Initial data commit

Task/Matrix-chain-multiplication/R/matrix-chain-multiplication.r

@@ -0,0 +1,51 @@
+aux <- function(i, j, u) {
+  k <- u[[i, j]]
+  if (k < 0) {
+    i
+  } else {
+    paste0("(", Recall(i, k, u), "*", Recall(i + k, j - k, u), ")")
+  }
+}
+
+chain.mul <- function(a) {
+  n <- length(a) - 1
+  u <- matrix(0, n, n)
+  v <- matrix(0, n, n)
+  u[, 1] <- -1
+
+  for (j in seq(2, n)) {
+    for (i in seq(n - j + 1)) {
+      v[[i, j]] <- Inf
+      for (k in seq(j - 1)) {
+        s <- v[[i, k]] + v[[i + k, j - k]] + a[[i]] * a[[i + k]] * a[[i + j]]
+        if (s < v[[i, j]]) {
+          u[[i, j]] <- k
+          v[[i, j]] <- s
+        }
+      }
+    }
+  }
+
+  list(cost = v[[1, n]], solution = aux(1, n, u))
+}
+
+chain.mul(c(5, 6, 3, 1))
+# $cost
+# [1] 48
+
+# $solution
+# [1] "(1*(2*3))"
+
+chain.mul(c(1, 5, 25, 30, 100, 70, 2, 1, 100, 250, 1, 1000, 2))
+# $cost
+# [1] 38120
+
+# $solution
+# [1] "((((((((1*2)*3)*4)*5)*6)*7)*(8*(9*10)))*(11*12))"
+
+chain.mul(c(1000, 1, 500, 12, 1, 700, 2500, 3, 2, 5, 14, 10))
+# $cost
+# [1] 1773740
+
+# $solution
+# [1] "(1*((((((2*3)*4)*(((5*6)*7)*8))*9)*10)*11))"