打家劫舍问题

"""
打家劫舍问题是一种典型的动态规划问题，按照房间的不同分布，其解法略有轻微的修改，下面分布以三个例子进行介绍
1）房子在一字排开，首尾不相连
2）房子成环形，首尾相连
3）房子成树状结构
"""

"""
1）房子在一字排开，首尾不相连
示例：
输入：[1,2,3,1] output = 4
输入：[2,7,9,3,1] output =12
"""

def rob_on_recursion(input_list):
    total_size = len(input_list)
    def dp(index):
        if index >= total_size:
            return 0
        res = max(dp(index + 1), input_list[index] + dp(index + 2))
        return res
    return dp(0)

def house_robber_I(input_list):
    dp = [0 for _ in range(len(input_list) + 2)] #状态转移矩阵
    for i in range(len(input_list)-1, -1, -1):
        dp[i] = max(input_list[i] + dp[i+2], dp[i + 1]) #状态转移公式，从后向前遍历
    return dp[0]

#状态压缩,优化空间复杂度
def house_robber_I_1(input_list):
    dp_i_2 = 0
    dp_i_1 = 0
    dp_i = 0
    for i in range(len(input_list)-1, -1, -1):
        dp_i = max(input_list[i] + dp_i_2, dp_i_1)
        dp_i_2 = dp_i_1
        dp_i_1 = dp_i
    return dp_i

"""
2）房子成环形，首尾相连
"""
def house_robber_II(input_list):
    size = len(input_list)
    res = max(
        rob(input_list, 0, size - 2), #选择第一间房子，放弃最后一间房子
        rob(input_list, 1, size - 1)  #选择最后一间房子，放弃选择第一间房子
    )
    return res

def rob(input_list, start, end):
    dp_i_2 = 0
    dp_i_1 = 0
    dp_i = 0
    for i in range(end, start-1, -1):
        dp_i = max(input_list[i] + dp_i_2, dp_i_1)
        dp_i_2 = dp_i_1
        dp_i_1 = dp_i
    return dp_i

"""
3）房子成树状结构
"""
class TreeNode(object):
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def house_robber_III(root):
    if root is None:
        return 0
    do_it = (root.val
             +
             (0 if root.left is None else house_robber_III(root.left.left) + house_robber_III(root.left.right))
             +
             (0 if root.right is None else house_robber_III(root.right.left) + house_robber_III(root.right.right))
             )
    not_do_it = house_robber_III(root.left) + house_robber_III(root.right)
    return max(do_it, not_do_it)


if __name__ == "__main__":
    input = [2,7,9,3,1]
    output = house_robber_I_1(input)
    print(output)