index.Rmd

---
title: "Vote combinations"
output:
  html_document:
    theme: paper
    code_folding: hide
    toc: true
    toc_float:
      collapsed: false
---

Initialization
===================

```{r}
# loading required libraries
packagesList <- c("dplyr","tidyr","arrangements","knitr","kableExtra","data.table","plotly")
packages <- suppressWarnings(suppressMessages(lapply(packagesList, function(x){ if(!require(x, character.only = T, quietly = T)){ install.packages(x); return(paste0("installed missing package: ", x)) } else paste0("required package is installed: ", x) } )))
options(stringsAsFactors = FALSE)
```


---------------


Solving the hard way
===================

### Three companies

```{r}
# Solving for three companies and three possible plans
companies <- c("A","B","C") # companies
possiblePlans <- c("Plan 1","Plan 2","Plan 3") # possible plans to be voted
# Plan 1
df <- NULL
for (c in 1:length(companies)){ # from 1 to n companies can commit for first plan
  possCombinations <- combinations(companies, c) # possible combinations for companies to commit to 
  for (comb in 1:nrow(possCombinations)){ 
    df <- rbind(df, paste(possCombinations[comb,],collapse=","))
  }
}
# Plan 2
ndf <- NULL
for (p in 1:nrow(df)){ # for each of possible combination already existent
  remainingCompanies <- setdiff(companies, unlist(strsplit(df[p,],","))) # remaining companies without a plan
  if(length(remainingCompanies)>0){
    for (c in 1:length(remainingCompanies)){ # from 1 to n remainingCompanies can commit to current plan
      possCombinations <- combinations(remainingCompanies, c) # possible combinations for companies to commit to 
      for (comb in 1:nrow(possCombinations)){
        ndf <- rbind(ndf, c(df[p,], paste(possCombinations[comb,],collapse=","))) 
      }
    }
  } else {
    ndf <- rbind(ndf, c(df[p,], "")) 
  }
}
# Plan 3
df <- ndf
ndf <- NULL
for (p in 1:nrow(df)){ # for each of possible combination already existent
  remainingCompanies <- setdiff(companies, unlist(strsplit(df[p,],","))) # remaining companies without a plan
  if(length(remainingCompanies)>0){
    for (c in 1:length(remainingCompanies)){ # from 1 to n remainingCompanies can commit to current plan
      possCombinations <- combinations(remainingCompanies, c) # possible combinations for companies to commit to 
      for (comb in 1:nrow(possCombinations)){ 
        ndf <- rbind(ndf, c(df[p,], paste(possCombinations[comb,],collapse=","))) 
      }
    }
  } else {
    ndf <- rbind(ndf, c(df[p,], "")) 
  }
}
#Removing duplicates
out <- data.frame(ndf)
out <- unite(out, aux, sep = "|", remove=F) 
out$aux <- duplicated(lapply(strsplit(out$aux,"\\|") , function(x){
  tmp <- sort(x)
  tmp <- tmp[!(tmp == "|")]
  return(tmp)}))
out <- out[!(out$aux),-which(names(out) == "aux")] 
names(out) <- paste("Plan ", seq(1,length(out),1))
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(out) `</b>

<b>Table:</b>

Table with all possible assembly vote combinations:

```{r, echo = FALSE} 
out %>%
  kable(row.names = FALSE) %>%
  kable_styling()
```


---------------


Generalizing the solution
===================

```{r}
#generalizing
createVoteTable <- function(companies, numberofPlans, df=NULL){
  if(is.null(df)){ #first run
    firstRun <- TRUE
    companies <- sort(companies)
    df <- data.frame("empty")
  } else{
    firstRun <- FALSE
  }
  dat <- NULL
  for (p in 1:nrow(df)){
    if(firstRun) {
      remainingCompanies <- companies
    } else {
      remainingCompanies <- companies[!(companies %in% unlist(strsplit(as.character(df[p,]),",")))]
    }
    if(length(remainingCompanies)>0){
      for (c in 1:length(remainingCompanies)){ # from 1 to n companies can commit for first plan
        possCombinations <- combinations(remainingCompanies, c) # possible combinations for companies to commit to 
        dat <- rbindlist(list(dat,rbindlist(lapply(1:nrow(possCombinations),function(comb) {
          if(firstRun)
            return(as.list(paste(possCombinations[comb,],collapse=",")))
          else
            return(c(as.list(df[p,]),paste(possCombinations[comb,],collapse=",")))
        }))))
      }
    } else {
      dat <- rbindlist(list(dat,c(as.list(df[p,]), ""))) 
    }
  }
  ndf <- data.frame(dat)
  #removing duplicate plans
  out <- as.data.frame(ndf)
  out <- unite(out, aux, sep = "|", remove=F)
  out$aux <- duplicated(lapply(strsplit(out$aux,"\\|") , function(x){
    tmp <- sort(x)
    tmp <- tmp[!(tmp == "|")]
    return(tmp)}))
  out <- out[!(out$aux),-which(names(out) == "aux")]
  out <- as.data.frame(out)
  numberofPlans = numberofPlans - 1
  if(numberofPlans == 0){
    names(out) <- paste("Plan ", seq(1,length(out),1))
    return(out)
  }
  createVoteTable(companies=companies, numberofPlans=numberofPlans, df=out)
} 
```



---------------


### Two companies

```{r}
# Two companies, two plans 
companies <- c("C1","C2") # companies
numberofPlans <- 2 # possible plans to be voted
result <- list()
result$'2' <- createVoteTable(companies,numberofPlans)
saveRDS(result$'2', file = paste0("result_2.rds"))
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'2') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations:

```{r, echo = FALSE} 
result$'2' %>%
  kable(row.names = FALSE) %>%
  kable_styling()
```



### Three companies

```{r}
# Three companies, Three plans 
companies <- as.vector(paste0("C",1:3)) # companies
numberofPlans <- 3 # possible plans to be voted
result$'3' <- createVoteTable(companies,numberofPlans)
saveRDS(result$'3', file = paste0("result_3.rds"))
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'3') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations:

<div style="height: 300px; overflow-y: scroll; overflow-x: hidden;">

```{r, echo = FALSE} 
result$'3' %>%
  kable(row.names = FALSE) %>%
  kable_styling()
```

</div>

### Four companies

```{r}
# Three companies, Three plans 
companies <- as.vector(paste0("C",1:4)) # companies
numberofPlans <- 4 # possible plans to be voted
result$'4' <- createVoteTable(companies,numberofPlans)
saveRDS(result$'4', file = paste0("result_4.rds"))
#result$'4' <- readRDS("result_4.rds") #loading previous calculated result
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'4') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations:

<div style="height: 300px; overflow-y: scroll; overflow-x: hidden;">

```{r, echo = FALSE} 
result$'4' %>%
  kable(row.names = FALSE) %>%
  kable_styling()
```

</div>

### Five companies

```{r}
# Three companies, Three plans 
companies <- as.vector(paste0("C",1:5)) # companies
numberofPlans <- 5 # possible plans to be voted
result$'5' <- createVoteTable(companies,numberofPlans)
saveRDS(result$'5', file = paste0("result_5.rds"))
#result$'5' <- readRDS("result_5.rds") #loading previous calculated result
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'5') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations:

<div style="height: 300px; overflow-y: scroll; overflow-x: hidden;">

```{r, echo = FALSE} 
result$'5' %>%
  kable(row.names = FALSE) %>%
  kable_styling()
```

</div>

### Six companies

```{r}
# Three companies, Three plans 
companies <- as.vector(paste0("C",1:6)) # companies
numberofPlans <- 6 # possible plans to be voted
result$'6' <- createVoteTable(companies,numberofPlans)
saveRDS(result$'6', file = paste0("result_6.rds"))
#result$'6' <- readRDS("result_6.rds") #loading previous calculated result
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'6') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations:

<div style="height: 300px; overflow-y: scroll; overflow-x: hidden;">

```{r, echo = FALSE} 
result$'6' %>%
  kable(row.names = FALSE) %>%
  kable_styling()
```

</div>

### Seven companies

```{r}
# Three companies, Three plans 
companies <- as.vector(paste0("C",1:7)) # companies
numberofPlans <- 7 # possible plans to be voted
result$'7' <- createVoteTable(companies,numberofPlans)
saveRDS(result$'7', file = paste0("result_5.rds"))
#result$'7' <- readRDS("result_7.rds") #loading previous calculated result
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'7') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations:

<div style="height: 300px; overflow-y: scroll; overflow-x: hidden;">

```{r, echo = FALSE} 
result$'7' %>%
  kable(row.names = FALSE) %>%
  kable_styling()
```

</div>

### Eight companies

```{r}
# Three companies, Three plans 
companies <- as.vector(paste0("C",1:8)) # companies
numberofPlans <- 8 # possible plans to be voted
#result$'8' <- createVoteTable(companies,numberofPlans)
#saveRDS(result$'8', file = paste0("result_5.rds"))
result$'8' <- readRDS("result_8.rds") #loading previous calculated result
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'8') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations:

<div style="height: 300px; overflow-y: scroll; overflow-x: hidden;">

```{r, echo = FALSE} 
result$'8' %>%
  kable(row.names = FALSE) %>%
  kable_styling()
```

</div>

### Nine companies

```{r}
# Three companies, Three plans 
companies <- as.vector(paste0("C",1:9)) # companies
numberofPlans <- 9 # possible plans to be voted
#result$'9' <- createVoteTable(companies,numberofPlans)
#saveRDS(result$'9', file = paste0("result_9.rds"))
result$'9' <- readRDS("result_9.rds") #loading previous calculated result
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'9') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations hidden due to size. 


### Ten companies

```{r}
# Three companies, Three plans 
companies <- as.vector(paste0("C",1:10)) # companies
numberofPlans <- 10 # possible plans to be voted
#result$'10' <- createVoteTable(companies,numberofPlans)
#saveRDS(result$'10', file = paste0("result_10.rds"))
result$'10' <- readRDS("result_10.rds") #loading previous calculated result
```

<b>Number:</b>

Combination number for different voting clusters: <b> `r nrow(result$'10') `</b>

<b>Table:</b>

Table with all possible assembly vote combinations hidden due to size. 

---------------


Chart Summary
===================


```{r}

df <- data.frame(Companies = seq(2,10,1), Combinations = unlist(lapply(1:9,function(i){return(nrow(result[[i]]))})))

plot_ly(df, x = ~Companies, y = ~Combinations, type = 'scatter', mode = 'lines+markers',
        hoverinfo = 'text',
        text = ~paste(Combinations, ' possible combinations.')) %>%
  layout(xaxis = list(title = "Companies/Plans"))


```