Added Matrix-chain multiplication

Author: SunmeetOberoi

Algorithms/Dynamic Programming/Matrix-chain multiplication.cpp

@@ -0,0 +1,98 @@
+#include<iostream>
+#include<vector>
+
+using namespace std;
+
+// Bottom-Up
+int** matrix_chain_order(vector<int> p) {
+
+	// size
+	int n = p.size() - 1;
+
+	// declaring and intialising result matrices
+	int** s = new int* [n];
+	int** m = new int* [n + 1];
+	for (int i = 0;i < n;i++) {
+		s[i] = new int[n + 1];
+		m[i] = new int[n + 1];
+		m[i][i] = 0;
+	}
+	m[n] = new int[n + 1];
+	m[n][n] = 0;
+
+	// calculating order
+	int q;
+	for (int l = 2;l <= n;l++) {
+		for (int i = 1;i <= n - l + 1;i++) {
+			int j = i + l - 1;
+			m[i][j] = INT_MAX;
+			for (int k = i;k < j;k++) {
+				q = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j];
+				if (q < m[i][j]) {
+					m[i][j] = q;
+					s[i][j] = k;
+				}
+			}
+		}
+	}
+	return s;
+}
+
+void print_optimal_parens(int** s, int i, int j) {
+	if (i == j)
+		cout << "A" << i;
+	else {
+
+		cout << "(";
+		print_optimal_parens(s, i, s[i][j]);
+		print_optimal_parens(s, s[i][j] + 1, j);
+		cout << ")";
+	}
+}
+
+
+// Top-Down
+int lookup_chain(int** m, vector<int> p, int i, int j) {
+	if (m[i][j] < INT_MAX)
+		return m[i][j];
+	if (i == j)
+		m[i][j] = 0;
+	else {
+		int q;
+		for (int k = i;k <= j - 1;k++) {
+			q = lookup_chain(m, p, i, k) + lookup_chain(m, p, k + 1, j) + p[i - 1] * p[k] * p[j];
+			if (q < m[i][j])
+				m[i][j] = q;
+		}
+	}
+	return m[i][j];
+}
+
+int memoized_matrix_chain(vector<int> p) {
+	int n = p.size() - 1;
+
+	int** m = new int*[n + 1];
+	for (int i = 0;i <= n;i++) {
+		m[i] = new int[n + 1];
+		for (int j = 0;j <= n;j++) {
+			m[i][j] = INT_MAX;
+		}
+	}
+	return lookup_chain(m, p, 1, n);
+}
+
+
+int main() {
+	vector<int> p;
+	int n;
+	cout << "Enter number of matrices to multiply: ";
+	cin >> n;
+	int temp;
+	for (int i = 0;i <= n;i++) {
+		cin >> temp;
+		p.push_back(temp);
+	}
+	print_optimal_parens(matrix_chain_order(p), 1, n);
+	cout << endl << "Total Calculations: " << memoized_matrix_chain(p); // calculated using top-down approach
+	return 0;
+}