用Dijkstra方法求下图中从[tex=0.857x1.0]KHZFMIr1Sj6hp/J1gGyQtA==[/tex]到各点的最短路。[img=511x212]17940c385dfe3fc.png[/img]
求解如下:(1)[tex=33.643x1.357]S5htN1Hl92WChvLh+ihsAkpCeHi49OQNad1cgu+FnYUud9O09O1Vr8BXbXu0yHRbu1CmE8/Fz5ur3Zr+3OYdSv/J3b2Hdo1ZDQKlV5PpGPGmj8Yuq7K5clnovZtXwsbqmv+Mob4ok+mQOFB6ecUVawFDaQQPMekVhtzJRT90kcES/YGOYiALzhQEfH0ePJjKqCO35hhpysJaFPH8Dur58KNS7hOZx6/jpO18t7BHu6Q=[/tex][tex=15.786x1.429]neewftuuQTFkiwr+XYQA9GYNKisWFmzMffCYbCHzezGstf4ryVMorXh0S+4m0HaSnwD1DLdBfaMZq28ER2Ii/6N9QytkOKmONluycKYkGHNVKw7w0hlqKSl6QW/EpGTiFe/wtHWGZFsoY81juVNpJg==[/tex],故可将[tex=2.429x1.357]3NecNZsDPDyFPDH1s69OH4vNMtZ+t4XnEVpXfYCrjnE=[/tex]修改为[tex=13.5x1.357]3NecNZsDPDyFPDH1s69OH/ErG5yPvVG171vS7s6nzEYBkZDX5WxYjMT/ShdSu7ArfaYfSMTzyrGLlQVCLaijUeVqYvEvi+CR/PCxsSi5zOU=[/tex][tex=15.571x1.357]neewftuuQTFkiwr+XYQA9Kryrliy20UeeZsXVJqgwVq/N+aM5RN48KahWhEGZ7alo2ubJsi1Z27RQgbDkvQbx6alw1aMUFyChtUBFLlzDBjSYmvVcyP/+V0TQdlxJgUm+Tm8LNqgmd4ESX+wLRtsEw==[/tex],故可将[tex=2.429x1.357]rXfz2pGF2B+gDOQYMaGMGXhiiv8C5GwIjljeIHY/sYg=[/tex]修改为[tex=13.5x1.357]rXfz2pGF2B+gDOQYMaGMGSHjdO/f1Yi0TOJ3dWnCQsPAkOfdcLDLTlyIOiTU7QOJbTQyf7g1TxdPYosolqj+nsUU24YKFkwRFYjJk5BAmO8=[/tex]因为[tex=12.643x1.357]JZCl3NHFZMZAuoWneybr4neDjhI1zbsPyxK1hkE+vHpibH4uRqEG+ETU0gYzh0xQbB1rPIPuA4Maoreiw5XziolsBylqQVQJrKZ5HI5vRdAcGAil7GEhtdeLHO3VX8yx[/tex],所以令[tex=17.0x1.357]UCQmjLxB/IOzM3x+mIx4DXIOMHDx0XAT8xpGjRQbPCr6QuCYjV951wyD2ntUDg6uMeDBPRW3zUCoxHWhXOs4Ne8ZmSvErr+drhlDJd23Yo0=[/tex](2)[tex=18.214x1.357]Bc7dJeiuEUJYcHY7Uh2gL8AAzvGO9b4whrXwdvkFZpgUyDkiY+Y65u8CXm71fysv9z63mh9kq1L6SLte4T1I+GXeoRXVtwza1o+lPHWn0PorCUr4a7vqic+2qzJmWRloj3L9xAm7RTofVhCw0z8BVA==[/tex]故[tex=2.429x1.357]uBApWx8nJMQgcnu1R7kJka9jDNMXbZyOOi91CX4hnhU=[/tex]修改为[tex=8.714x1.357]TONCYS+PBqdebRWNe7DDEo2iRE7M0sxzn9WW/zWVAq6+7kt1MLaT3l2uLDBGZru0QTexoBAHnpz54Y5OKyd5Jw==[/tex]修改为2,[tex=16.714x1.357]mTryFuqNd/e4TEYg+Gr6fR/a/1Nz6GJY9Q5nbd4rF5yoDTAiPjtcGC/Y8yTtVnhb/cuCODhz/FdapzNVlwBqtKVnnVTmtXSOFOYc7Z35AO2EVBUsKEXYSgguYOrjtBjGGxikAe0uN52ne1vRERmXuw==[/tex][tex=13.071x1.357]JZCl3NHFZMZAuoWneybr4sFTzllyla1OYJunBScbtrzBljE3XtGWRXDpyecI3BVPJ90jWCdDNnOTZ2JmH2tQ6fZlSXvQa4NetIHC5nK6V3/jHMZ20lYdUiSnca09cmtL[/tex]令[tex=12.286x1.357]sDVuFt8A4OCz2ff6iZlmTdqLpJIzkGhWqqlWvkEfSefJ1iesD4/eXtL7jxjVklMo114RLhvNDU5do1HdT2hnLJSHJYGFietiB1FYea6ExeI=[/tex](3)[tex=26.286x1.357]15PCsPmROvOeDtJBQI1MiUHoBs4GogqaRsI9XbZt7odDPR5vbc+7ZRT4xEiD841EbxJ/tmHfaTaX6EmHQ6mAtO5uNCPMQByob10Hsb8Tjl6kScp2KXWTdVAQKT/pltYI7xtoMQGc1XNUuYDrPiQrDqQet8w6CY3y1iD/RZ5PJMIbj6tQB5pBuBjJ8tE5DZkKKS2S2Ng0iEYvQKiT4Zs5pw==[/tex]因[tex=8.929x1.357]sDVuFt8A4OCz2ff6iZlmTVrnWuBsJ35Zi77ElOGsYM8zZMfMzscCid/6AVFmTGKr[/tex]故将[tex=2.429x1.357]66gSLknZjnKnOR/Pw/Uz3lYEJeaf7liu40Vk1/RgZeY=[/tex]修改为4,[tex=2.429x1.357]QzaU6GeR+FIiC85sjLOEUKA7pRsvOWSA9f+0ba2Gfqg=[/tex]修改为5.因为[tex=12.786x1.357]JZCl3NHFZMZAuoWneybr4lg5CL74bNGqa/eAMKrQ+Cr4GFEUW6KJWszyeCxoC197N1jxb0sIgYp5Jo5uvNJOCIo3BA08nmrKV0XDDGWPtcDV8e2qks4i8v1e87JePQRd[/tex],所以令[tex=13.786x1.357]HtxBpC1gBfHoyGkN/A6eOS7GDzYw+F5OctVeXDjZknO+72ISvfr4Hb89ePj1eJDjAf0i4iumZwJUh7CVue4bKbOVq1YGToQ34aUcaOAD/Kc=[/tex]。(4)[tex=2.214x1.0]JFX21XbMMIet0LwF42jWaA==[/tex]:修改[tex=2.429x1.357]t/0/RmlCuitoV/SFLUDd7bJ5LzDOFR9ZCmi8IAf7raM=[/tex]为[tex=6.571x1.357]HtxBpC1gBfHoyGkN/A6eOaizMg4WiEZB1B/oR/dSV64=[/tex],修改[tex=2.429x1.357]QzaU6GeR+FIiC85sjLOEUJ4V7bf446jfPjcSHtlNNjk=[/tex]为9;修改[tex=2.429x1.357]eW1OeSd2VNUMFRwZRUfb5LfdzV/vsDKQldO8h6eam+M=[/tex]为[tex=7.571x1.357]HtxBpC1gBfHoyGkN/A6eOQ5ReGdi4fcgyqkGb9s8SzDOUMolSr0LZf3ebfMRet9O[/tex]修改[tex=2.429x1.357]QzaU6GeR+FIiC85sjLOEUM5arTI6Nvc6TupuLeZRAro=[/tex]为9.[tex=15.571x1.357]JZCl3NHFZMZAuoWneybr4sFTzllyla1OYJunBScbtrxaF6pKvhi984BiZvbigMWvYuw5n8Hrmyj7KzSQQhrCZuF0IZZxISIq1Lh+2+8wYp7NXB9wVKW8P2foLuJOrTLhDBkLKADTsK8ac1soNLzp/g==[/tex],令[tex=14.643x1.357]WRTUDQjHbJxxzaB5jGHEbL57piDPPUfH1PO1g9FMRyseYIls5N42SoA3YuH26Tk78yY5hIE3cHorO2Twef2JRshBBtDspqqHM4QPV34yQ9WqUrBneQ2ELJ0QiqaeGOr+[/tex]。(5)[tex=4.857x1.357]COnnvmeg1+SK994LjXP0EV4uvVGuEdm0wCUoAbOTrg0=[/tex]修改为[tex=9.214x1.357]WRTUDQjHbJxxzaB5jGHEbN9Vv/yih52eSmtcA/S74TatDt53zuCDfN++zG0v/1fm7iAEzPsCgwt7k7hBlnuhgQ==[/tex]修改为4.[tex=16.071x1.357]JZCl3NHFZMZAuoWneybr4lEC3va4uc+928xoa+d39zUeNyuu2AVjrAsmq86AxlMjnUd0fScHHz5UTxHCnMz3E77aOiJV4qnFZbMozqFKcwIcV5z+I5cATGrLrarX/RuCcVjF+EQ42HIEokUWZSw86g==[/tex],令[tex=20.643x1.357]sDVuFt8A4OCz2ff6iZlmTTiDUqSwsrOnrJMQdYgONHwWW4iBR8y+Gh6U1F8yTGysGr6GcPQWZg+MrllUB0Jr2hAedSlA4s726aaRxA8xfuQB54uzxkWjP4F/s18nRgJnnfps3H1hRG19MI5NEe5e6iYiKPBK8XvYB/D2BbQswNmBiBAo83ctn8yllQc6xpvM[/tex](6)[tex=4.857x1.357]5nR+fe9NtImqZHl5DYmYxpPUtMdXDW/acDWCm5NVSEw=[/tex]修改为[tex=9.214x1.357]pdupUsT/e9Yuox6wKbCu9K5L4Ibc5Bnvwj8136XjDoxknJNiIOWFYJDPcYyJz1AtfUzVYYuzHsvH0B23FagCeQ==[/tex]修改为6.[tex=16.071x1.357]JZCl3NHFZMZAuoWneybr4lEC3va4uc+928xoa+d39zXyhjGf2zph0g2QEMnHhLHIDQsh+wU5zer2A/3zrbidYD3zwCmYcJnfuS6fgxLBtVY1yOz65xg+FvejD7zhqQMr9764yI3o1wKSAPJRJYM7eQ==[/tex],令[tex=17.5x1.357]EO6mmw41tR07gcIVJ67A/wgSHsLX9XB/MgdeLUtkUmTIRzlopfl8vx2XDPuEO0e+3GJ3u79LdnSSSMfuPRQ3/4dxBPBWjA9IQ0+aPYaFLgYZ5aP/MZ6yIKafYT9rSCf0ps3f/2Lzoanz+nwNZCpQ3A==[/tex](7)[tex=5.214x1.357]Km5I8TPwvnxGxw+5ESGkiHWDe663tjYj7Row66AtiHY=[/tex]修改为[tex=10.143x1.357]EO6mmw41tR07gcIVJ67A/z6ggkTnrNhQ1plQl1XK+KOjnVOWsuvVddYXUyzFrV1zn0bthCcSNBSoG616oChlnQ==[/tex]修改为8.[tex=16.429x1.357]JZCl3NHFZMZAuoWneybr4ir6ff4kF0z7Fp+zYoPfmyJq/GyvkPRz/oGYlyeUHUOcV9WNqTiZ05dydv03h6FAICmsWc4JREUoUDLT8ZXqqdfF8as+a0zarNLDZpZTHybBb829XNyH9cZdWamHZW4v1A==[/tex],令[tex=22.857x1.357]xELFLpiQd04p+v7wyGzFab8lW3KhDLhnLGgya6o+OZcFnES5uj/9Wf+5ej5gmtX/X6N7qV8sFlhFwx/4Tsd540kTmcPRercwToxzxJLFXXVGHK9qXZXqnNirkO3qsYDASSOkJXqICMxn5v8/v5n0kV5NB5opIHOCKYXIXOQ/5tWVlOqxpvY41bQV/X6/P+Wn2CMxoKj2k3TWMCtDWujiBQ==[/tex](8)[tex=5.214x1.357]r/5tXPUjwU990mMLqhHurY6dhTfcmHHAbqB2lIH0NXk=[/tex]修改为15,[tex=2.714x1.357]QzaU6GeR+FIiC85sjLOEUA0a95+rdkqYe0YAoQzMkNw=[/tex]修改为7.[tex=20.714x1.357]JZCl3NHFZMZAuoWneybr4ir6ff4kF0z7Fp+zYoPfmyInTG9qAUEmvGVoT7rRci5Aab0N7ik32RtS4SYKTkI9V6L3N2dtJdIeh61ldqM03QxjzGv5eM9P8SW29Cp7kor6LTK/u9FaBV75y7+x8XXkNdVFcNHk8L9XcTEsxAgTcfk//f9lVkNjPd9qlthwRvhH[/tex]令[tex=30.929x1.357]Y25oLZtFHdcx/xN/UaMXGnnzg1gKyiUIEuitt+f+IIVB+TwGR0/d+7ArwtYfHNEB6WKxh4Bp0W8Kt0NZdpf4PXGSZhOmAmAs7INg7ew6KZp3C2m5tZkpN0t25cis9VL/x1grrUpemZZulBuVyY3HdmvKn8hz3UrHjr/AciaoRqnR94dZdVThGgRqzezUSHWGzRn7tmA6A31IeZUNcQt16wBOVcIgHQPSH2TAjvks+M8=[/tex](9)[tex=1.643x1.0]TWyQPkzJnA8APHltg9WJBQ==[/tex]:对已经标号[tex=5.5x1.357]6z8GLK6Fkr3lILuln8Fl7zAI+JB1C0MAnKNua+u9DXfdPYHdcR72vL5sWN7enL5S[/tex],但[tex=0.857x1.0]cwfJhBQlVC/G439SwWDVnQ==[/tex]已标号;对已经标号[tex=1.214x1.0]of3x41mCocj7RV3EVtcc4A==[/tex],有[tex=4.929x1.357]iGtyXoWyHpTMA9UPe/AstzAefOMdLlp+Ewi2ZOLASGTfxYW5aM5pemaXUq52mdZ+[/tex],则[tex=2.714x1.357]1jbQ12902WUf5ffp8KbwBJdMBAG6Q0nyNjCdxYV6wI4=[/tex]修改为[tex=16.214x1.357]rPeTWHM+Hgss3dBCAuS+FJPjbKZr52HNsI9wad3O0Fv6spZbfuH0YqTDn5tkf/fjIyIXGFpzjQinoMMHYD0u3QJui3TVthmQINNoM39xztA=[/tex],所以[tex=20.786x1.357]tAOmn9zpTTMQXsL2JyYb6DX0pNN4hC0FBEWFVYxexTX8Qb+dXbpRHNYG0CBpW7BsRt10m7ApRigcys1W43+U6fVsLR8j4e6xf8q+UvDk1pzDw8i1ajXsOuX+ClafC4m3ACfeVatQTUVqEiPlNcimxddflmjN7DyH3oG00OZUI8Q=[/tex][tex=22.643x14.357]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[/tex]
举一反三
- 在下图中,用Dijkstra方法求从[tex=0.857x1.0]KHZFMIr1Sj6hp/J1gGyQtA==[/tex]到各点的最短路。[img=387x175]17940f1e914f764.png[/img]
- 求下图中从[tex=0.857x1.0]PiGrv8EQTcGrBqYP+1Jgrg==[/tex]到各点的最短路。[img=373x192]17940d9eeafb72e.png[/img]
- 有向图D如图10-51所示:[img=204x185]1789bfc69c3e922.png[/img](1)求D的邻接矩阵A。(2)D中[tex=0.857x1.0]KHZFMIr1Sj6hp/J1gGyQtA==[/tex]到[tex=0.857x1.0]zb8WifRi/MJi7e38L3ZkVQ==[/tex]长度为4的路有多少?(3)D中[tex=0.857x1.0]KHZFMIr1Sj6hp/J1gGyQtA==[/tex]到自身长度为3的回路有多少?(4)D中长度为4的路数为多少?其中有几条回路?(5)D中长度小于等于4的路有多少?其中有多少条回路?(6)D是哪类连通图?
- 用[tex=3.929x1.214]LwEtGvTGj1URnOeaanEEJQ==[/tex]算法求下图中[tex=0.857x1.0]PiGrv8EQTcGrBqYP+1Jgrg==[/tex]到[tex=1.214x1.0]of3x41mCocj7RV3EVtcc4A==[/tex]的最短路径及其长度。[img=609x292]1777ab26168ff78.png[/img]
- 使用Dijkstra算法求下图中从顶点1到其他各顶点的最短路径,依次得到的各最短路径的目标顶点是( )。[img=486x241]1803a36958ef0bd.png[/img] A: 5, 2, 3, 4, 6 B: 5, 2, 3, 6, 4 C: 5, 2, 4, 3, 6 D: 5, 2, 6, 3, 4
内容
- 0
使用Dijkstra算法求下图中从顶点1到其他各顶点的最短路径,依次得到的各最短路径的目标顶点是( )。[img=347x139]17da66214259e51.png[/img] A: 5, 2, 4, 3, 6 B: 5, 2, 3, 6, 4 C: 5, 2, 6, 3, 4 D: 5, 2, 3, 4, 6
- 1
使用Dijkstra算法求下图中从顶点1到其他各顶点的最短路径,依次得到的各最短路径的目标顶点是( )。[img=347x139]17869f9902e54b4.png[/img] A: 5, 2, 6, 3, 4 B: 5, 2, 4, 3, 6 C: 5, 2, 3, 6, 4 D: 5, 2, 3, 4, 6
- 2
针对下图利用Dijkstra算法求从顶点1到其他点的最短路径,下面最短路径不正确的有( )。[img=282x148]18034f8a426af08.png[/img] A: 1,5,2 B: 1,5,6,3 C: 1,2,4 D: 1,5,6
- 3
针对下图利用Dijkstra算法求从顶点1到其他点的最短路径,下面最短路径不正确的有( )。[img=282x148]18034f899a775a5.png[/img] A: 1,2,4 B: 1,5,2 C: 1,5,6,3 D: 1,5,6
- 4
使用迪杰斯特拉(Dijkstra)算法求下图中从顶点1到其它各顶点的最短路径,依次得到的各最短路径的目标顶点是()。[img=312x162]178694686633dcb.png[/img] A: 5, 2, 3, 6, 4 B: 5, 2, 4, 3, 6 C: 5, 2, 3, 4, 6 D: 5, 2, 6, 3, 4