| 12 ᠰᠠᠷᠠ ᠶᠢᠨ 13 ᠤ ᠡᠳᠦᠷ᠂ ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠨᠠᠮ ᠤᠨ ᠬᠤᠷᠢᠶᠠᠨ ᠤ ᠳᠡᠳ᠋ ᠱᠦᠵᠢ᠂ ᠬᠤᠰᠢᠭᠤᠨ ᠳᠠᠷᠤᠭᠠ ᠴᠠᠩ ᠴᠢᠩ ᠰᠢᠨᠡ ᠪᠠᠷᠭᠤ ᠪᠠᠷᠠᠭᠤᠨ | ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠨᠤᠲᠤᠭ ᠪᠡᠯᠴᠢᠭᠡᠷ ᠤᠨ ᠳᠠᠭᠠᠭᠠᠴᠠ ᠠᠴᠠ ᠬᠡᠲᠦᠷᠡᠲᠡᠯᠡ ᠮᠠᠯᠵᠢᠬᠤ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠢ ᠰᠢᠰᠲ᠋ᠧᠮ ᠲᠠᠢ ᠰᠢᠢᠳᠪᠦᠷᠢᠯᠡᠵᠦ᠂ ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠮᠠᠯ ᠠᠵᠤ | ᠠᠬᠤᠢ ᠶᠢᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢ ᠬᠤᠪᠢᠷᠠᠭᠤᠯᠤᠨ ᠲᠠᠰ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠶᠢ ᠠᠬᠢᠭᠤᠯᠬᠤ ᠵᠢᠯᠤᠭᠤᠳᠬᠤ ᠭᠠᠵᠠᠷ ᠤᠨ ᠠᠵᠢᠯ ᠤᠨ ᠲᠣᠬᠢᠷᠠᠭᠤᠯᠤᠯᠲᠠ ᠶᠢᠨ ᠬᠤᠷᠠᠯ ᠢ ᠡᠷᠭᠢᠯᠡᠨ | ᠬᠤᠷᠠᠯᠳᠤᠭᠤᠯᠪᠠ᠃ ᠳᠡᠭᠡᠳᠦ ᠱᠠᠲᠤᠨ ᠤ ᠬᠠᠮᠢᠶᠠ ᠪᠦᠬᠦᠢ ᠬᠤᠷᠠᠯ ᠤᠨ ᠵᠣᠷᠢᠭ ᠰᠠᠨᠠᠭᠠ ᠶᠢ ᠭᠦᠨᠵᠡᠭᠡᠢ ᠲᠤᠤᠱᠯᠠᠭᠤᠯᠤᠨ ᠨᠠᠶᠢᠳᠠᠪᠤᠷᠢᠵᠢᠭᠤᠯᠵᠤ᠂ ᠮᠠᠨ ᠤ | ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠮᠠᠯ ᠠᠵᠤ ᠠᠬᠤᠢ ᠶᠢᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢ ᠬᠤᠪᠢᠷᠠᠭᠤᠯᠤᠨ ᠲᠠᠰ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠠᠵᠢᠯ ᠢ ᠠᠬᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠠᠶᠢᠳᠠᠯ ᠤᠨ ᠬᠠᠷᠢᠭᠤ | ᠮᠡᠳᠡᠭᠦᠯᠦᠯᠲᠡ ᠶᠢ ᠰᠣᠨᠣᠰᠴᠤ᠂ ᠠᠵᠢᠯ ᠢ ᠠᠬᠢᠭᠤᠯᠬᠤ ᠶᠠᠪᠤᠴᠠ ᠳᠤ ᠣᠷᠣᠰᠢᠵᠤ ᠪᠠᠶᠢᠭᠠ ᠬᠦᠴᠢᠷᠳᠡᠯ ᠪᠠ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠢ ᠵᠠᠳᠠᠯᠤᠨ ᠰᠢᠢᠳᠪᠦᠷᠢᠯᠡᠵᠦ᠂ | ᠣᠳᠣᠬᠠᠨ ᠤ ᠪᠠ ᠬᠤᠶᠢᠰᠢᠳᠠ ᠶᠢᠨ ᠬᠡᠰᠡᠭ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠤ ᠭᠤᠣᠯᠳᠠᠯᠭᠠ ᠲᠠᠢ ᠠᠵᠢᠯ ᠢ ᠲᠣᠬᠢᠷᠠᠭᠤᠯᠤᠨ ᠪᠠᠶᠢᠷᠢᠯᠠᠭᠤᠯᠪᠠ᠃ | ᠬᠤᠷᠠᠯ ᠳᠡᠭᠡᠷᠡ᠂ ᠡᠯᠡ ᠰᠤᠮᠤ ᠪᠠᠯᠭᠠᠰᠤ ᠶᠢᠨ ᠬᠢᠨ ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠮᠠᠯ ᠠᠵᠤ ᠠᠬᠤᠢ ᠶᠢᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢ ᠬᠤᠪᠢᠷᠠᠭᠤᠯᠤᠨ ᠲᠡᠰ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠠᠵᠢᠯ ᠢ | ᠠᠬᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠠᠶᠢᠳᠠᠯ ᠤᠨ ᠲᠤᠬᠠᠢ ᠬᠠᠷᠢᠭᠤ ᠮᠡᠳᠡᠭᠦᠯᠦᠯᠲᠡ ᠬᠢᠪᠡ︔ ᠡᠯᠡ ᠳᠠᠭᠠᠭᠠᠴᠢᠯᠠᠨ ᠬᠤᠯᠪᠣᠭᠠᠯᠠᠬᠤ ᠵᠢᠯᠤᠭᠤᠳᠬᠤ ᠳᠤᠭᠤᠶᠢᠯᠠᠩ ᠤᠨ ᠳᠠᠷᠤᠭᠠ ᠲᠣᠰ | ᠲᠣᠰ ᠠᠵᠢᠯ ᠤᠨ ᠱᠠᠭᠠᠷᠳᠠᠯᠭᠠ ᠳᠤᠷᠠᠳᠪᠠ᠃ | ᠲᠠᠷᠠᠭᠠᠴᠢ ᠶᠢᠨ ᠠᠯᠬᠤᠮ ᠤᠨ ᠠᠵᠢᠯ ᠢ ᠰᠠᠶᠢᠲᠤᠷ ᠬᠢᠬᠦ ᠲᠤᠬᠠᠢ ᠴᠠᠩ ᠴᠢᠩ᠂ ᠪᠥᠬᠦ ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠳᠡᠭᠡᠳᠦ ᠳᠣᠣᠷᠠᠳᠤ ᠱᠠᠲᠤ ᠪᠠᠷ ᠢᠶᠠᠨ ᠦᠵᠡᠯ | ᠰᠠᠨᠠᠭᠠ ᠲᠠᠨᠢᠯᠲᠠ ᠪᠠᠨ ᠳᠡᠭᠡᠭᠰᠢᠯᠡᠭᠦᠯᠵᠦ᠂ ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠮᠠᠯ ᠠᠵᠤ ᠠᠬᠤᠢ ᠶᠢᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢ ᠬᠤᠪᠢᠷᠠᠭᠤᠯᠤᠨ ᠲᠠᠰ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠠᠵᠢᠯ ᠢ ᠰᠠᠶᠢᠲᠤᠷ ᠬᠢᠬᠦ | ᠳᠡᠭᠡᠳᠦ ᠬᠡᠮᠵᠢᠶᠡᠨ ᠤ ᠤᠬᠠᠮᠰᠠᠷ ᠢᠶᠠᠨ ᠦᠨᠡᠨᠬᠦ ᠴᠢᠩᠭᠠᠳᠬᠠᠵᠤ᠂ ᠬᠠᠳᠠᠭᠠᠰᠤ ᠬᠠᠳᠠᠬᠤ ᠵᠣᠷᠢᠭ ᠰᠠᠨᠠᠭᠠ ᠪᠠᠷ ᠬᠤᠲᠠ ᠶᠢᠨ ᠨᠠᠮ ᠤᠨ ᠬᠤᠷᠢᠶᠠ᠂ ᠵᠠᠰᠠᠭ ᠤᠨ | ᠣᠷᠳᠣᠨ ᠵᠢᠴᠢ ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠨᠠᠮ ᠤᠨ ᠬᠤᠷᠢᠶᠠ᠂ ᠵᠠᠰᠠᠭ ᠤᠨ ᠣᠷᠳᠣᠨ ᠤ ᠰᠢᠢᠳᠪᠦᠷᠢᠲᠦ ᠪᠣᠳᠣᠯᠭᠠ ᠶᠢᠨ ᠪᠠᠶᠢᠷᠢᠯᠠᠭᠤᠯᠤᠯᠲᠠ ᠶᠢ ᠦᠨᠡᠨᠬᠦ ᠨᠠᠷᠢᠯᠢᠭ | ᠨᠠᠶᠢᠳᠠᠪᠤᠷᠢᠵᠢᠭᠤᠯᠬᠤ ᠬᠡᠷᠡᠭᠲᠡᠢ᠃ ᠳᠡᠭᠡᠳᠦ ᠱᠠᠲᠤᠨ ᠤ ᠲᠥᠷᠥ ᠶᠢᠨ ᠪᠣᠳᠣᠯᠭᠠ ᠶᠢ ᠰᠠᠶᠢᠲᠤᠷ ᠬᠡᠷᠡᠭᠯᠡᠵᠦ᠂ ︽ᠨᠠᠮ ᠤᠨ ᠬᠤᠷᠢᠳᠤᠭᠠᠷ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠤ ᠲᠥᠪ | ᠬᠤᠷᠢᠶᠠᠨ ᠤ ᠭᠤᠷᠪᠠᠳᠤᠭᠠᠷ ᠪᠥᠬᠦᠳᠡ ᠬᠤᠷᠠᠯ ᠤᠨ ᠵᠣᠷᠢᠭ ᠰᠠᠨᠠᠭᠠ ᠶᠢ ᠭᠦᠨᠵᠡᠭᠡᠢ ᠲᠤᠤᠱᠯᠠᠭᠤᠯᠤᠨ ᠨᠠᠶᠢᠳᠠᠪᠤᠷᠢᠵᠢᠭᠤᠯᠬᠤ ᠲᠤᠬᠠᠢ ᠥᠪᠥᠷ ᠮᠣᠩᠭᠤᠯ ᠤᠨ | ᠥᠪᠡᠷᠲᠡᠭᠡᠨ ᠵᠠᠰᠠᠬᠤ ᠣᠷᠣᠨ ᠤ ᠨᠠᠮ ᠤᠨ ᠬᠤᠷᠢᠶᠠ ᠶᠢᠨ ᠰᠠᠨᠠᠯ︾ ᠵᠢᠴᠢ ᠬᠥᠯᠥᠨ ᠪᠤᠶᠢᠷ ᠬᠤᠲᠠ ᠶᠢᠨ ︽1+N+M︾ ᠨᠢᠭᠡ ᠴᠣᠭᠴᠠᠵᠢᠭᠤᠯᠤᠭᠰᠠᠨ | ᠠᠵᠢᠯᠯᠠᠭᠠᠨ ᠤ ᠰᠢᠰᠲ᠋ᠧᠮ ᠵᠡᠷᠭᠡ ᠬᠠᠮᠢᠶᠠ ᠪᠦᠬᠦᠢ ᠲᠥᠷᠥ ᠶᠢᠨ ᠪᠣᠳᠣᠯᠭᠠ ᠶᠢ ᠮᠠᠨ ᠤ ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠬᠢᠬᠦ ᠠᠵᠢᠯ ᠢ ᠰᠠᠶᠢᠲᠤᠷ ᠠᠳᠬᠤᠬᠤ ᠶᠢᠨ | ︽ᠠᠯᠲᠠᠨ ᠲᠦᠯᠬᠢᠭᠦᠷ︾ ᠪᠣᠯᠭᠠᠵᠤ᠂ ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠮᠠᠯ ᠠᠵᠤ ᠠᠬᠤᠢ ᠶᠢᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢ ᠬᠤᠪᠢᠷᠠᠭᠤᠯᠤᠨ ᠲᠠᠰ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠠᠵᠢᠯ ᠤᠨ ᠪᠣᠳᠠᠲᠤ ᠦᠷᠡ | ᠪᠦᠲᠦᠮᠵᠢ ᠣᠯᠬᠤ ᠶᠢ ᠠᠬᠢᠭᠤᠯᠬᠤ ᠬᠡᠷᠡᠭᠲᠡᠢ᠃ ᠤᠶᠤᠨ ᠤ ᠤᠭᠤᠲᠠ ᠶᠢᠨ ᠦᠢᠯᠡᠳᠦᠯ ᠢ ᠰᠠᠶᠢᠲᠤᠷ ᠪᠠᠳᠠᠷᠠᠭᠤᠯᠤᠨ᠂ ᠮᠠᠯᠴᠢᠳ ᠢᠶᠠᠷ ᠭᠤᠣᠯ ᠴᠣᠭᠴᠠ ᠪᠣᠯᠭᠠᠬᠤ ᠶᠢ | ᠪᠠᠷᠢᠮᠲᠠᠯᠠᠵᠤ᠂ ᠮᠠᠯᠴᠢᠳ ᠤᠨ ᠬᠦᠰᠡᠯ ᠰᠠᠨᠠᠭᠠ ᠶᠢ ᠭᠦᠢᠴᠡᠳ ᠬᠦᠨᠳᠦᠳᠬᠡᠨ᠂ ᠭᠠᠵᠠᠷ ᠣᠷᠣᠨ ᠤ ᠪᠠᠶᠢᠳᠠᠯ ᠳᠤ ᠲᠣᠬᠢᠷᠠᠭᠤᠯᠤᠨ᠂ ᠬᠠᠨᠳᠤᠰᠢ ᠳᠤ ᠲᠣᠬᠢᠷᠠᠭᠤᠯᠤᠨ | ᠴᠢᠳᠠᠮᠠᠭᠠᠢ ᠪᠠᠷ ᠵᠢᠯᠤᠭᠤᠳᠴᠤ᠂ ᠲᠦᠷᠦᠯ ᠬᠤᠪᠢᠶᠠᠨ ᠬᠡᠷᠡᠭᠵᠢᠭᠦᠯᠵᠦ᠂ ᠤᠯᠠᠮᠵᠢᠯᠠᠯᠲᠤ ᠮᠠᠯ ᠠᠵᠤ ᠠᠬᠤᠢ ᠶᠢᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢ ᠬᠤᠪᠢᠷᠠᠭᠤᠯᠤᠨ ᠲᠡᠰ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ | ᠠᠵᠢᠯ ᠤᠨ ᠡᠷᠡᠭᠦᠯ ᠪᠥᠭᠡᠳ ᠡᠮᠬᠢ ᠳᠢᠭᠯᠢᠮ ᠲᠠᠢ ᠶᠠᠪᠤᠭᠳᠠᠬᠤ ᠶᠢ ᠠᠬᠢᠭᠤᠯᠬᠤ ᠬᠡᠷᠡᠭᠲᠡᠢ ᠭᠡᠵᠦ ᠴᠢᠬᠤᠯᠠᠴᠢᠯᠠᠪᠠ᠃ | ᠴᠠᠩ ᠴᠢᠩ᠂ ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠰᠢᠭᠤᠳ ᠬᠠᠷᠢᠶᠠ ᠬᠠᠮᠢᠶᠠ ᠪᠦᠬᠦᠢ ᠰᠠᠯᠠᠭᠠ ᠮᠥᠴᠢᠷ ᠤᠳ ᠠᠵᠢᠯ ᠤᠨ ᠬᠠᠷᠢᠭᠤᠴᠠᠯᠭᠠ ᠶᠢ ᠪᠣᠳᠠᠲᠠᠶᠢᠵᠢᠭᠤᠯᠤᠨ᠂ | ᠵᠣᠬᠢᠴᠠᠭᠤᠯᠤᠨ ᠬᠠᠮᠵᠢᠯᠴᠠᠬᠤ ᠶᠢ ᠦᠨᠡᠨᠬᠦ ᠴᠢᠩᠭᠠᠳᠬᠠᠬᠤ ᠬᠡᠷᠡᠭᠲᠡᠢ︔ ᠵᠢᠯᠤᠭᠤᠳᠬᠤ ᠭᠠᠵᠠᠷ ᠤᠨ ᠠᠵᠢᠯᠯᠠᠬᠤ ᠳᠤᠭᠤᠶᠢᠯᠠᠩ ᠤᠳ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠶᠢᠨ | ᠠᠬᠢᠴᠠ ᠶᠢ ᠴᠠᠭ ᠲᠤᠬᠠᠢ ᠳᠤᠨᠢ ᠮᠥᠷᠳᠡᠨ ᠡᠵᠡᠮᠳᠡᠬᠦ ᠬᠡᠷᠡᠭᠲᠡᠢ︔ ᠡᠯᠡ ᠰᠤᠮᠤ ᠪᠠᠯᠭᠠᠰᠤ᠂ ᠭᠠᠴᠠᠭᠠ ︽ᠭᠤᠷᠪᠠ ᠶᠢ ᠬᠤᠪᠢᠷᠠᠭᠤᠯᠬᠤ︾ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠪᠠ ︽ | ᠭᠤᠷᠪᠠ ᠶᠢ ᠨᠢᠭᠡ ᠴᠣᠭᠴᠠᠵᠢᠭᠤᠯᠬᠤ︾ ᠶᠡᠷᠦᠩᠬᠡᠶᠢᠯᠡᠭᠰᠡᠨ ᠬᠠᠮᠲᠤᠷᠠᠯᠴᠠᠭᠠ ᠶᠢᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠭᠤᠣᠯᠳᠠᠯᠭᠠ᠂ ᠲᠥᠷᠥ ᠶᠢᠨ ᠪᠣᠳᠣᠯᠭᠠ ᠶᠢᠨ ᠱᠠᠭᠠᠷᠳᠠᠯᠭᠠ ᠪᠠ | ᠠᠵᠢᠯᠯᠠᠭᠠᠨ ᠤ ᠴᠤᠪᠤᠷᠠᠯ ᠢ ᠪᠥᠬᠦ ᠲᠠᠯᠠ ᠪᠠᠷ ᠣᠶᠢᠯᠠᠭᠠᠨ ᠡᠵᠡᠮᠰᠢᠵᠦ᠂ ᠦᠨᠡᠨᠬᠦ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠬᠢᠬᠦ ᠠᠵᠢᠯ ᠤᠨ ᠬᠠᠰᠢᠷ ᠮᠡᠷᠭᠡᠵᠢᠯᠲᠡᠨ ᠪᠣᠯᠬᠤ ᠬᠡᠷᠡᠭᠲᠡᠢ᠃ | ᠪᠥᠬᠦ ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠳᠡᠭᠡᠳᠦ ᠳᠣᠣᠷᠠᠳᠤ ᠱᠠᠲᠤ ᠪᠠᠷ ᠢᠶᠠᠨ ᠬᠠᠷᠠᠯᠲᠠ ᠳᠠᠭᠠᠨ ᠠᠩᠬᠠᠷᠤᠯ ᠢᠶᠠᠨ ᠲᠥᠪᠯᠡᠷᠡᠭᠦᠯᠵᠦ᠂ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠨ ᠬᠦᠴᠦᠯᠡᠵᠦ᠂ ᠬᠡᠯᠪᠡᠷᠢ ᠶᠢ | ᠬᠤᠪᠢᠷᠠᠭᠤᠯᠤᠨ ᠲᠠᠰ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠪᠠ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠬᠥᠭᠵᠢᠯᠲᠡ ᠶᠢᠨ ᠡᠯᠡ ᠵᠦᠢᠯ ᠤᠨ ᠠᠵᠢᠯ ᠢ ᠪᠥᠬᠦ ᠬᠦᠴᠦᠨ ᠢᠶᠠᠷ ᠢᠶᠠᠨ ᠰᠠᠶᠢᠲᠤᠷ ᠠᠳᠬᠤᠵᠤ᠂ ᠠᠮᠢ | ᠠᠬᠤᠢ ᠶᠢᠨ ᠣᠷᠣᠰᠢᠨ ᠰᠠᠭᠤᠬᠤ ᠳᠤ ᠲᠣᠬᠢᠯᠢᠭ᠂ ᠦᠢᠯᠡᠳᠪᠦᠷᠢᠯᠡᠯ ᠥᠨᠳᠥᠷ ᠪᠦᠲᠦᠮᠵᠢᠲᠡᠶ᠂ ᠠᠮᠢᠳᠤᠷᠠᠯ ᠪᠠᠶᠠᠨ ᠴᠢᠨᠡᠭᠡᠯᠢᠭ ᠮᠠᠯᠵᠢᠬᠤ ᠣᠷᠣᠨ ᠤ | ᠣᠳᠣᠬᠢᠴᠢᠯᠠᠯᠲᠠ ᠶᠢᠨ ᠬᠠᠷᠠᠯᠲᠠ ᠶᠢ ᠲᠦᠷᠭᠡᠨ ᠪᠡᠶᠡᠯᠡᠭᠦᠯᠬᠦ ᠶᠢᠨ ᠲᠥᠯᠥᠭᠡ ᠴᠥᠬᠦᠷᠡᠰᠢ ᠦᠭᠡᠢ ᠴᠢᠷᠮᠠᠶᠢᠬᠤ ᠬᠡᠷᠡᠭᠲᠡᠢ ᠭᠡᠵᠦ ᠱᠠᠭᠠᠷᠳᠠᠪᠠ᠃ |