Merge pull request TheAlgorithms#14 from himanshub16/dp/basic-algos

Add dynamic programming algorithms

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))
+}
+*/

dynamic-programming/matrix-multiplication.go

@@ -0,0 +1,61 @@
+// matrix chain multiplication problem
+// https://en.wikipedia.org/wiki/Matrix_chain_multiplication
+// www.geeksforgeeks.org/dynamic-programming-set-8-matrix-chain-multiplication/
+
+// package main
+package matrixChainMultiplication
+
+import "fmt"
+
+func min(a, b int) int {
+	if a > b {
+		return b
+	} else {
+		return a
+	}
+}
+
+func matrixChainRec(D []int, i, j int) int {
+	// d[i-1] x d[i] : dimension of matrix i
+	if i == j {
+		return 0
+	}
+	q := 1 << 32
+	for k := i; k < j; k++ {
+		prod := matrixChainRec(D, i, k) + matrixChainRec(D, k+1, j) + D[i-1]*D[k]*D[j]
+		q = min(prod, q)
+	}
+	return q
+}
+
+func matrixChainDp(D []int) int {
+	// d[i-1] x d[i] : dimension of matrix i
+	N := len(D)
+
+	dp := make([][]int, N) // dp[i][j] = matrixChainRec(D, i, j)
+	for i := 0; i < N; i++ {
+		dp[i] = make([]int, N)
+		dp[i][i] = 0
+	}
+
+	for l := 2; l < N; l++ {
+		for i := 1; i < N-l+1; i++ {
+			j := i + l - 1
+			dp[i][j] = 1 << 31
+			for k := i; k < j; k++ {
+				prod := dp[i][k] + dp[k+1][j] + D[i-1]*D[k]*D[j]
+				dp[i][j] = min(prod, dp[i][j])
+			}
+		}
+	}
+
+	return dp[1][N-1]
+}
+
+/*
+func main() {
+	D := []int{2, 2, 2, 2, 2} // 4 matrices
+	fmt.Print(matrixChainRec(D, 1, 4), "\n")
+	fmt.Print(matrixChainDp(D), "\n")
+}
+*/

dynamic-programming/rod-cutting.go

@@ -0,0 +1,60 @@
+// Solution to Rod cutting problem
+// https://en.wikipedia.org/wiki/Cutting_stock_problem
+// http://www.geeksforgeeks.org/dynamic-programming-set-13-cutting-a-rod/
+
+package dpRodCutting
+
+// package main
+
+import "fmt"
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	} else {
+		return b
+	}
+
+}
+
+// solve the problem recursively: initial approach
+func cutRodRec(price []int, length int) int {
+	if length == 0 {
+		return 0
+	}
+
+	q := -1
+	for i := 1; i <= length; i++ {
+		q = max(q, price[i]+cutRodRec(price, length-i))
+	}
+	return q
+}
+
+// solve the same problem using dynamic programming
+func cutRodDp(price []int, length int) int {
+	r := make([]int, length+1) // a.k.a the memoization array
+	r[0] = 0                   // cost of 0 length rod is 0
+
+	for j := 1; j <= length; j++ { // for each length (subproblem)
+		q := -1
+		for i := 1; i <= j; i++ {
+			q = max(q, price[i]+r[j-i]) // avoiding recursive call
+		}
+		r[j] = q
+	}
+
+	return r[length]
+}
+
+/*
+func main() {
+	length := 10
+	price := []int{0, 1, 5, 8, 9, 17, 17, 17, 20, 24, 30}
+	// price := []int{0, 10, 5, 8, 9, 17, 17, 17, 20, 24, 30}
+
+	// fmt.Print(price[5]+price[length-5], "\n")
+
+	fmt.Print(cutRodRec(price, length), "\n")
+	fmt.Print(cutRodDp(price, length), "\n")
+}
+*/