Add Interpolation Search in R (#228)

Author: Siddhram

searches/interpolation_search.r

@@ -0,0 +1,56 @@
+# Interpolation Search in R – works on sorted arrays with uniformly distributed values
+
+#' Performs interpolation search on a sorted numeric vector.
+#'
+#' @param arr Numeric vector sorted in ascending order.
+#' @param target Numeric value to search for in arr.
+#' @return The 1-based index of target in arr if found; otherwise -1.
+#' @details Interpolation search estimates the position of target using
+#' linear interpolation, which is efficient on uniformly distributed data.
+#' Time complexity: average O(log log n), worst-case O(n). Requires a sorted array.
+interpolation_search <- function(arr, target) {
+  n <- length(arr)
+  if (n == 0) return(-1)
+  low <- 1
+  high <- n
+
+  # Guard: if target is outside the bounds, fail early
+  if (target < arr[low] || target > arr[high]) return(-1)
+
+  while (low <= high && target >= arr[low] && target <= arr[high]) {
+    # Avoid division by zero when all values in range are equal
+    if (arr[low] == arr[high]) {
+      if (arr[low] == target) return(low)
+      return(-1)
+    }
+
+    # Estimate position using linear interpolation
+    pos <- low + floor((target - arr[low]) * (high - low) / (arr[high] - arr[low]))
+
+    # Bounds safety in case of numerical issues
+    if (pos < low) pos <- low
+    if (pos > high) pos <- high
+
+    if (arr[pos] == target) {
+      return(pos)
+    } else if (arr[pos] < target) {
+      low <- pos + 1
+    } else {
+      high <- pos - 1
+    }
+  }
+
+  return(-1)
+}
+
+# --- Demonstration (simple usage, mirrors other search files) ---
+arr <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100) # sorted input array
+target <- 70 # value to search
+
+idx <- interpolation_search(arr, target)
+
+if (idx == -1) {
+  cat("Element", target, "not found in the array.\n")
+} else {
+  cat("Element", target, "found at position", idx, ".\n")
+}