go: add logic for matrix min-sum-path traversal

* also print the path both as a graph and as a vector of coordinates

matrix.go

@@ -7,6 +7,7 @@ import (
 	"log"
 	"os"
 	"strconv"
+	"strings"
 	"time"
 )
 
@@ -99,11 +100,81 @@ func convertMatrix(strmatrix [][]string) matrix {
 	return m
 }
 
+// fmtPath efficiently formats positional values for printing.
+func fmtPath(x, y, val int) string {
+	s := "[" + strconv.Itoa(x) + "," + strconv.Itoa(y) + "] (" +
+		strconv.Itoa(val) + ")"
+	return s
+}
+
 // traverseMatrix traverses the given matrix in such a manner as to accumulate
 // the smallest possible sum. allowed movements are down and to the right.
-func traverseMatrixMinSumPath(m matrix) { //nolint:unparam
-	// ad unparam: m will be used shortly.
+// it also prints a cute ascii path of traversal.
+func traverseMatrixMinSumPath(m matrix) {
 	start := time.Now()
 
-	log.Printf("traversing the matrix took: %s", time.Since(start))
+	cols := len(m.rows[0])
+	rows := len(m.rows)
+	// current column.
+	col := 0
+	// current row index.
+	i := 0
+	sum := m.rows[i][col]
+	traversing := true
+	path := "init"
+	graph := "x"
+
+	log.Printf("matrix cols: %d, rows: %d\n", cols, rows)
+
+	for traversing {
+		path += ", " + fmtPath(i, col, m.rows[i][col])
+
+		nextCol := col + 1
+		nextRow := i + 1
+
+		switch {
+		case nextCol < cols && nextRow < rows:
+			// can go either way.
+			right := m.rows[i][col+1]
+			down := m.rows[i+1][col]
+
+			if right < down {
+				col++
+
+				sum += right
+				graph += "x"
+			} else {
+				i++
+
+				sum += down
+				graph += "\n" + strings.Repeat(" ", col) + "x"
+			}
+
+		case nextRow == rows && nextCol < cols:
+			// can only go right.
+			col++
+			sum += m.rows[i][col]
+			graph += "x"
+
+		case nextCol == cols && nextRow < rows:
+			// can only go down.
+			i++
+			sum += m.rows[i][col]
+			graph += "\n" + strings.Repeat(" ", col) + "x"
+
+		default:
+			path += ", finish"
+
+			log.Printf(
+				"traversal concluded with sum: %d\n"+
+					"graph:\n%s\n"+
+					"traversal path:\n%s\n\n",
+				sum, graph, path,
+			)
+
+			traversing = false
+		}
+	}
+
+	log.Printf("traversing the matrix took: %s\n", time.Since(start))
 }