add longest palindromic subsequence

Author: himanshub16

dynamic-programming/longest-palindromic-subsequence.go

@@ -0,0 +1,65 @@
+// longest palindromic subsequence
+// http://www.geeksforgeeks.org/dynamic-programming-set-12-longest-palindromic-subsequence/
+
+package longestPalindromicSubsequence
+
+// package main
+
+import "fmt"
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
+}
+
+func lpsRec(word string, i, j int) int {
+	if i == j {
+		return 1
+	}
+	if i > j {
+		return 0
+	}
+	if word[i] == word[j] {
+		return 2 + lpsRec(word, i+1, j-1)
+	}
+	return max(lpsRec(word, i, j-1), lpsRec(word, i+1, j))
+}
+
+func lpsDp(word string) int {
+	N := len(word)
+	dp := make([][]int, N)
+
+	for i := 0; i < N; i++ {
+		dp[i] = make([]int, N)
+		dp[i][i] = 1
+	}
+
+	for l := 2; l <= N; l++ {
+		// for length l
+		for i := 0; i < N-l+1; i++ {
+			j := i + l - 1
+			if word[i] == word[j] {
+				if l == 2 {
+					dp[i][j] = 2
+				} else {
+					dp[i][j] = 2 + dp[i+1][j-1]
+				}
+			} else {
+				dp[i][j] = max(dp[i+1][j], dp[i][j-1])
+			}
+		}
+	}
+
+	return dp[1][N-1]
+}
+
+/*
+func main() {
+	// word := "aaabbbbababbabbabbabf"
+	word := "aaaabbbba"
+	fmt.Printf("%d\n", lpsRec(word, 0, len(word)-1))
+	fmt.Printf("%d\n", lpsDp(word))
+}
+*/