基于贪心算法和Floyd-Warshall算法的钢板最优切割路径问题的python代码，输出切割路径图像

基于贪心算法的钢板最优切割路径问题的Python代码如下：

import numpy as np
import matplotlib.pyplot as plt

def greedy_cutting(width, height, cuts):
    # 初始化钢板
    board = np.zeros((height, width))

    # 对每一次切割进行贪心选择
    for cut in cuts:
        best_score = float('inf')
        best_position = None

        # 在每个位置尝试切割
        for i in range(height - cut + 1):
            for j in range(width - cut + 1):
                # 计算当前位置的得分
                score = np.sum(board[i:i+cut, j:j+cut])

                # 更新最优得分和位置
                if score < best_score:
                    best_score = score
                    best_position = (i, j)

        # 在最优位置进行切割
        board[best_position:best_position+cut, best_position:best_position+cut[0]] = 1

    return board

# 示例输入
width = 10
height = 6
cuts = [(2, 3), (4, 2), (3, 4)]

# 调用贪心算法进行切割
board = greedy_cutting(width, height, cuts)

# 绘制切割路径图像
plt.imshow(board, cmap='gray')
plt.show()

基于Floyd-Warshall算法的钢板最优切割路径问题的Python代码如下：

import numpy as np
import matplotlib.pyplot as plt

def floyd_warshall_cutting(width, height, cuts):
    # 初始化钢板
    board = np.zeros((height, width))

    # 构建邻接矩阵
    graph = np.full((len(cuts)+2, len(cuts)+2), float('inf'))
    for i in range(len(cuts)):
        graph[i][i] = 0
        graph[i][i+1] = 0
        graph[i+1][i] = 0
        graph[i+1][i+1] = 0

    # 计算每个切割之间的最短路径
    for i in range(len(cuts)):
        for j in range(i+1, len(cuts)+1):
            graph[i][j] = np.sum(board[:cuts[j-1], :cuts[j-1]])
            graph[j][i] = np.sum(board[:cuts[j-1], :cuts[j-1]])

    # 使用Floyd-Warshall算法计算最短路径
    for k in range(len(cuts)+2):
        for i in range(len(cuts)+2):
            for j in range(len(cuts)+2):
                graph[i][j] = min(graph[i][j], graph[i][k] + graph[k][j])

    # 根据最短路径进行切割
    for i in range(len(cuts)):
        if graph[i][len(cuts)+1] < float('inf'):
            board[:cuts[i][1], :cuts[i]] = 1

    return board

# 示例输入
width = 10
height = 6
cuts = [(2, 3), (4, 2), (3, 4)]

# 调用Floyd-Warshall算法进行切割
board = floyd_warshall_cutting(width, height, cuts)

# 绘制切割路径图像
plt.imshow(board, cmap='gray')
plt.show()

请注意，以上代码仅为示例，实际应用中可能需要根据具体需求进行适当的修改。