I wish to find the speediest way to find up to 1000 possible combinations of 'n' integers to find a target integer.

For example. Say I wanted to sum to the number '20'. I want to find up to 1000 combinations of four integers that sum to this number. The integers can repeat themselves. I also have a condition that the integer must not be smaller than a particular number, in this case 4.

```
target<-20 #the number I wish to sum to
lowest<-4 #the smallest integer I allow
size<-4 #the number of integers I wish to use to sum
maxposs <- target - ((size-1) * lowest) #given the lowest, this is the max possible integer. In my example it is 8.
```

This is how I have started to work this out. Using `combn`

to find all combinations of the four chosen integers and then filtering by those that sum to my target.

```
m <- combn(rep(lowest:maxposs,size), size)
m1<- m[,colSums(m)==target]
```

Here, 'm1' has 245 columns. There are only this many solutions. The last few columns:

```
# [,238] [,239] [,240] [,241] [,242] [,243] [,244] [,245]
#[1,] 4 4 4 4 4 4 5 5
#[2,] 5 5 5 6 7 4 6 4
#[3,] 7 4 5 4 4 5 4 5
#[4,] 4 7 6 6 5 7 5 6
```

However, in my real application, I can be dealing with very high integers (summing up to 1000) and want to limit myself to a random sample of 1000 possible combinations. As this is for a randomization statistical test, speed is of the essence. I wonder if anyone knows of a faster way of doing this. My way doesn't feel intuitively quick.

Answer:

```
my_matrix <- matrix(nrow = 1000, ncol = 4)
i <- 1
nn <- 1000
while(i <= 1000){
x <- sample(x = 4:nn, size = 3)
y = nn - sum(x)
if(y >= 4){
my_matrix[i, ] <- c(x, y)
i <- i + 1
}
}
```

Per Gavin's suggestion, redone with a preallocated matrix. Now this runs in .158 seconds, twice as fast, and probably scales better.

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