计算选择资源的最佳路线

Question

以下是规则（Halite 3）：

在每个转弯处，您都必须为自己的飞船做出一个决定。您可以向右移动，向左移动，向上移动，向下移动或保持静止（并收集资源）。

移动战舰会花费战舰当前可用资源的10％。 保持静止不花一分钱，您可以选择当前电池可用资源的25％。如果一艘船没有足够的资源来支付10％的移动费用，那么他将被固定在此转弯的单元上（不能为负）。

我的目标：该船从中心（0）开始，并应在此点尽可能少地返回（X数量的资源）。

我该如何计算船舶为实现目标所应采用的最有效的路径（圆角）？

这里有一些代码可以计算随机地图（该地图在每个游戏中都是随机的）：

import random

how_Big = 11 
center_Pos = int(how_Big/2) #how_Big must be even

game_Map = [[random.randint(1,500) for i in range(how_Big)] for x in range(how_Big)]
game_Map[center_Pos][center_Pos] = 0

for y in range(how_Big):
    print(game_Map[y])

[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 479, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 172, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]

我不太确定如何开始。是否有已知的算法？

谢谢

其他信息：

• 矩阵是每个单元格开头的可用资源。
• 运输从0个资源开始。
• 轮船在一个单元格上保持不动来获得资源 （收集该单元资源的25％）。
• 船舶通过移动来花费（自己的货物）资源（成本为10％ 当前单元的可用资源）。
• 无论如何都可以返回路径（例如，moves = [“ up”， “ still”，“ still”，“ up”，“ still”，“ still”，“ down”，“ down”]））。 蛮力接受。
• X是我希望我的船上货物拥有的最小数量 返回中心。
• 地图始终有一个中心单元格
• 收集或使用的资源总是四舍五入到最接近的整数
• 由舰船收集的资源从牢房中移除

以下是可能发生的情况的示例：

move_Dict = {
    "up": [-1, 0],
    "down": [1, 0],
    "right": [0, 1],
    "left": [0, -1],
    "still": [0, 0],
}

moves = ["up", "still", "still", "up", "still", "still", "down", "down"]
position = [5, 5]
cargo = 0

print("initial map :")
for y in range(how_Big):
        print(game_Map[y])

for move in moves:
    if move == "still":
        ressources_Collected = round(game_Map[position[0]][position[1]] * 0.25)
        cargo += ressources_Collected
        game_Map[position[0]][position[1]] -= ressources_Collected
    else:
        ressources_Used = round(game_Map[position[0]][position[1]] * 0.10)
        cargo -= ressources_Used
        position = [position[0]+move_Dict[move][0], position[1]+move_Dict[move][1]]

    print(f"ship is at position {position}, cargo = {cargo}")
    for y in range(how_Big):
        print(game_Map[y])

输出：

initial map :
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 479, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 172, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
ship is at position [4, 5], cargo = 0
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 479, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 172, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
ship is at position [4, 5], cargo = 43
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 479, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 129, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
ship is at position [4, 5], cargo = 75
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 479, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 97, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
ship is at position [3, 5], cargo = 65
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 479, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 97, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
ship is at position [3, 5], cargo = 185
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 359, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 97, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
ship is at position [3, 5], cargo = 275
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 269, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 97, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
ship is at position [4, 5], cargo = 248
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 269, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 97, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
ship is at position [5, 5], cargo = 238
[110, 179, 97, 467, 347, 336, 368, 298, 107, 84, 123]
[415, 86, 12, 75, 354, 74, 250, 221, 51, 254, 252]
[368, 235, 389, 1, 155, 186, 149, 135, 458, 243, 344]
[391, 480, 485, 358, 416, 269, 270, 354, 203, 436, 146]
[62, 132, 490, 33, 445, 97, 127, 274, 130, 77, 356]
[239, 11, 459, 245, 214, 0, 324, 162, 58, 394, 202]
[241, 395, 46, 78, 191, 384, 203, 191, 56, 474, 237]
[85, 480, 181, 98, 122, 482, 90, 351, 257, 266, 182]
[398, 125, 195, 423, 219, 290, 140, 166, 413, 499, 428]
[213, 367, 142, 471, 141, 407, 382, 229, 332, 455, 53]
[207, 12, 319, 54, 246, 274, 474, 312, 170, 374, 188]
[Finished in 0.1s]