{"published":"2026-04-10 14:12:01","version":"1.0","url":"https://info.atcoder.jp/entry/algorithm_lectures/min_plus_convolution","image_url":"https://cdn.user.blog.st-hatena.com/default_entry_og_image/158934417/1702097020779738","provider_name":"Hatena Blog","categories":["\u51f8\u6027","min-plus \u7573\u307f\u8fbc\u307f","\u7573\u307f\u8fbc\u307f"],"author_name":"atcoder","blog_title":"AtCoderInfo","title":"\u51f8\u6570\u5217\u306e min-plus \u7573\u307f\u8fbc\u307f","author_url":"https://blog.hatena.ne.jp/atcoder/","description":"\u89e3\u8aac\u52d5\u753b\u306f\u3053\u3061\u3089\u3067\u3059\uff0e 1. \u6982\u8981 $2$ \u3064\u306e\u6574\u6570\u5217\uff08\u307e\u305f\u306f\u5b9f\u6570\u5217\uff09$A = (A _ 0, A _ 1, \\ldots, A _ {N})$, $B = (B _ 0, B _ 1, \\ldots, B _ {M})$ \u306b\u5bfe\u3057\u3066\uff0c $C _ k = \\min _ {i + j = k}(A _ i + B _ j)$ \u306b\u3088\u308a\u5b9a\u7fa9\u3055\u308c\u308b\u5217 $C = (C _ 0, \\ldots, C _ {N+M})$ \u3092 $A, B$ \u306e min-plus \u7573\u307f\u8fbc\u307f\u3068\u3044\u3044\u307e\u3059\uff0e $A, B$ \u306e\u3046\u3061\u5c11\u306a\u304f\u3068\u3082\u4e00\u65b9\u306b\u51f8\u6027\u304c\u3042\u308b\u5834\u5408\u306b\u306f min-plus \u7573\u307f\u8fbc\u307f\u3092\u9ad8\u901f\u306b\u884c\u3048\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e \u672c\u8a18\u4e8b\u3067\u2026","provider_url":"https://hatena.blog","type":"rich","blog_url":"https://info.atcoder.jp/","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Finfo.atcoder.jp%2Fentry%2Falgorithm_lectures%2Fmin_plus_convolution\" title=\"\u51f8\u6570\u5217\u306e min-plus \u7573\u307f\u8fbc\u307f - AtCoderInfo\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","width":"100%","height":"190"}