Very Frequent
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# Simulation

Authors: Darren Yao, Allen Li

Directly simulating the problem statement, which many Bronze problems allow you to do.

Resources
IUSACOThis module is based on Chapter 5 of Darren Yao's book

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

### Statement

Alice and Bob are standing on a 2D plane. Alice starts at the point $(0, 0)$, and Bob starts at the point $(R, S)$ ($1 \leq R, S \leq 1000$). Every second, Alice moves $M$ units to the right, and $N$ units up. Every second, Bob moves $P$ units to the left, and $Q$ units down. ($1 \leq M, N, P, Q \leq 10$). Determine if Alice and Bob will ever meet (be at the same point at the same time), and if so, when.

#### Input Format

The first line of the input contains $R$ and $S$.

The second line of the input contains $M$, $N$, $P$, and $Q$.

#### Output Format

Please output a single integer containing the number of seconds after the start at which Alice and Bob meet. If they never meet, please output $-1$.

Solution

## Example 2

### Statement

There are $N$ buckets ($5 \leq N \leq 10^5$), each with a certain capacity $C_i$ ($1 \leq C_i \leq 100$). One day, after a rainstorm, each bucket is filled with $A_i$ units of water ($1\leq A_i \leq C_i$). Charlie then performs the following process: he pours bucket $1$ into bucket $2$, then bucket $2$ into bucket $3$, and so on, up until pouring bucket $N-1$ into bucket $N$. When Charlie pours bucket $B$ into bucket $B+1$, he pours as much as possible until bucket $B$ is empty or bucket $B+1$ is full. Find out how much water is in each bucket once Charlie is done pouring.

#### Input Format

The first line of the input contains $N$.

The second line of the input contains the capacities of the buckets, $C_1, C_2, \dots, C_N$.

The third line of the input contains the amount of water in each bucket $A_1, A_2, \dots, A_N$.

#### Output Format

Please print one line of output, containing $N$ space-separated integers: the final amount of water in each bucket once Charlie is done pouring.

Solution

## Problems

### Easier

StatusSourceProblem NameDifficultyTagsSolution
BronzeEasy
Show Tags

Nested Loop

External Sol
BronzeEasy
Show Tags

Single Loop

External Sol
BronzeEasy
Show Tags

Nested Loop

External Sol
BronzeEasy
Show Tags

Single Loop

External Sol
BronzeEasyExternal Sol

### Harder

StatusSourceProblem NameDifficultyTagsSolution
BronzeNormal
BronzeNormal
BronzeNormalExternal Sol
BronzeNormal
BronzeNormal
BronzeHardExternal Sol
BronzeHard