鍏ㄩ潰鐨勬€荤粨銆傛垜鎶婅繖閮ㄥ垎鐞嗚鎬荤粨涓衡€滀竴涓ā鍨嬩笁涓壒寰佲€濄€?/span>

棣栧厛锛屾垜浠潵鐪嬶紝浠€涔堟槸鈥?/span>涓€涓ā鍨?/span>鈥濓紵瀹冩寚鐨勬槸鍔ㄦ€佽鍒掗€傚悎瑙ｅ喅鐨勯棶棰樼殑妯″瀷銆傛垜鎶婅繖涓ā鍨嬪畾涔変负鈥?/span>澶氶樁娈靛喅绛栨渶浼樿В妯″瀷鈥濄€備笅闈㈡垜鍏蜂綋鏉ョ粰浣犺璁层€?/span>

鎴戜滑涓€鑸槸鐢ㄥ姩鎬佽鍒掓潵瑙ｅ喅鏈€浼橀棶棰樸€傝€岃В鍐抽棶棰樼殑杩囩▼锛岄渶瑕佺粡鍘嗗涓喅绛栭樁娈点€傛瘡涓喅绛栭樁娈甸兘瀵瑰簲鐫€涓€缁勭姸鎬併€傜劧鍚庢垜浠鎵句竴缁勫喅绛栧簭鍒楋紝缁忚繃杩欑粍鍐崇瓥搴忓垪锛岃兘澶熶骇鐢熸渶缁堟湡鏈涙眰瑙ｇ殑鏈€浼樺€笺€?/span>

鐜板湪锛屾垜浠啀鏉ョ湅锛屼粈涔堟槸鈥?/span>涓変釜鐗瑰緛鈥濓紵瀹冧滑鍒嗗埆鏄?/span>鏈€浼樺瓙缁撴瀯銆?/span>鏃犲悗鏁堟€?/span>鍜?/span>閲嶅瀛愰棶棰?/span>銆傝繖涓変釜姒傚康姣旇緝鎶借薄锛屾垜鏉ラ€愪竴璇︾粏瑙ｉ噴涓€涓嬨€?/span>

1. 鏈€浼樺瓙缁撴瀯

鏈€浼樺瓙缁撴瀯鎸囩殑鏄紝闂鐨勬渶浼樿В鍖呭惈瀛愰棶棰樼殑鏈€浼樿В銆傚弽杩囨潵璇村氨鏄紝鎴戜滑鍙互閫氳繃瀛愰棶棰樼殑鏈€浼樿В锛屾帹瀵煎嚭闂鐨勬渶浼樿В銆傚鏋滄垜浠妸鏈€浼樺瓙缁撴瀯锛屽搴斿埌鎴戜滑鍓嶉潰瀹氫箟鐨勫姩鎬佽鍒掗棶棰樻ā鍨嬩笂锛岄偅鎴戜滑涔熷彲浠ョ悊瑙ｄ负锛屽悗闈㈤樁娈电殑鐘舵€佸彲浠ラ€氳繃鍓嶉潰闃舵鐨勭姸鎬佹帹瀵煎嚭鏉ャ€?/span>

2. 鏃犲悗鏁堟€?/span>

鏃犲悗鏁堟€ф湁涓ゅ眰鍚箟锛岀涓€灞傚惈涔夋槸锛屽湪鎺ㄥ鍚庨潰闃舵鐨勭姸鎬佺殑鏃跺€欙紝鎴戜滑鍙叧蹇冨墠闈㈤樁娈电殑鐘舵€佸€硷紝涓嶅叧蹇冭繖涓姸鎬佹槸鎬庝箞涓€姝ヤ竴姝ユ帹瀵煎嚭鏉ョ殑銆傜浜屽眰鍚箟鏄紝鏌愰樁娈电姸鎬佷竴鏃︾‘瀹氾紝灏变笉鍙椾箣鍚庨樁娈电殑鍐崇瓥褰卞搷銆傛棤鍚庢晥鎬ф槸涓€涓潪甯糕€滃鏉锯€濈殑瑕佹眰銆傚彧瑕佹弧瓒冲墠闈㈡彁鍒扮殑鍔ㄦ€佽鍒掗棶棰樻ā鍨嬶紝鍏跺疄鍩烘湰涓婇兘浼氭弧瓒虫棤鍚庢晥鎬с€?/span>

3. 閲嶅瀛愰棶棰?/span>

杩欎釜姒傚康姣旇緝濂界悊瑙ｃ€傚墠闈竴鑺傦紝鎴戝凡缁忓娆℃彁杩囥€傚鏋滅敤涓€鍙ヨ瘽姒傛嫭涓€涓嬶紝閭ｅ氨鏄紝涓嶅悓鐨勫喅绛栧簭鍒楋紝鍒拌揪鏌愪釜鐩稿悓鐨勯樁娈垫椂锛屽彲鑳戒細浜х敓閲嶅鐨勭姸鎬併€?/span>

鈥滀竴涓ā鍨嬩笁涓壒寰佲€濆疄渚嬪墫鏋?/span>

鈥滀竴涓ā鍨嬩笁涓壒寰佲€濊繖閮ㄥ垎鏄悊璁虹煡璇嗭紝姣旇緝鎶借薄锛屼綘鐪嬩簡涔嬪悗鍙兘杩樻槸鏈夌偣鎳碉紝鏈夌浼兼噦闈炴噦鐨勬劅瑙夛紝娌″叧绯伙紝杩欎釜寰堟甯搞€傛帴涓嬫潵锛屾垜缁撳悎涓€涓叿浣撶殑鍔ㄦ€佽鍒掗棶棰橈紝鏉ョ粰浣犺缁嗚В閲娿€?/span>

鍋囪鎴戜滑鏈変竴涓?n 涔樹互 n 鐨勭煩闃?w[n][n]銆傜煩闃靛瓨鍌ㄧ殑閮芥槸姝ｆ暣鏁般€傛瀛愯捣濮嬩綅缃湪宸︿笂瑙掞紝缁堟浣嶇疆鍦ㄥ彸涓嬭銆傛垜浠皢妫嬪瓙浠庡乏涓婅绉诲姩鍒板彸涓嬭銆傛瘡娆″彧鑳藉悜鍙虫垨鑰呭悜涓嬬Щ鍔ㄤ竴浣嶃€備粠宸︿笂瑙掑埌鍙充笅瑙掞紝浼氭湁寰堝涓嶅悓鐨勮矾寰勫彲浠ヨ蛋銆傛垜浠妸姣忔潯璺緞缁忚繃鐨勬暟瀛楀姞璧锋潵鐪嬩綔璺緞鐨勯暱搴︺€傞偅浠庡乏涓婅绉诲姩鍒板彸涓嬭鐨勬渶鐭矾寰勯暱搴︽槸澶氬皯鍛紵

鎴戜滑鍏堢湅鐪嬶紝杩欎釜闂鏄惁绗﹀悎鈥滀竴涓ā鍨嬧€濓紵

浠?(0, 0) 璧板埌 (n-1, n-1)锛屾€诲叡瑕佽蛋 2*(n-1) 姝ワ紝涔熷氨瀵瑰簲鐫€ 2*(n-1) 涓樁娈点€傛瘡涓樁娈甸兘鏈夊悜鍙宠蛋鎴栬€呭悜涓嬭蛋涓ょ鍐崇瓥锛屽苟涓旀瘡涓樁娈甸兘浼氬搴斾竴涓姸鎬侀泦鍚堛€?/span>

鎴戜滑鎶婄姸鎬佸畾涔変负 min_dist(i, j)锛屽叾涓?i 琛ㄧず琛岋紝j 琛ㄧず鍒椼€俶in_dist 琛ㄨ揪寮忕殑鍊艰〃绀轰粠 (0, 0) 鍒拌揪 (i, j) 鐨勬渶鐭矾寰勯暱搴︺€傛墍浠ワ紝杩欎釜闂鏄竴涓闃舵鍐崇瓥鏈€浼樿В闂锛岀鍚堝姩鎬佽鍒掔殑妯″瀷銆?/span>

鎴戜滑鍐嶆潵鐪嬶紝杩欎釜闂鏄惁绗﹀悎鈥滀笁涓壒寰佲€濓紵

鎴戜滑鍙互鐢ㄥ洖婧畻娉曟潵瑙ｅ喅杩欎釜闂銆傚鏋滀綘鑷繁鍐欎竴涓嬩唬鐮侊紝鐢讳竴涓嬮€掑綊鏍戯紝灏变細鍙戠幇锛岄€掑綊鏍戜腑鏈夐噸澶嶇殑鑺傜偣銆傞噸澶嶇殑鑺傜偣琛ㄧず锛屼粠宸︿笂瑙掑埌鑺傜偣瀵瑰簲鐨勪綅缃紝鏈夊绉嶈矾绾匡紝杩欎篃鑳借鏄庤繖涓棶棰樹腑瀛樺湪閲嶅瀛愰棶棰樸€?/span>

濡傛灉鎴戜滑璧板埌 (i, j) 杩欎釜浣嶇疆锛屾垜浠彧鑳介€氳繃 (i-1, j)锛?i, j-1) 杩欎袱涓綅缃Щ鍔ㄨ繃鏉ワ紝涔熷氨鏄锛屾垜浠兂瑕佽绠?(i, j) 浣嶇疆瀵瑰簲鐨勭姸鎬侊紝鍙渶瑕佸叧蹇?(i-1, j)锛?i, j-1) 涓や釜浣嶇疆瀵瑰簲鐨勭姸鎬侊紝骞朵笉鍏冲績妫嬪瓙鏄€氳繃浠€涔堟牱鐨勮矾绾垮埌杈捐繖涓や釜浣嶇疆鐨勩€傝€屼笖锛屾垜浠粎浠呭厑璁稿線涓嬪拰寰€鍙崇Щ鍔紝涓嶅厑璁稿悗閫€锛屾墍浠ワ紝鍓嶉潰闃舵鐨勭姸鎬佺‘瀹氫箣鍚庯紝涓嶄細琚悗闈㈤樁娈电殑鍐崇瓥鎵€鏀瑰彉锛屾墍浠ワ紝杩欎釜闂绗﹀悎鈥滄棤鍚庢晥鎬р€濊繖涓€鐗瑰緛銆?/span>

鍒氬垰瀹氫箟鐘舵€佺殑鏃跺€欙紝鎴戜滑鎶婁粠璧峰浣嶇疆 (0, 0) 鍒?(i, j) 鐨勬渶灏忚矾寰勶紝璁颁綔 min_dist(i, j)銆傚洜涓烘垜浠彧鑳藉線鍙虫垨寰€涓嬬Щ鍔紝鎵€浠ワ紝鎴戜滑鍙湁鍙兘浠?(i, j-1) 鎴栬€?(i-1, j) 涓や釜浣嶇疆鍒拌揪 (i, j)銆備篃灏辨槸璇达紝鍒拌揪 (i, j) 鐨勬渶鐭矾寰勮涔堢粡杩?(i, j-1)锛岃涔堢粡杩?(i-1, j)锛岃€屼笖鍒拌揪 (i, j) 鐨勬渶鐭矾寰勮偗瀹氬寘鍚埌杈捐繖涓や釜浣嶇疆鐨勬渶鐭矾寰勪箣涓€銆傛崲鍙ヨ瘽璇村氨鏄紝min_dist(i, j) 鍙互閫氳繃 min_dist(i, j-1) 鍜?min_dist(i-1, j) 涓や釜鐘舵€佹帹瀵煎嚭鏉ャ€傝繖灏辫鏄庯紝杩欎釜闂绗﹀悎鈥滄渶浼樺瓙缁撴瀯鈥濄€?/span>

min_dist(i, j) = w[i][j] + min(min_dist(i, j-1), min_dist(i-1, j))

涓ょ鍔ㄦ€佽鍒掕В棰樻€濊矾鎬荤粨

鍒氬垰鎴戣浜嗭紝濡備綍閴村埆涓€涓棶棰樻槸鍚﹀彲浠ョ敤鍔ㄦ€佽鍒掓潵瑙ｅ喅銆傜幇鍦紝鎴戝啀鎬荤粨涓€涓嬶紝鍔ㄦ€佽鍒掕В棰樼殑涓€鑸€濊矾锛岃浣犻潰瀵瑰姩鎬佽鍒掗棶棰樼殑鏃跺€欙紝鑳藉鏈夌珷鍙惊锛屼笉鑷充簬鏉熸墜鏃犵瓥銆?/span>

鎴戜釜浜鸿寰楋紝瑙ｅ喅鍔ㄦ€佽鍒掗棶棰橈紝涓€鑸湁涓ょ鎬濊矾銆傛垜鎶婂畠浠垎鍒彨浣滐紝鐘舵€佽浆绉昏〃娉曞拰鐘舵€佽浆绉绘柟绋嬫硶銆?/span>

1. 鐘舵€佽浆绉昏〃娉?/span>

涓€鑸兘鐢ㄥ姩鎬佽鍒掕В鍐崇殑闂锛岄兘鍙互浣跨敤鍥炴函绠楁硶鐨勬毚鍔涙悳绱㈣В鍐炽€傛墍浠ワ紝褰撴垜浠嬁鍒伴棶棰樼殑鏃跺€欙紝鎴戜滑鍙互鍏堢敤绠€鍗曠殑鍥炴函绠楁硶瑙ｅ喅锛岀劧鍚庡畾涔夌姸鎬侊紝姣忎釜鐘舵€佽〃绀轰竴涓妭鐐癸紝鐒跺悗瀵瑰簲鐢诲嚭閫掑綊鏍戙€備粠閫掑綊鏍戜腑锛屾垜浠緢瀹规槗鍙互鐪嬪嚭鏉ワ紝鏄惁瀛樺湪閲嶅瀛愰棶棰橈紝浠ュ強閲嶅瀛愰棶棰樻槸濡備綍浜х敓鐨勩€備互姝ゆ潵瀵绘壘瑙勫緥锛岀湅鏄惁鑳界敤鍔ㄦ€佽鍒掕В鍐炽€?/span>

鎵惧埌閲嶅瀛愰棶棰樹箣鍚庯紝鎺ヤ笅鏉ワ紝鎴戜滑鏈変袱绉嶅鐞嗘€濊矾锛岀涓€绉嶆槸鐩存帴鐢?/span>鍥炴函鍔犫€滃蹇樺綍鈥?/span>鐨勬柟娉曪紝鏉ラ伩鍏嶉噸澶嶅瓙闂銆備粠鎵ц鏁堢巼涓婃潵璁诧紝杩欒窡鍔ㄦ€佽鍒掔殑瑙ｅ喅鎬濊矾娌℃湁宸埆銆傜浜岀鏄娇鐢ㄥ姩鎬佽鍒掔殑瑙ｅ喅鏂规硶锛?/span>鐘舵€佽浆绉昏〃娉?/span>銆傜涓€绉嶆€濊矾锛屾垜灏变笉璁蹭簡锛屼綘鍙互鐪嬬湅涓婁竴鑺傜殑涓や釜渚嬪瓙銆傛垜浠噸鐐规潵鐪嬬姸鎬佽浆绉昏〃娉曟槸濡備綍宸ヤ綔鐨勩€?/span>

鎴戜滑鍏堢敾鍑轰竴涓姸鎬佽〃銆傜姸鎬佽〃涓€鑸兘鏄簩缁寸殑锛屾墍浠ヤ綘鍙互鎶婂畠鎯宠薄鎴愪簩缁存暟缁勩€傚叾涓紝姣忎釜鐘舵€佸寘鍚笁涓彉閲忥紝琛屻€佸垪銆佹暟缁勫€笺€傛垜浠牴鎹喅绛栫殑鍏堝悗杩囩▼锛屼粠鍓嶅線鍚庯紝鏍规嵁閫掓帹鍏崇郴锛屽垎闃舵濉厖鐘舵€佽〃涓殑姣忎釜鐘舵€併€傛渶鍚庯紝鎴戜滑灏嗚繖涓€掓帹濉〃鐨勮繃绋嬶紝缈昏瘧鎴愪唬鐮侊紝灏辨槸鍔ㄦ€佽鍒掍唬鐮佷簡銆?/span>

灏界澶ч儴鍒嗙姸鎬佽〃閮芥槸浜岀淮鐨勶紝浣嗘槸濡傛灉闂鐨勭姸鎬佹瘮杈冨鏉傦紝闇€瑕佸緢澶氬彉閲忔潵琛ㄧず锛岄偅瀵瑰簲鐨勭姸鎬佽〃鍙兘灏辨槸楂樼淮鐨勶紝姣斿涓夌淮銆佸洓缁淬€傞偅杩欎釜鏃跺€欙紝鎴戜滑灏变笉閫傚悎鐢ㄧ姸鎬佽浆绉昏〃娉曟潵瑙ｅ喅浜嗐€備竴鏂归潰鏄洜涓洪珮缁寸姸鎬佽浆绉昏〃涓嶅ソ鐢诲浘琛ㄧず锛屽彟涓€鏂归潰鏄洜涓轰汉鑴戠‘瀹炲緢涓嶆搮闀挎€濊€冮珮缁寸殑涓滆タ銆?/span>

鐜板湪锛屾垜浠潵鐪嬩竴涓嬶紝濡備綍濂楃敤杩欎釜鐘舵€佽浆绉昏〃娉曪紝鏉ヨВ鍐充箣鍓嶉偅涓煩闃垫渶鐭矾寰勭殑闂锛?/span>

浠庤捣鐐瑰埌缁堢偣锛屾垜浠湁寰堝绉嶄笉鍚岀殑璧版硶銆傛垜浠彲浠ョ┓涓炬墍鏈夎蛋娉曪紝鐒跺悗瀵规瘮鎵惧嚭涓€涓渶鐭蛋娉曘€備笉杩囧浣曟墠鑳芥棤閲嶅鍙堜笉閬楁紡鍦扮┓涓惧嚭鎵€鏈夎蛋娉曞憿锛熸垜浠彲浠ョ敤鍥炴函绠楁硶杩欎釜姣旇緝鏈夎寰嬬殑绌蜂妇绠楁硶銆?/span>

鍥炴函绠楁硶鐨勪唬鐮佸疄鐜板涓嬫墍绀恒€備唬鐮佸緢鐭紝鑰屼笖鎴戝墠闈篃鍒嗘瀽杩囧緢澶氬洖婧畻娉曠殑渚嬮锛岃繖閲屾垜灏变笉澶氬仛瑙ｉ噴浜嗭紝浣犺嚜宸辨潵鐪嬬湅銆?/span>

private int minDist = Integer.MAX_VALUE; // 鍏ㄥ眬鍙橀噺鎴栬€呮垚鍛樺彉閲?/span>// 璋冪敤鏂瑰紡锛歮inDistBacktracing(0, 0, 0, w, n);public void minDistBT(int i, int j, int dist, int[][] w, int n) { // 鍒拌揪浜唍-1, n-1杩欎釜浣嶇疆浜嗭紝杩欓噷鐪嬬潃鏈夌偣濂囨€搱锛屼綘鑷繁涓句釜渚嬪瓙鐪嬩笅 if (i == n && j == n) { if (dist < minDist) minDist = dist; return; } if (i < n) { // 寰€涓嬭蛋锛屾洿鏂癷=i+1, j=j minDistBT(i + 1, j, dist+w[i][j], w, n); } if (j < n) { // 寰€鍙宠蛋锛屾洿鏂癷=i, j=j+1 minDistBT(i, j+1, dist+w[i][j], w, n); }}

鏈変簡鍥炴函浠ｇ爜涔嬪悗锛屾帴涓嬫潵锛屾垜浠鐢诲嚭閫掑綊鏍戯紝浠ユ鏉ュ鎵鹃噸澶嶅瓙闂銆傚湪閫掑綊鏍戜腑锛屼竴涓姸鎬侊紙涔熷氨鏄竴涓妭鐐癸級鍖呭惈涓変釜鍙橀噺 (i, j, dist)锛屽叾涓?i锛宩 鍒嗗埆琛ㄧず琛屽拰鍒楋紝dist 琛ㄧず浠庤捣鐐瑰埌杈?(i, j) 鐨勮矾寰勯暱搴︺€備粠鍥句腑锛屾垜浠湅鍑猴紝灏界 (i, j, dist) 涓嶅瓨鍦ㄩ噸澶嶇殑锛屼絾鏄?(i, j) 閲嶅鐨勬湁寰堝銆傚浜?(i, j) 閲嶅鐨勮妭鐐癸紝鎴戜滑鍙渶瑕侀€夋嫨 dist 鏈€灏忕殑鑺傜偣锛岀户缁€掑綊姹傝В锛屽叾浠栬妭鐐瑰氨鍙互鑸嶅純浜嗐€?/span>

鏃㈢劧瀛樺湪閲嶅瀛愰棶棰橈紝鎴戜滑灏卞彲浠ュ皾璇曠湅涓嬶紝鏄惁鍙互鐢ㄥ姩鎬佽鍒掓潵瑙ｅ喅鍛紵

鎴戜滑鐢诲嚭涓€涓簩缁寸姸鎬佽〃锛岃〃涓殑琛屻€佸垪琛ㄧず妫嬪瓙鎵€鍦ㄧ殑浣嶇疆锛岃〃涓殑鏁板€艰〃绀轰粠璧风偣鍒拌繖涓綅缃殑鏈€鐭矾寰勩€傛垜浠寜鐓у喅绛栬繃绋嬶紝閫氳繃涓嶆柇鐘舵€侀€掓帹婕旇繘锛屽皢鐘舵€佽〃濉ソ銆備负浜嗘柟渚夸唬鐮佸疄鐜帮紝鎴戜滑鎸夎鏉ヨ繘琛屼緷娆″～鍏呫€?/span>

寮勬噦浜嗗～琛ㄧ殑杩囩▼锛屼唬鐮佸疄鐜板氨绠€鍗曞浜嗐€傛垜浠皢涓婇潰鐨勮繃绋嬶紝缈昏瘧鎴愪唬鐮侊紝灏辨槸涓嬮潰杩欎釜鏍峰瓙銆傜粨鍚堢潃浠ｇ爜銆佸浘鍜屾枃瀛楁弿杩帮紝搴旇鏇村鏄撶悊瑙ｆ垜璁茬殑鍐呭銆?/span>

public int minDistDP(int[][] matrix, int n) { int[][] states = new int[n][n]; int sum = 0; for (int j = 0; j < n; ++j) { // 鍒濆鍖?span class="code-snippet__attr">states鐨勭涓€琛屾暟鎹?/span> sum += matrix[0][j]; states[0][j] = sum; } sum = 0; for (int i = 0; i < n; ++i) { // 鍒濆鍖?span class="code-snippet__attr">states鐨勭涓€鍒楁暟鎹?/span> sum += matrix[i][0]; states[i][0] = sum; } for (int i = 1; i < n; ++i) { for (int j = 1; j < n; ++j) { states[i][j] = matrix[i][j] + Math.min(states[i][j-1], states[i-1][j]); } } return states[n-1][n-1];}

2. 鐘舵€佽浆绉绘柟绋嬫硶

鐘舵€佽浆绉绘柟绋嬫硶鏈夌偣绫讳技閫掑綊鐨勮В棰樻€濊矾銆傛垜浠渶瑕佸垎鏋愶紝鏌愪釜闂濡備綍閫氳繃瀛愰棶棰樻潵閫掑綊姹傝В锛屼篃灏辨槸鎵€璋撶殑鏈€浼樺瓙缁撴瀯銆傛牴鎹渶浼樺瓙缁撴瀯锛屽啓鍑洪€掑綊鍏紡锛屼篃灏辨槸鎵€璋撶殑鐘舵€佽浆绉绘柟绋嬨€傛湁浜嗙姸鎬佽浆绉绘柟绋嬶紝浠ｇ爜瀹炵幇灏遍潪甯哥畝鍗曚簡銆備竴鑸儏鍐典笅锛屾垜浠湁涓ょ浠ｇ爜瀹炵幇鏂规硶锛屼竴绉嶆槸閫掑綊鍔犫€滃蹇樺綍鈥?/span>锛屽彟涓€绉嶆槸杩唬閫掓帹銆?/span>

鎴戜滑杩樻槸鎷垮垰鎵嶇殑渚嬪瓙鏉ヤ妇渚嬨€傛渶浼樺瓙缁撴瀯鍓嶉潰宸茬粡鍒嗘瀽杩囦簡锛屼綘鍙互鍥炶繃澶村幓鍐嶇湅涓嬨€備负浜嗘柟渚夸綘鏌ョ湅锛屾垜鎶婄姸鎬佽浆绉绘柟绋嬫斁鍒拌繖閲屻€?/span>

min_dist(i, j) = w[i][j] + min(min_dist(i, j-1), min_dist(i-1, j))

杩欓噷鎴戝己璋冧竴涓嬶紝鐘舵€佽浆绉绘柟绋嬫槸瑙ｅ喅鍔ㄦ€佽鍒掔殑鍏抽敭銆?/span>濡傛灉鎴戜滑鑳藉啓鍑虹姸鎬佽浆绉绘柟绋嬶紝閭ｅ姩鎬佽鍒掗棶棰樺熀鏈笂灏辫В鍐充竴澶у崐浜嗭紝鑰岀炕璇戞垚浠ｇ爜闈炲父绠€鍗曘€備絾鏄緢澶氬姩鎬佽鍒掗棶棰樼殑鐘舵€佹湰韬氨涓嶅ソ瀹氫箟锛岀姸鎬佽浆绉绘柟绋嬩篃灏辨洿涓嶅ソ鎯冲埌銆?/span>

涓嬮潰鎴戠敤閫掑綊鍔犫€滃蹇樺綍鈥濈殑鏂瑰紡锛屽皢鐘舵€佽浆绉绘柟绋嬬炕璇戞垚鏉ヤ唬鐮侊紝浣犲彲浠ョ湅鐪嬨€傚浜庡彟涓€绉嶅疄鐜版柟寮忥紝璺熺姸鎬佽浆绉昏〃娉曠殑浠ｇ爜瀹炵幇鏄竴鏍风殑锛屽彧鏄€濊矾涓嶅悓銆?/span>

private int[][] matrix = {{1锛?锛?锛?}, {2锛?锛?锛?}锛寋5锛?锛?锛?}锛寋6锛?锛?锛?}};private int n = 4;private int[][] mem = new int[4][4];public int minDist(int i, int j) { // 璋冪敤minDist(n-1, n-1); if (i == 0 && j == 0) return matrix[0][0]; if (mem[i][j] > 0) return mem[i][j]; int minLeft = Integer.MAX_VALUE; if (j-1 >= 0) { minLeft = minDist(i, j-1); } int minUp = Integer.MAX_VALUE; if (i-1 >= 0) { minUp = minDist(i-1, j); }  int currMinDist = matrix[i][j] + Math.min(minLeft, minUp); mem[i][j] = currMinDist; return currMinDist;}

涓ょ鍔ㄦ€佽鍒掕В棰樻€濊矾鍒拌繖閲屽氨璁插畬浜嗐€傛垜瑕佸己璋冧竴鐐癸紝涓嶆槸姣忎釜闂閮藉悓鏃堕€傚悎杩欎袱绉嶈В棰樻€濊矾銆傛湁鐨勯棶棰樺彲鑳界敤绗竴绉嶆€濊矾鏇存竻鏅帮紝鑰屾湁鐨勯棶棰樺彲鑳界敤绗簩绉嶆€濊矾鏇存竻鏅帮紝鎵€浠ワ紝浣犺缁撳悎鍏蜂綋鐨勯鐩潵鐪嬶紝鍒板簳閫夋嫨鐢ㄥ摢绉嶈В棰樻€濊矾銆?/span>

鍥涚绠楁硶鎬濇兂姣旇緝鍒嗘瀽

鍒颁粖澶╀负姝紝鎴戜滑宸茬粡瀛︿範浜嗗洓绉嶇畻娉曟€濇兂锛岃椽蹇冦€佸垎娌汇€佸洖婧拰鍔ㄦ€佽鍒掋€備粖澶╃殑鍐呭涓昏璁蹭簺鐞嗚鐭ヨ瘑锛屾垜姝ｅソ涓€鍧楀効涔熷垎鏋愪竴涓嬭繖鍥涚绠楁硶锛岀湅鐪嬪畠浠箣闂存湁浠€涔堝尯鍒拰鑱旂郴銆?/span>

濡傛灉鎴戜滑灏嗚繖鍥涚绠楁硶鎬濇兂鍒嗕竴涓嬬被锛岄偅璐績銆佸洖婧€佸姩鎬佽鍒掑彲浠ュ綊涓轰竴绫伙紝鑰屽垎娌诲崟鐙彲浠ヤ綔涓轰竴绫伙紝鍥犱负瀹冭窡鍏朵粬涓変釜閮戒笉澶т竴鏍枫€備负浠€涔堣繖涔堣鍛紵鍓嶄笁涓畻娉曡В鍐抽棶棰樼殑妯″瀷锛岄兘鍙互鎶借薄鎴愭垜浠粖澶╄鐨勯偅涓闃舵鍐崇瓥鏈€浼樿В妯″瀷锛岃€屽垎娌荤畻娉曡В鍐崇殑闂灏界澶ч儴鍒嗕篃鏄渶浼樿В闂锛屼絾鏄紝澶ч儴鍒嗛兘涓嶈兘鎶借薄鎴愬闃舵鍐崇瓥妯″瀷銆?/span>

鍥炴函绠楁硶鏄釜鈥滀竾閲戞补鈥濄€傚熀鏈笂鑳界敤鐨勫姩鎬佽鍒掋€佽椽蹇冭В鍐崇殑闂锛屾垜浠兘鍙互鐢ㄥ洖婧畻娉曡В鍐炽€傚洖婧畻娉曠浉褰撲簬绌蜂妇鎼滅储銆傜┓涓炬墍鏈夌殑鎯呭喌锛岀劧鍚庡姣斿緱鍒版渶浼樿В銆備笉杩囷紝鍥炴函绠楁硶鐨勬椂闂村鏉傚害闈炲父楂橈紝鏄寚鏁扮骇鍒殑锛屽彧鑳界敤鏉ヨВ鍐冲皬瑙勬ā鏁版嵁鐨勯棶棰樸€傚浜庡ぇ瑙勬ā鏁版嵁鐨勯棶棰橈紝鐢ㄥ洖婧畻娉曡В鍐崇殑鎵ц鏁堢巼灏卞緢浣庝簡銆?/span>

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-娣卞叆鍘熺悊-  

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