Slide 6
Slide 6 text
/25
6
アルゴリズムの設計指針
最適な分割を仮定 n = i1 + i2 + · · · + ik
AAACBHicbVDLSgMxFM3UV62vUZfdBIsgCGWmCroRim5cVrAPaIeSSTNtaCYzJHeEMnThxl9x40IRt36EO//GdDoLbT2Qy8m595Dc48eCa3Ccb6uwsrq2vlHcLG1t7+zu2fsHLR0lirImjUSkOj7RTHDJmsBBsE6sGAl9wdr++GbWbz8wpXkk72ESMy8kQ8kDTgkYqW+XJb7CvO/iU1NrpvYGEejsNu7bFafqZMDLxM1JBeVo9O0v46ZJyCRQQbTuuk4MXkoUcCrYtNRLNIsJHZMh6xoqSci0l2ZLTPGxUQY4iJQ5EnCm/nakJNR6EvpmMiQw0ou9mfhfr5tAcOmlXMYJMEnnDwWJwBDhWSJ4wBWjICaGEKq4+SumI6IIBZNbyYTgLq68TFq1qntWrd2dV+rXeRxFVEZH6AS56ALV0S1qoCai6BE9o1f0Zj1ZL9a79TEfLVi55xD9gfX5AwFRlSU=
分割された棒の長さ
rn = pi1
+ pi2
+ · · · + pik
AAACEnicbZDLSgMxFIbPeK31VnXpJlgERSgzVdCNUHTjsoK9QDsMmTTThmYyQ5IRytBncOOruHGhiFtX7nwbM+0I2vpD4OM/5yQ5vx9zprRtf1kLi0vLK6uFteL6xubWdmlnt6miRBLaIBGPZNvHinImaEMzzWk7lhSHPqctf3id1Vv3VCoWiTs9iqkb4r5gASNYG8srHUtPoEsUeynznDE6mVI1o24v0urHGY69Utmu2BOheXByKEOuulf6NDeQJKRCE46V6jh2rN0US80Ip+NiN1E0xmSI+7RjUOCQKjedrDRGh8bpoSCS5giNJu7viRSHSo1C33SGWA/UbC0z/6t1Eh1cuCkTcaKpINOHgoQjHaEsH9RjkhLNRwYwkcz8FZEBlphok2LRhODMrjwPzWrFOa1Ub8/Ktas8jgLswwEcgQPnUIMbqEMDCDzAE7zAq/VoPVtv1vu0dcHKZ/bgj6yPbwt3m9c=
最適な収益
個に分割
k
AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOl5rhfrrhVdw6ySrycVCBHo1/+6g1ilkYoDRNU667nJsbPqDKcCZyWeqnGhLIxHWLXUkkj1H42P3RKzqwyIGGsbElD5urviYxGWk+iwHZG1Iz0sjcT//O6qQmv/YzLJDUo2WJRmApiYjL7mgy4QmbExBLKFLe3EjaiijJjsynZELzll1dJu1b1Lqq15mWlfpPHUYQTOIVz8OAK6nAHDWgBA4RneIU359F5cd6dj0VrwclnjuEPnM8f09OM8w==
rn = max (pn, r1 + rn 1, r2 + rn 2, . . . , rn 1 + r1)
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
部分構造最適性に着目
長さが と の2つの金属棒に切断,
それぞれの金属棒を最適に
分割することで得られる総収入
n i
AAAB6nicbVBNS8NAEJ34WetX1aOXxSJ4sSRV0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvSKQw6Lrfzsrq2vrGZmGruL2zu7dfOjhsmjjVjDdYLGPdDqjhUijeQIGStxPNaRRI3gpGt1O/9cS1EbF6xHHC/YgOlAgFo2ilB3UueqWyW3FnIMvEy0kZctR7pa9uP2ZpxBUySY3peG6CfkY1Cib5pNhNDU8oG9EB71iqaMSNn81OnZBTq/RJGGtbCslM/T2R0ciYcRTYzoji0Cx6U/E/r5NieO1nQiUpcsXmi8JUEozJ9G/SF5ozlGNLKNPC3krYkGrK0KZTtCF4iy8vk2a14l1UqveX5dpNHkcBjuEEzsCDK6jBHdShAQwG8Ayv8OZI58V5dz7mrStOPnMEf+B8/gAGqI2g
i
AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJu+XK27VnYOsEi8nFcjR6Je/eoOYpRFKwwTVuuu5ifEzqgxnAqelXqoxoWxMh9i1VNIItZ/ND52SM6sMSBgrW9KQufp7IqOR1pMosJ0RNSO97M3E/7xuasJrP+MySQ1KtlgUpoKYmMy+JgOukBkxsYQyxe2thI2ooszYbEo2BG/55VXSrlW9i2qteVmp3+RxFOEETuEcPLiCOtxBA1rAAOEZXuHNeXRenHfnY9FacPKZY/gD5/MH0MuM8Q==
切断なし
上式をもっと簡略化 rn = max
1in
(pi + rn i)
AAACHnicbVDLSgMxFM3UV62vqks3wSJUxDJTFd0IRTcuK9gHdMqQSTNtaCYzJnfEMvRL3PgrblwoIrjSvzF9LLR6INzDOfdyc48fC67Btr+szNz8wuJSdjm3srq2vpHf3KrrKFGU1WgkItX0iWaCS1YDDoI1Y8VI6AvW8PuXI79xx5TmkbyBQczaIelKHnBKwEhe/kR5Ep9jNyT3Xuq4gt1ijsdFDk0JoBh7HB9g5aXykA9dxbs92PfyBbtkj4H/EmdKCmiKqpf/cDsRTUImgQqidcuxY2inRAGngg1zbqJZTGifdFnLUElCptvp+Lwh3jNKBweRMk8CHqs/J1ISaj0IfdMZEujpWW8k/ue1EgjO2imXcQJM0smiIBEYIjzKCne4YhTEwBBCFTd/xbRHFKFgEs2ZEJzZk/+SernkHJXK18eFysU0jizaQbuoiBx0iiroClVRDVH0gJ7QC3q1Hq1n6816n7RmrOnMNvoF6/MbSKqhXA==
分割を左端から切り出された長さ の金属棒と
右側に残る長さ の部分とみなす
i
AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJu+XK27VnYOsEi8nFcjR6Je/eoOYpRFKwwTVuuu5ifEzqgxnAqelXqoxoWxMh9i1VNIItZ/ND52SM6sMSBgrW9KQufp7IqOR1pMosJ0RNSO97M3E/7xuasJrP+MySQ1KtlgUpoKYmMy+JgOukBkxsYQyxe2thI2ooszYbEo2BG/55VXSrlW9i2qteVmp3+RxFOEETuEcPLiCOtxBA1rAAOEZXuHNeXRenHfnY9FacPKZY/gD5/MH0MuM8Q==
n i
AAAB6nicbVBNS8NAEJ34WetX1aOXxSJ4sSRV0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvSKQw6Lrfzsrq2vrGZmGruL2zu7dfOjhsmjjVjDdYLGPdDqjhUijeQIGStxPNaRRI3gpGt1O/9cS1EbF6xHHC/YgOlAgFo2ilB3UueqWyW3FnIMvEy0kZctR7pa9uP2ZpxBUySY3peG6CfkY1Cib5pNhNDU8oG9EB71iqaMSNn81OnZBTq/RJGGtbCslM/T2R0ciYcRTYzoji0Cx6U/E/r5NieO1nQiUpcsXmi8JUEozJ9G/SF5ozlGNLKNPC3krYkGrK0KZTtCF4iy8vk2a14l1UqveX5dpNHkcBjuEEzsCDK6jBHdShAQwG8Ayv8OZI58V5dz7mrStOPnMEf+B8/gAGqI2g