Traveling salesman

dynamic_programming/traveling_salesman.r

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+# Traveling Salesman Problem (TSP) using Dynamic Programming + Bitmasking
+# ------------------------------------------------------------
+# Given a cost matrix, find the minimum cost to visit all cities exactly once
+# and return to the starting city.
+
+INF <- 1e9  # a large number representing infinity
+
+# TSP function
+tsp <- function(mask, pos, cost, dp, n) {
+  # Base case: all cities visited, return to starting city
+  if (mask == (1 << n) - 1) {
+    return(cost[pos + 1, 1])  # return to city 0
+  }
+
+  # Return already computed result
+  if (dp[mask + 1, pos + 1] != -1) {
+    return(dp[mask + 1, pos + 1])
+  }
+
+  ans <- INF
+
+  # Try visiting all unvisited cities
+  for (city in 0:(n - 1)) {
+    if ((mask & (1 << city)) == 0) {
+      newAns <- cost[pos + 1, city + 1] + tsp(mask | (1 << city), city, cost, dp, n)
+      ans <- min(ans, newAns)
+    }
+  }
+
+  dp[mask + 1, pos + 1] <<- ans
+  return(ans)
+}
+
+# Example usage
+main <- function() {
+  # Cost matrix: symmetric distances between cities
+  cost <- matrix(
+    c(0, 20, 42, 35,
+      20, 0, 30, 34,
+      42, 30, 0, 12,
+      35, 34, 12, 0),
+    nrow = 4, byrow = TRUE
+  )
+
+  n <- nrow(cost)
+  dp <- matrix(-1, nrow = (1 << n), ncol = n)  # DP table
+
+  # Start from city 0, with only city 0 visited (mask = 1)
+  result <- tsp(1, 0, cost, dp, n)
+  cat("Minimum Traveling Cost:", result, "\n")
+}
+
+# Run example
+main()