go: add «1976. Number of Ways to Arrive at Destination»

URL:	https://leetcode.com/problems/number-of-ways-to-arrive-at-destination/
Signed-off-by: Matej Focko <me@mfocko.xyz>

go/number-of-ways-to-arrive-at-destination.go

@@ -0,0 +1,61 @@
+package main
+
+func countPaths(n int, roads [][]int) int {
+	type Entry struct {
+		time uint64
+		ways uint64
+	}
+
+	const MOD uint64 = 1_000_000_007
+
+	dp := make([][]Entry, n)
+	for i := range n {
+		dp[i] = make([]Entry, n)
+	}
+
+	// Initialize for trivial values
+	for p := 0; p < n*n; p++ {
+		u, v := p/n, p%n
+
+		if u != v {
+			dp[u][v].time = uint64(1e12)
+			dp[u][v].ways = 0
+		} else {
+			dp[u][v].time = 0
+			dp[u][v].ways = 1
+		}
+	}
+
+	// add edges
+	for _, road := range roads {
+		u, v, t := road[0], road[1], road[2]
+
+		// time
+		dp[u][v].time = uint64(t)
+		dp[v][u].time = uint64(t)
+
+		// ways
+		dp[u][v].ways = 1
+		dp[v][u].ways = 1
+	}
+
+	// Floyd-Warshall
+	for t := 0; t < n*n*n; t++ {
+		v, u, w := (t/n)/n, (t/n)%n, t%n
+
+		if u != v && v != w {
+			newTime := dp[u][v].time + dp[v][w].time
+
+			if newTime < dp[u][w].time {
+				// shorter path
+				dp[u][w].time = newTime
+				dp[u][w].ways = (dp[u][v].ways * dp[v][w].ways) % MOD
+			} else if newTime == dp[u][w].time {
+				// same time, but another way
+				dp[u][w].ways = (dp[u][w].ways + dp[u][v].ways*dp[v][w].ways) % MOD
+			}
+		}
+	}
+
+	return int(dp[n-1][0].ways)
+}