\uc548\ub155\ud558\uc138\uc694, \uc5ec\ub7ec\ubd84! \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 \uc678\ud310\uc6d0\uc758 \uc21c\ud68c \ubb38\uc81c(TSP, Traveling Salesman Problem)<\/strong>\ub97c \ud574\uacb0\ud558\ub294 \uc54c\uace0\ub9ac\uc998\uc744 \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. TSP\ub294 \uc8fc\uc5b4\uc9c4 \ub3c4\uc2dc\ub97c \ucd5c\uc18c \ube44\uc6a9\uc73c\ub85c \ubaa8\ub450 \uc21c\ud68c\ud55c \ud6c4, \ub2e4\uc2dc \uc2dc\uc791\ud588\ub358 \ub3c4\uc2dc\uc5d0 \ub3cc\uc544\uc624\ub294 \uacbd\ub85c\ub97c \ucc3e\ub294 \ubb38\uc81c\uc785\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \uace0\uc804\uc801\uc778 \uc870\ud569 \ucd5c\uc801\ud654 \ubb38\uc81c \uc911 \ud558\ub098\ub85c, \uc5ec\ub7ec \uac00\uc9c0 \uc811\uadfc \ubc29\ubc95\uc774 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n \uc8fc\uc5b4\uc9c4 N\uac1c\uc758 \ub3c4\uc2dc\uac00 \uc788\uace0, \uac01 \ub3c4\uc2dc \uac04\uc758 \uc774\ub3d9 \ube44\uc6a9\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ubaa8\ub4e0 \ub3c4\uc2dc\ub97c \ud55c \ubc88\uc529 \ubc29\ubb38\ud558\uace0 \uc2dc\uc791\ud55c \ub3c4\uc2dc\ub85c \ub3cc\uc544\uc624\ub294 \ucd5c\uc18c \ube44\uc6a9 \uacbd\ub85c\ub97c \uad6c\ud558\ub294 \uac83\uc774 \ubaa9\ud45c\uc785\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 \ub2e4\uc74c\uacfc \uac19\uc740 \uc785\ucd9c\ub825 \ud615\uc2dd\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 \ub2e4\uc591\ud55c \uc54c\uace0\ub9ac\uc998\uc774 \uc874\uc7ac\ud558\uc9c0\ub9cc, \uc5ec\uae30\uc11c\ub294 DFS(Depth-First Search)<\/strong>\uc640 \uba54\ubaa8\uc774\uc81c\uc774\uc158(Memoization)<\/strong> \uae30\ubc95\uc744 \uc0ac\uc6a9\ud55c \uc811\uadfc \ubc29\uc2dd\uc744 \uc124\uba85\ud558\uaca0\uc2b5\ub2c8\ub2e4. \ub2e4\uc74c\uc740 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ub2e8\uacc4\uc785\ub2c8\ub2e4.<\/p>\n TSP \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574\uc11c\ub294 \ubaa8\ub4e0 \uac00\ub2a5\ud55c \uacbd\ub85c\ub97c \ucc3e\uc544\uc57c \ud569\ub2c8\ub2e4. \uc644\uc804 \ud0d0\uc0c9\uc744 \ud1b5\ud574 \ubaa8\ub4e0 \uacbd\uc6b0\uc758 \uc218\ub97c \ub530\uc838 \ucd5c\uc18c \ube44\uc6a9\uc744 \uacc4\uc0b0\ud560 \uc218 \uc788\uc9c0\ub9cc, \ub3c4\uc2dc\uc758 \uc218\uac00 \uc99d\uac00\ud560\uc218\ub85d \uacbd\uc6b0\uc758 \uc218\ub294 \uae30\ud558\uae09\uc218\uc801\uc73c\ub85c \uc99d\uac00\ud558\ubbc0\ub85c \ud6a8\uc728\uc801\uc778 \ubc29\ubc95\uc774 \ud544\uc694\ud569\ub2c8\ub2e4.<\/p>\n \ube44\ud2b8 \ub9c8\uc2a4\ud06c\ub97c \uc0ac\uc6a9\ud558\uc5ec \uac01 \ub3c4\uc2dc\uc758 \ubc29\ubb38 \uc5ec\ubd80\ub97c \uae30\ub85d\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, 4\uac1c\uc758 \ub3c4\uc2dc\uac00 \uc788\uc744 \uacbd\uc6b0, \uac01 \ub3c4\uc2dc\ub97c \ube44\ud2b8\ub85c \ud45c\ud604\ud558\uc5ec 0b0000\uc5d0\uc11c 0b1111\uae4c\uc9c0\uc758 \uacbd\uc6b0\ub97c \ub9cc\ub4e4 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \ubc29\ubc95\uc744 \ud1b5\ud574 \uac01 \ub3c4\uc2dc\ub97c \ubc29\ubb38\ud588\ub294\uc9c0 \uc5ec\ubd80\ub97c \uac04\ud3b8\ud558\uac8c \ud655\uc778\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n DFS\ub97c \uc774\uc6a9\ud558\uc5ec \ubaa8\ub4e0 \uacbd\ub85c\ub97c \ud0d0\uc0c9\ud558\uba74\uc11c \ube44\uc6a9\uc744 \uacc4\uc0b0\ud558\ub418, \uc774\ubbf8 \uacc4\uc0b0\ud55c \uacbd\ub85c\ub294 \uc800\uc7a5\ud558\uc5ec \uc911\ubcf5 \uacc4\uc0b0\uc744 \ud53c\ud558\ub294 \uba54\ubaa8\uc774\uc988 \uae30\ubc95\uc744 \ud65c\uc6a9\ud569\ub2c8\ub2e4. \uc544\ub798\ub294 \uc774\ub97c \uad6c\ud604\ud55c \ud30c\uc774\uc36c \ucf54\ub4dc\uc785\ub2c8\ub2e4:<\/p>\n \uc704 \ucf54\ub4dc\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc8fc\uc694 \ud568\uc218\ub85c \uad6c\uc131\ub429\ub2c8\ub2e4:<\/p>\n \uc704 \uc54c\uace0\ub9ac\uc998\uc758 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub294 \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 \uc678\ud310\uc6d0\uc758 \uc21c\ud68c \ubb38\uc81c(TSP)\uc5d0 \ub300\ud55c \uac1c\ub150 \ubc0f \uc54c\uace0\ub9ac\uc998 \uad6c\ud604 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uc558\uc2b5\ub2c8\ub2e4. TSP \ubb38\uc81c\ub294 \ub2e4\uc591\ud55c \ubb38\uc81c \ud574\uacb0 \uae30\ubc95\uc744 \ud65c\uc6a9\ud560 \uc218 \uc788\ub294 \uc88b\uc740 \uc608\uc81c\uc774\uba70, \uae4a\uc740 \uc774\ud574\ub97c \ud1b5\ud574 \ub2e4\ub978 \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\uc5d0\ub3c4 \uc801\uc6a9\ud560 \uc218 \uc788\ub294 \uc0ac\uace0\ub97c \uae30\ub974\ub294\ub370 \ub3c4\uc6c0\uc774 \ub429\ub2c8\ub2e4.<\/p>\n \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c TSP\uc640 \uad00\ub828\ub41c \ubb38\uc81c\ub97c \ub9cc\ub098\uac8c \ub420 \uacbd\uc6b0, \uc704\uc640 \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \uc811\uadfc\ud574 \ubcf4\uc2dc\uba74 \uc88b\uc744 \uac83\uc785\ub2c8\ub2e4. \uc774\uc81c \uc5ec\ub7ec\ubd84\uc774 \uc774 \ubb38\uc81c\ub97c \ub3c5\ub9bd\uc801\uc73c\ub85c \ud574\uacb0\ud560 \uc218 \uc788\ub3c4\ub85d \ub354\uc6b1 \uc5f0\uc2b5\ud558\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4. \uac10\uc0ac\ud569\ub2c8\ub2e4!<\/p>\n <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"1. \ubb38\uc81c \uc124\uba85<\/h2>\n
\uc785\ub825<\/h3>\n
\n
\ucd9c\ub825<\/h3>\n
\n
2. \ubb38\uc81c \ud574\uacb0 \uacfc\uc815<\/h2>\n
Step 1: \ubb38\uc81c \uc774\ud574\ud558\uae30<\/h3>\n
Step 2: \ube44\ud2b8 \ub9c8\uc2a4\ud06c\ub85c \ubc29\ubb38 \ub3c4\uc2dc \uae30\ub85d\ud558\uae30<\/h3>\n
Step 3: DFS \ubc0f \uba54\ubaa8\uc774\uc81c\uc774\uc158 \uad6c\ud604\ud558\uae30<\/h3>\n
from sys import maxsize\n\ndef tsp(curr_city, visited, n, cost_matrix, memo):\n if visited == (1 << n) - 1: # All cities visited\n return cost_matrix[curr_city][0] or maxsize # Return to starting city or maxsize if not possible\n\n if memo[curr_city][visited] != -1:\n return memo[curr_city][visited] # Return already computed cost\n\n min_cost = maxsize\n for city in range(n):\n if visited & (1 << city) == 0: # City not visited\n new_cost = cost_matrix[curr_city][city] + tsp(city, visited | (1 << city), n, cost_matrix, memo)\n min_cost = min(min_cost, new_cost)\n\n memo[curr_city][visited] = min_cost\n return min_cost\n\ndef solve_tsp(n, cost_matrix):\n memo = [[-1] * (1 << n) for _ in range(n)]\n return tsp(0, 1, n, cost_matrix, memo) # Start from city 0 with only city 0 visited\n\n# Example usage\nif __name__ == \"__main__\":\n n = 4 # Number of cities\n cost_matrix = [\n [0, 10, 15, 20],\n [10, 0, 35, 25],\n [15, 35, 0, 30],\n [20, 25, 30, 0]\n ]\n result = solve_tsp(n, cost_matrix)\n print(f\"Minimum cost: {result}\")\n <\/code><\/pre>\nStep 4: \ucf54\ub4dc \uc124\uba85<\/h3>\n
\n
tsp(curr_city, visited, n, cost_matrix, memo)<\/code>: \ud604\uc7ac \ub3c4\uc2dc, \ubc29\ubb38\ud55c \ub3c4\uc2dc\uc758 \ube44\ud2b8\ub9c8\uc2a4\ud06c, \ub3c4\uc2dc\uc758 \uc218, \ube44\uc6a9 \ud589\ub82c, \uadf8\ub9ac\uace0 \uba54\ubaa8\uc774\uc81c\uc774\uc158\uc744 \uc704\ud55c \ub9ac\uc2a4\ud2b8\ub97c \ub9e4\uac1c\ubcc0\uc218\ub85c \ubc1b\uc544, \ucd5c\uc18c \ube44\uc6a9\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\nsolve_tsp(n, cost_matrix)<\/code>: \uba54\ubaa8\uc774\uc81c\uc774\uc158 \ub9ac\uc2a4\ud2b8\ub97c \ucd08\uae30\ud654\ud558\uace0 TSP \uae30\ub2a5\uc744 \uc218\ud589\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\nStep 5: \uc2dc\uac04 \ubcf5\uc7a1\ub3c4 \ubd84\uc11d<\/h3>\n
O(n^2 * 2^n)<\/code>\uc785\ub2c8\ub2e4. \uc5ec\uae30\uc11c n<\/code>\uc740 \ub3c4\uc2dc\uc758 \uac1c\uc218, 2^n<\/code>\ub294 \ubaa8\ub4e0 \ube44\ud2b8\ub9c8\uc2a4\ud06c \uc870\ud569\uc758 \uc218\uc785\ub2c8\ub2e4. \ub530\ub77c\uc11c \ub3c4\uc2dc\uc758 \uac1c\uc218\uac00 \ub9ce\uc544\uc9c8\uc218\ub85d \uacc4\uc0b0\ub7c9\uc774 \uae09\uaca9\ud788 \uc99d\uac00\ud560 \uc218 \uc788\uc73c\ubbc0\ub85c, \uc2e4\uc81c \ubb38\uc81c\uc5d0\uc11c\ub294 \ub3c4\uc2dc \uac1c\uc218\ub97c 10\uac1c \uc774\ud558\ub85c \uc81c\ud55c\ud569\ub2c8\ub2e4.<\/p>\n3. \uacb0\ub860<\/h2>\n