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quick_sort <- function(x) {

 if (length(x) <= 1) return(x)

 pivot <- x[1]
 left <- quick_sort(x[x < pivot])
 right <- quick_sort(x[x > pivot])
 return(c(left, pivot, right))
}
# Binary Search implementation
binary_search <- function(x, target) {
 low <- 1
 high <- length(x)
 
 while (low <= high) {
 mid <- floor((low + high) / 2)
 if (x[mid] == target) {
 return(mid)
 } else if (x[mid] < target) {
 low <- mid + 1
 } else {
 high <- mid - 1