shunfurh 于 2017.01.16 22:40 提问

The Lost House

Description
One day a snail climbed up to a big tree and finally came to the end of a branch. What a different feeling to look down from such a high place he had never been to before! However, he was very tired due to the long time of climbing, and fell asleep. An unbelievable thing happened when he woke up ---- he found himself lying in a meadow and his house originally on his back disappeared! Immediately he realized that he fell off the branch when he was sleeping! He was sure that his house must still be on the branch he had been sleeping on. The snail began to climb the tree again, since he could not live without his house.

When reaching the first fork of the tree, he sadly found that he could not remember the route that he climbed before. In order to find his lovely house, the snail decided to go to the end of every branch. It was dangerous to walk without the protection of the house, so he wished to search the tree in the best way.

Fortunately, there lived many warm-hearted worms in the tree that could accurately tell the snail whether he had ever passed their places or not before he fell off.

Now our job is to help the snail. We pay most of our attention to two parts of the tree ---- the forks of the branches and the ends of the branches, which we call them key points because key events always happen there, such as choosing a path, getting the help from a worm and arriving at the house he is searching for.

Assume all worms live at key points, and all the branches between two neighboring key points have the same distance of 1. The snail is now at the first fork of the tree.

Our purpose is to find a proper route along which he can find his house as soon as possible, through the analysis of the structure of the tree and the locations of the worms. The only restriction on the route is that he must not go down from a fork until he has reached all the ends grown from this fork.

The house may be left at the end of any branches in an equal probability. We focus on the mathematical expectation of the distance the snail has to cover before arriving his house. We wish the value to be as small as possible.

As illustrated in Figure-1, the snail is at the key point 1 and his house is at a certain point among 2, 4 and 5. A worm lives at point 3, who can tell the snail whether his house is at one of point 4 and 5 or not. Therefore, the snail can choose two strategies. He can go to point 2 first. If he cannot find the house there, he should go back to point 1, and then reaches point 4 (or 5) by point 3. If still not, he has to return point 3, then go to point 5 (or 4), where he will undoubtedly find his house. In this choice, the snail covers distances of 1, 4, 6 corresponding to the circumstances under which the house is located at point 2, 4 (or 5), 5 (or 4) respectively. So the expectation value is (1 + 4 + 6) / 3 = 11 / 3. Obviously, this strategy does not make full use of the information from the worm. If the snail goes to point 3 and gets useful information from the worm first, and then chooses to go back to point 1 then towards point 2, or go to point 4 or 5 to take his chance, the distances he covers will be 2, 3, 4 corresponding to the different locations of the house. In such a strategy, the mathematical expectation will be (2 + 3 + 4) / 3 = 3, and it is the very route along which the snail should search the tree.

Input
The input contains several sets of test data. Each set begins with a line containing one integer N, no more than 1000, which indicates the number of key points in the tree. Then follow N lines describing the N key points. For convenience, we number all the key points from 1 to N. The key point numbered with 1 is always the first fork of the tree. Other numbers may be any key points in the tree except the first fork. The i-th line in these N lines describes the key point with number i. Each line consists of one integer and one uppercase character 'Y' or 'N' separated by a single space, which represents the number of the previous key point and whether there lives a worm ('Y' means lives and 'N' means not). The previous key point means the neighboring key point in the shortest path between this key point and the key point numbered 1. In the above illustration, the previous key point of point 2 or 3 is point 1, while the previous key point of point 4 or 5 is point 3. This integer is -1 for the key point 1, means it has no previous key point. You can assume a fork has at most eight branches. The first set in the sample input describes the above illustration.

A test case of N = 0 indicates the end of input, and should not be processed.
Output
Output one line for each set of input data. The line contains one float number with exactly four digits after the decimal point, which is the mathematical expectation value.
Sample Input
5
-1 N
1 N
1 Y
3 N
3 N
10
-1 N
1 Y
1 N
2 N
2 N
2 N
3 N
3 Y
8 N
8 N
6
-1 N
1 N
1 Y
1 N
3 N
3 N
0
Sample Output
3.0000
5.0000
3.5000

1个回答

caozhy      2017.01.23 23:50

【树状数组】PKU-2057-The Lost House

poj-2057 The Lost House

POJ 2057 The lost house

【POJ2057】The Lost House【TreeDP】
【题目链接】 比较经典的一道TreeDP。 因为概率是相等的，所以我们只需要计算最小步数即可，最后答案再除以叶子节点个数。 设leaf[u]表示以u为根的子树中叶子节点的个数。 设fail[u]表示以u为根的子树中，从u出发，找房子失败后，回到u点，按最优策略走的步数。 设succ[u]表示以u为根的子树中，从u出发，并成功找到房子，按最优策略走的步数。 最优策略即我们要找
poj2057——the lost house

POJ 2057 The Lost House

poj 2057 The Lost House

pku2057 The Lost House
<br /> <br />一个N（N<=1000）个节点树上，树最多是八叉。有一个蜗牛把壳丢在了某个叶子节点。它从根节点出发沿树枝走去找壳。某些内点上有蚜虫，会告诉你下面叶子上是否有壳。为蜗牛找决定一个路径，使蜗牛找到壳的路径长度的期望值最小值，即所有可能的路径长度和的平均值。<br /> <br /> <br />这道题比较经典，首先对于每一个以i为根的子树，记b[i]为在以i为根的子树中找没有找到的时候所经历的路径长度（包括从父亲到他的边），以f[i]表示在以i为根的子树中找到的期望步数，以s[i]表示
POJ 2057 The Lost House 树形DP+贪心

【Poj 2507】The Lost House（树型dp）
【Poj 2507】The Lost House（树型dp） Time Limit: 3000MS   Memory Limit: 30000K Total Submissions: 2457   Accepted: 1020 Description One day a snail climbed up to a big tree and f