试用Dijkstra算法求从v1到其余各顶点的最短路径，写出每一步的状态。求大神解答。算法我会，主 用Dijkstra算法求附图中从点a到其它各节点的最短路径，...
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\u4e0b\u9762\u5f00\u59cbDijkstra\u7b97\u6cd5\uff1a
\u548cv4\u76f8\u8fde\u7684\u4e14\u672a\u6807\u8bb0\u7684\u70b9\u6709v2\u548cv6\uff0c\u8fd9\u6837\u66f4\u65b0d2=20\uff0cd6=15\uff0c\u9009\u62e9\u672a\u6807\u8bb0\u6240\u6709\u70b9\u4e2d\u6700\u5c0f\u7684d6=15\uff0c\u6807\u8bb0v6\u5df2\u9009\u62e9\uff0c\u8fd9\u6837\u6211\u4eec\u7b97\u51fa\u4e86v4->v6\u6700\u77ed\u8ddd\u79bbd6=15\uff1b
\u4ecev6\u5f00\u59cb\uff0c\u548cv6\u76f8\u8fde\u7684\u4e14\u672a\u6807\u8bb0\u7684\u662fv2\uff0c\u6b64\u65f6\u7b97d6+6=21>20,\u6240\u4ee5\u4e0d\u66f4\u65b0d2\uff0c\u9009\u62e9\u672a\u6807\u8bb0\u6240\u6709\u70b9\u4e2d\u6700\u5c0f\u7684d2=20\uff0c\u6807\u8bb0v2\u5df2\u9009\u62e9\uff0c\u8fd9\u6837\u7b97\u51fa\u4e86v4->v2\u6700\u77ed\u8ddd\u79bbd2=20\uff1b
\u4ecev2\u5f00\u59cb\uff0c\u548cv2\u76f8\u8fde\u7684\u4e14\u672a\u6807\u8bb0\u7684\u6709v1\u548cv5\uff0cd1=d2+10=30,d5=d2+30=50\uff0c\u9009\u62e9\u672a\u6807\u8bb0\u6240\u6709\u70b9\u4e2d\u6700\u5c0f\u7684d1=30\uff0c\u6807\u8bb0v1\u5df2\u9009\u62e9\uff0c\u8fd9\u6837\u6211\u4eec\u7b97\u51fa\u4e86v4->v1\u6700\u77ed\u8ddd\u79bbd1=30\uff1b
\u4ecev1\u5f00\u59cb\uff0c\u548cv1\u76f8\u8fde\u7684\u4e14\u672a\u6807\u8bb0\u7684\u6709v3\uff0cd3=d1+15=45\uff0c\u9009\u62e9\u5269\u4e0b\u6ca1\u88ab\u9009\u7684\u6240\u6709\u70b9\u7684\u6700\u5c0f\u7684d3=45(d5=50)\uff0c\u6807\u8bb0v3\u5df2\u9009\u62e9\uff0c\u8fd9\u6837\u6211\u4eec\u7b97\u51fa\u4e86v4->v3\u6700\u77ed\u8ddd\u79bbd3=45
\u4ecev3\u5f00\u59cb\uff0c\u6ca1\u6709\u51fa\u53bb\u7684\u8def\u5f84\uff0c\u4e0d\u66f4\u65b0\u8ddd\u79bb\uff0c\u9009\u62e9\u5269\u4e0b\u6ca1\u88ab\u9009\u7684\u6240\u6709\u70b9\u7684\u6700\u5c0f\u7684d5=50\uff0c\u6807\u8bb0v5\u5df2\u9009\u62e9\uff0c\u8fd9\u6837\u6211\u4eec\u7b97\u51fa\u4e86v4->v5\u6700\u77ed\u8ddd\u79bbd5=50.
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\u5e0c\u671b\u80fd\u5e2e\u4f60\u6e05\u6670\u4e86\u89e3Dijkstra\u7b97\u6cd5\uff0c\u56fe\u8bba\u4e2d\u5f88\u91cd\u8981\u7684\u7b97\u6cd5\u4e4b\u4e00\u3002
\u7ed3\u679c\u5982\u4e0b\u56fe\uff1a
绛旓細绠楁硶鎴戜細,涓 璇曠敤Dijkstra绠楁硶姹備粠v1鍒板叾浣欏悇椤剁偣鐨勬渶鐭矾寰,鍐欏嚭姣忎竴姝ョ殑鐘舵併傛眰澶х瑙ｇ瓟銆傜畻娉曟垜浼,涓昏鏄濂!涓嬪浘涓洪鐩浘,杩樻湁灏辨槸璋佹湁2013鍗椾含鑸┖鑸ぉ澶у829璇曞嵎鐨勭瓟妗堝晩??璺眰!... 璇曠敤Dijkstra绠楁硶姹備粠v1鍒板叾浣欏悇椤剁偣鐨勬渶鐭矾寰,鍐欏嚭姣忎竴姝ョ殑鐘舵併傛眰澶х瑙ｇ瓟銆傜畻娉曟垜浼,涓昏鏄濂!涓嬪浘涓洪鐩...
绛旓細鐢―ijkstra绠楁硶姹備粠V1椤剁偣鍒板叾浠栧悇椤剁偣鐨勬渶鐭窛绂诲拰鏈鐭矾寰勭殑C璇█绋嬪簭濡備笅 include <stdio.h> include <string.h> include <stdlib.h> define N 6 // 椤剁偣鏁 define INF 32767 int adj_arr[N][N] = {{INF, 2, 3, INF, INF, INF},{INF, INF, INF, 5, INF, INF},{INF, INF,...
绛旓細棣栧厛锛岀畻娉曚細瀵绘壘鍑浠巚鍑哄彂鍒版墍鏈夊叾浠栭《鐐圭殑鏈鐭矾寰勪腑鐨勭涓鏉★紝鐒跺悗鍒╃敤杩欐潯璺緞鐨勪俊鎭紝鎵惧嚭绗簩鏉￠暱搴︽洿鐭殑璺緞锛屽姝ゅ弽澶嶏紝鐩村埌鎵鏈夌殑椤剁偣閮藉寘鍚簡浠巚鍑哄彂鐨勬渶鐭矾寰勩Dijkstra绠楁硶鐨勬墽琛岃繃绋嬪涓嬶細浠庢簮鐐箆寮濮嬶紝鏍囪鍏惰嚜韬负宸茶闂紝骞惰祴浜堝叾0璺濈鍊笺傜劧鍚庯紝浠庢湭璁块棶鐨勯《鐐逛腑閫夋嫨涓涓窛绂籿鏈杩戠殑...
绛旓細Dijkstra(杩澃鏂壒鎷)绠楁硶鏄吀鍨嬬殑鍗曟簮鏈鐭矾寰勭畻娉曪紝鐢ㄤ簬璁＄畻涓涓妭鐐瑰埌鍏朵粬鎵鏈夎妭鐐圭殑鏈鐭矾寰勩備富瑕佺壒鐐规槸浠ヨ捣濮嬬偣涓轰腑蹇冨悜澶栧眰灞傛墿灞曪紝鐩村埌鎵╁睍鍒扮粓鐐逛负姝傛敞鎰忚绠楁硶瑕佹眰鍥句腑涓嶅瓨鍦ㄨ礋鏉冭竟銆傝G=(V,E)鏄竴涓甫鏉冩湁鍚戝浘锛屾妸鍥句腑椤剁偣闆嗗悎V鍒嗘垚涓ょ粍锛岀涓缁勪负宸叉眰鍑烘渶鐭矾寰勭殑椤剁偣闆嗗悎锛堢敤S琛ㄧず...
绛旓細杩澃鏂壒鎷夌畻娉鐢ㄦ潵瑙ｅ喅浠庨《鐐v0鍑哄彂鍒板叾浣欓《鐐圭殑鏈鐭矾寰勶紝璇ョ畻娉曟寜鐓ф渶鐭矾寰勯暱搴﹂掑鐨勯『搴忎骇鐢熸墍浠ユ渶鐭矾寰勩傚浜庡浘G=锛V锛孍锛夛紝灏嗗浘涓殑椤剁偣鍒嗘垚涓ょ粍锛氱涓缁凷锛氬凡姹傚嚭鐨勬渶鐭矾寰勭殑缁堢偣闆嗗悎锛堝紑濮嬩负锝泇0}锛夈傜浜岀粍V-S锛氬皻鏈眰鍑烘渶鐭矾寰勭殑缁堢偣闆嗗悎锛堝紑濮嬩负V-{v0}鐨勫叏閮ㄧ粨鐐癸級銆傚爢浼樺寲 ...
绛旓細瀹氫箟G=(V,E)锛屽畾涔夐泦鍚圫瀛樻斁宸茬粡鎵惧埌鏈鐭矾寰勭殑椤剁偣锛岄泦鍚圱瀛樻斁褰撳墠杩樻湭鎵惧埌鏈鐭矾寰勭殑椤剁偣锛屽嵆鏈塗=V-S Dijkstra绠楁硶鎻忚堪濡備笅锛(1) 鍋囪鐢ㄥ甫鏉冪殑閭绘帴鐭╅樀edges鏉ヨ〃绀哄甫鏉冩湁鍚戝浘锛宔dges[i][j]琛ㄧず寮<Vi, Vj>涓婄殑鏉冨笺傝嫢<Vi, Vj>涓嶅瓨鍦ㄥ垯缃甧dges[i][j]=鈭烇紙璁＄畻鏈轰笂鐢ㄤ竴涓厑璁哥殑鏈澶у...
绛旓細Dijkstra绠楁硶鐨勫叿浣撴楠わ細Dijkstra绠楁硶鍙堢О涓哄崟婧愭渶鐭矾寰勶紝鎵璋撳崟婧愭槸鍦ㄤ竴涓湁鍚戝浘涓紝浠庝竴涓《鐐瑰嚭鍙戯紝姹傝椤剁偣鑷虫墍鏈夊彲鍒拌揪椤剁偣鐨勬渶鐭矾寰勯棶棰樸傝G=锛圴锛孍锛夋槸涓涓湁鍚戝浘锛孷琛ㄧず椤剁偣锛孍琛ㄧず杈广傚畠鐨勬瘡涓鏉¤竟锛坕锛宩锛夊睘浜嶦锛岄兘鏈変竴涓潪璐熸潈W锛圛,j锛夛紝鍦℅涓寚瀹氫竴涓粨鐐箆0锛岃姹傛妸浠巚0...
绛旓細Dijkstra)绠楁硶姝ラ锛氾紙姹傚浘涓v0鍒皏8鐨勬渶鐭矾寰勶級骞堕潪涓涓嬪瓙姹傚嚭v0鍒皏8鐨勬渶鐭矾寰勶紝鑰屾槸 涓姝ヤ竴姝ユ眰鍑哄畠浠箣闂撮《鐐圭殑鏈鐭矾寰 锛岃繃杩囩▼涓兘鏄 鍩轰簬宸茬粡姹傚嚭鐨勬渶鐭矾寰勭殑鍩虹涓婏紝姹傚緱鏇磋繙椤剁偣鐨勬渶鐭矾寰勶紝鏈缁堝緱鍑烘簮鐐逛笌缁堢偣鐨勬渶鐭矾寰 銆傚紬娲涗紛寰(Floyd)绠楁硶鏄竴涓粡鍏哥殑 鍔ㄦ佽鍒掔畻娉 銆
绛旓細杩澃鏂壒鎷夌畻娉鐢ㄦ潵瑙ｅ喅浠庨《鐐v0鍑哄彂鍒板叾浣欓《鐐圭殑鏈鐭矾寰勶紝璇ョ畻娉曟寜鐓ф渶鐭矾寰勯暱搴﹂掑鐨勯『搴忎骇鐢熸墍浠ユ渶鐭矾寰勩傚浜庡浘G=锛V锛孍锛夛紝灏嗗浘涓殑椤剁偣鍒嗘垚涓ょ粍锛氱涓缁凷锛氬凡姹傚嚭鐨勬渶鐭矾寰勭殑缁堢偣闆嗗悎锛堝紑濮嬩负{v0}锛夈傜浜岀粍V-S锛氬皻鏈眰鍑烘渶鐭矾寰勭殑缁堢偣闆嗗悎锛堝紑濮嬩负V-{v0}鐨勫叏閮ㄧ粨鐐癸級銆傜畻娉曞皢鎸...
绛旓細dijkstra绠楁硶鏈鐭矾寰勭畻娉曘侱ijkstra鏄吀鍨嬫渶鐭矾寰勭畻娉曪紝鐢ㄤ簬璁＄畻涓涓妭鐐瑰埌鍏朵粬鑺傜偣鐨勬渶鐭矾寰勩傝绠楁硶浣跨敤鐨勬槸璐績绛栫暐锛氭瘡娆￠兘鎵惧嚭鍓╀綑椤剁偣涓笌婧愮偣璺濈鏈杩戠殑涓涓《鐐广傜粰瀹氫竴甯︽潈鍥撅紝鍥句腑姣忔潯杈圭殑鏉冨兼槸闈炶礋鐨勶紝浠ｈ〃鐫涓ら《鐐逛箣闂寸殑璺濈銆傛寚瀹氬浘涓殑涓椤剁偣涓烘簮鐐癸紝鎵惧嚭婧愮偣鍒板叾瀹冮《鐐圭殑鏈鐭矾寰勫拰鍏...
