使用Python编写三种利用动态规划，贪心，回溯，分治等优化算法解决图着色问题的算法代码

动态规划求解图着色问题代码：

def graph_coloring_dp(graph, colors):
    n = len(graph)
    dp = [[float('inf') for j in range(colors)] for i in range(n)]
    for i in range(n):
        for j in range(colors):
            if i == 0:
                dp[i][j] = 1
            else:
                for k in range(colors):
                    if graph[i][k] == 1 and j != k:
                        dp[i][j] = min(dp[i][j], dp[i-1][k]+1)
    return min(dp[-1])

贪心求解图着色问题代码：

def graph_coloring_greedy(graph, colors):
    color_map = {}
    for node in range(len(graph)):
        available_colors = set(range(1, colors+1))
        for neighbor in graph[node]:
            if neighbor in color_map:
                if color_map[neighbor] in available_colors:
                    available_colors.remove(color_map[neighbor])
        color_map[node] = min(available_colors)
    return max(color_map.values())

回溯求解图着色问题代码：

def graph_coloring_backtrack(graph, colors):
    def backtrack(node):
        nonlocal min_color
        if node == len(graph):
            min_color = min(min_color, max(color_map))
            return
        for color in range(1, colors+1):
            if is_valid(node, color):
                color_map[node] = color
                backtrack(node+1)
                color_map[node] = 0
    
    def is_valid(node, color):
        for neighbor in graph[node]:
            if color_map[neighbor] == color:
                return False
        return True
    
    color_map = [0] * len(graph)
    min_color = float('inf')
    backtrack(0)
    return min_color

分治求解图着色问题代码：

def graph_coloring_divide_conquer(graph, colors):
    def divide_conquer(nodes):
        if len(nodes) == 1:
            return 1
        left_nodes = nodes[:len(nodes)//2]
        right_nodes = nodes[len(nodes)//2:]
        left_color = divide_conquer(left_nodes)
        right_color = divide_conquer(right_nodes)
        return max(left_color, right_color)
    
    return divide_conquer(list(range(len(graph))))

注意：以上代码未考虑所有情况，仅供参考。