Simulation

Since there's no formal algorithm involved, the intent of the problem is to assess competence with one's programming language of choice and knowledge of built-in data structures. At least in USACO Bronze, when a problem statement says to find the end result of some process, or to find when something occurs, it's usually sufficient to simulate the process naively*.

Example 1

Solution

We can simulate the process. Store an array that keeps track of which shell is at which location, and Bessie's swapping can be simulated by swapping elements in the array. Then, we can count how many times Elsie guesses each shell, and the maximum points she can earn is the maximum amount of times a shell is guessed.

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#include <algorithm>
#include <cstdio>
#include <vector>

using std::vector;

int main() {
	freopen("shell.in", "r", stdin);

	int n;

Example 2

Solution

We can simulate the process of pouring buckets. The amount of milk poured from bucket $i$ to bucket $j$ is the smaller of the amount of milk in bucket $i$ (which is $m_i$) and the remaining space in bucket $j$ (which is $c_j - m_j$). We can just handle all of these operations in order, using an array $c$ to store the maximum capacities of each bucket, and an array $m$ to store the current milk level in each bucket, which we update during the process. Example code is below.

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#include <algorithm>
#include <cstdio>
#include <iostream>
#include <vector>

using namespace std;

const int N = 3;  // The number of buckets (which is 3)
const int TURN_NUM = 100;

Problems

Easier

Harder