From 4698b931bb471f09409dadaadb9a7686ad638716 Mon Sep 17 00:00:00 2001
From: Sanjay Majhi <47259000+sanjaymajhi@users.noreply.github.com>
Date: Sat, 3 Oct 2020 11:56:03 +0530
Subject: [PATCH] Create MinCostPath.cpp

Given a cost matrix cost[][] and a position (m, n) in cost[][], write a function that returns cost of minimum cost path to reach (m, n) from (0, 0). Each cell of the matrix represents a cost to traverse through that cell. Total cost of a path to reach (m, n) is sum of all the costs on that path (including both source and destination). You can only traverse down, right and diagonally lower cells from a given cell, i.e., from a given cell (i, j), cells (i+1, j), (i, j+1) and (i+1, j+1) can be traversed. You may assume that all costs are positive integers.
---
 .../Dynamic Programming/C++/MinCostPath.cpp   | 39 +++++++++++++++++++
 1 file changed, 39 insertions(+)
 create mode 100644 Algorithms/Dynamic Programming/C++/MinCostPath.cpp

diff --git a/Algorithms/Dynamic Programming/C++/MinCostPath.cpp b/Algorithms/Dynamic Programming/C++/MinCostPath.cpp
new file mode 100644
index 0000000..e768d5c
--- /dev/null
+++ b/Algorithms/Dynamic Programming/C++/MinCostPath.cpp	
@@ -0,0 +1,39 @@
+#include <bits/stdc++.h> 
+#define endl "\n" 
+using namespace std; 
+
+const int row = 3; 
+const int col = 3; 
+
+int minCost(int cost[row][col]) { 
+
+	// for 1st column 
+	for (int i=1 ; i<row ; i++){ 
+		cost[i][0] += cost[i-1][0]; 
+	} 
+
+	// for 1st row 
+	for (int j=1 ; j<col ; j++){ 
+		cost[0][j] += cost[0][j-1]; 
+	} 
+
+	// for rest of the 2d matrix 
+	for (int i=1 ; i<row ; i++) { 
+		for (int j=1 ; j<col ; j++) { 
+			cost[i][j] += min(cost[i-1][j-1], min(cost[i-1][j], cost[i][j-1])); 
+		} 
+	} 
+
+	// returning the value in last cell 
+	return cost[row-1][col-1]; 
+} 
+int main(int argc, char const *argv[]) 
+{	 
+	int cost[row][col] = { {1, 2, 3}, 
+							{4, 8, 2}, 
+							{1, 5, 3} }; 
+
+	cout << minCost(cost) << endl; 
+	return 0; 
+} 
+