最大样本

如果我想对数字进行采样来创建向量，我会这样做：

set.seed(123)
x <- sample(1:100,200, replace = TRUE)
sum(x)
# [1] 10228

如果我想采样 20 个总和为 100 的随机数，然后采样 30 个数字，但总和仍为 100，该怎么办？我想这比看起来更具挑战性。?sample谷歌搜索并没有给我提供任何线索。如果与所需总和不够接近（例如在 5 以内），则进行采样然后拒绝，我猜可能需要一些时间。

有更好的方法来实现这一目标吗？

一个例子是：

foo(10,100) # ten random numbers that sum to 100. (not including zeros)
# 10,10,20,7,8,9,4,10,2,20

使用 R 的尝试

# Config
n <- 20L
target <- 100L
vec <- seq(100)
set.seed(123)

# R repeat loop
sumto_repeat <- function(vec,n,target) {
  res <- integer()
  repeat {
    cat("begin:",sum(res),length(res),"\n")
    res <- c( res, sample(vec,1) )
    if( sum(res)<target & length(res)==(n-1) ) {
      res[length(res)+1] <- target - sum(res)
    }
    # cat("mid:",sum(res),length(res),"\n")
    if(sum(res)>target) res <- res[-length(res)]
    if( length(res)>n | length(res)<n & sum(res)==target ) {
      res <- res[-sample(seq(length(res)),1)]
    }
    # cat("end:",sum(res),length(res),"\n")
    # cat(dput(res),"\n")
    if( sum(res)==target & length(res)==n ) break
  }
  res
}

test <- sumto_repeat(vec=vec,n=n,target=target)
> sum(test)
[1] 100
> length(test)
[1] 20

另外，我会考虑一下您想从哪个发行版中提取。我think有几种不同的方法可以让它精确地求和target with n元素（例如，您可以使最后一个元素始终为target - sum(res)）可能有也可能没有不同的分布影响。

Rcpp 中的一个非常相似的算法，速度很快！

cpp_src <- '
Rcpp::IntegerVector xa = clone(x); // Vector to be sampled
Rcpp::IntegerVector na(n); // Number of elements in solution
Rcpp::IntegerVector sa(s); // Sum of solution

int nsampled;
int currentSum;
int dropRandomIndex;
int numZeroes;
Rcpp::IntegerVector remainingQuantity(1);
int maxAttempts = 100;

// Create container for our results
Rcpp::IntegerVector res(maxAttempts);
std::fill( res.begin(), res.end(), NA_INTEGER );

// Calculate min/max so that we can draw random integers from within range
Rcpp::IntegerVector::iterator mn = std::min_element(xa.begin(), xa.end()) ;
Rcpp::IntegerVector::iterator mx = std::max_element(xa.begin(), xa.end()) ;
std::cout << "mx = " << *mx << std::endl;

// Now draw repeatedly
nsampled = 0;
for( int i = 0; i < maxAttempts; i++ ) {
  std::cout << "\\n" << i;
  int r = *mn + (rand() % (int)(*mx - *mn + 1));
  res[i] = xa[r+1];
  // Calculate n and s for current loop iteration
  numZeroes = 0;
  for( int j = 0; j < maxAttempts; j++) 
    if(res[j]==0) numZeroes++;
  std::cout << " nz= " << numZeroes ;
  nsampled = maxAttempts - sum( is_na(res) ) - numZeroes - 1;
  currentSum = std::accumulate(res.begin(),res.begin()+i,0); // Cant just use Rcpp sugar sum() here because it freaks at the NAs
  std::cout << " nsamp= " << nsampled << " sum= " << currentSum;
  if(nsampled == na[0]-1) {  
    std::cout << " One element away. ";
    remainingQuantity[0] = sa[0] - currentSum;
    std::cout << "remainingQuantity = " << remainingQuantity[0];
    if( (remainingQuantity[0] > 0) && (remainingQuantity[0]) < *mx ) {
      std::cout << "Within range.  Prepare the secret (cheating) weapon!\\n";
      std::cout << sa[0] << " ";
      std::cout << currentSum << " ";
      std::cout << remainingQuantity[0] << std::endl;
      if( i != maxAttempts ) {
        std::cout << "Safe to add one last element on the end.  Doing so.\\n";
        res[i] = remainingQuantity[0];
      }
      currentSum = sa[0];
      nsampled++;
      if(nsampled == na[0] && currentSum == sa[0]) std::cout << "It should end after this...nsamp= " << nsampled << " and currentSum= " << currentSum << std::endl;
      break;
    } else {
      std::cout << "Out of striking distance.  Dropping random element\\n";
      dropRandomIndex = 0 + (rand() % (int)(i - 0 + 1));
      res[dropRandomIndex] = 0;
    }
  }
  if(nsampled == na[0] && currentSum == sa[0]) {
      std::cout << "Success!\\n";
      for(int l = 0; l <= i+1; l++) 
        std::cout << res[l] << " " ;
      break;
  }
  if(nsampled == na[0] && currentSum != sa[0]) {
    std::cout << "Reached number of elements but sum is ";
    if(currentSum > sa[0]) {
      std::cout << "Too high. Blitz everything and start over!\\n";
      for(int k = 0; k < res.size(); k++) {
        res[k] = NA_INTEGER;
      }
    } else {
      std::cout << "Too low.  \\n";

    }
  }
  if( nsampled < na[0] && currentSum >= sa[0] ) {
    std::cout << "Too few elements but at or above the sum cutoff.  Dropping a random element and trying again.\\n";
    dropRandomIndex = 0 + (rand() % (int)(i - 0 + 1));
    res[dropRandomIndex] = 0;
  }
}
return res;
'

sumto <- cxxfunction( signature(x="integer", n="integer", s="integer"), body=cpp_src, plugin="Rcpp", verbose=TRUE )

testresult <- sumto(x=x, n=20L, s=1000L)
testresult <- testresult[!is.na(testresult)]
testresult <- testresult[testresult!=0]
testresult
cumsum(testresult)
length(testresult)

用几个不同的值进行尝试，并产生有效的答案，除非它跑掉了。这里有一个警告，如果它远离所需的元素数量并且在“惊人的距离”内，那么它就会作弊——例如它不只是绘制最后一个值，而是计算该数字是否有效。

基准测试

See gist用于比较代码。