URAL 1928 1962 1939 1994

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• URAL1928 Another Ecology Problem
• URAL1962 In Chinese Restaurant
• URAL1939 First Seal
• URAL1994 The Emperor’s plan

URAL1928 Another Ecology Problem

Let dp[n][centra][0] be the maximum money the centra can get when there is n billions zollars in the budget and is the current centra’s turn to request for money, and let dp[n][centra][1] be the minimum money the contender can get when money is maximized for the current centra. For $i le n$, dp[n][centra][0]=dp[n-i][1-centra][1] + i, dp[n][centra][1]=dp[n⑴][1-centra][0], and when $k > n$, dp[n][centra][0]=m, dp[n][centra][1]=0. Find the maximum dp[n][centra][0] and the minimum dp[n][centra][1] to solve this problem.

Accepted Code

URAL1962 In Chinese Restaurant

The people form chains and circle. The circle (number of nodes is greater than 2) could only appear when there is only one set and $n=m$, and the answer is 2 if $n>2$. Each chain should contain at most 1 inner cycle which indicates two people want to sit with each other. For every chain it could be reversed, and it could be placed anywhere except the chain contains people 1. Denote the number of chains by k, the permutation of the chains is $(k⑴)!$, denote the number of chains whose node number is larger than 1 as l, the number of available arrangements is $(k⑴)! cdot 2^l$.

Accepted Code

URAL1939 First Seal

Let $t=frac{H-h}{x}$, $S\_1=v cdot t - l$, $S\_2=frac{v^2}{2a}$, if $S_1 < S_2$ then the vehicle will fall to pieces anyway.

Accepted Code

URAL1994 The Emperor’s plan

Let dp[x][y] be the expected number of senators before night, x is the number of senators and y is the number of spies. In each night, y senators will be removed thus x -= y is executed. In each day, enumerate $0 le i le x + y$ and $0 le j le min(i, y)$ where $i$ is the number of people to be excluded, $j$ is the number of spies in them. The expectation dp[x][y] will be $max\_{i=0}^{x+y}sum\_{j=0}^{min(i, y)}dp[x - (i - j)][y - j] cdot frac{C\_{x}^{i - j} cdot C\_{y}^{j}}{C\_{x+y}^{i}}$.

Accepted Code