Added solutions

Author: avidLearnerInProgress

minimum_path_sum.cpp

@@ -0,0 +1,38 @@
+
+/*
+ int minPathSum(vector<vector<int>>& grid) {
+        // DP problem
+        // DP[i,j] -> minimum sum of reaching i,j
+        int rows = grid.size();
+        int cols = grid[0].size();
+        
+        // DP grid (rows X cols) initialized to grid[0][0] element
+        vector<vector<int>> DP(rows,vector<int>(cols,grid[0][0]));
+        
+        // Fill first column (0) 
+        // DP[i,0] = prefix sum along first column = DP[i-1,0] + grid[i][0]
+        for (int i=1;i<rows;++i) {
+            DP[i][0] = DP[i-1][0] + grid[i][0];
+        }
+        
+        // Fill first row (0)
+        // DP[0,i] = prefix sum along first row = DP[0,i-1] + grid[0][i]
+        for (int i=1;i<cols;++i) {
+            DP[0][i] = DP[0][i-1] + grid[0][i];
+        }
+        
+        // Fill the rest of the matrix
+        // We can only go right and down 
+        // i,j can be reached from the above it (i-1,j) OR from its left (i,j-1) 
+        // We minimize the cost for both
+        for (int i=1;i<rows;++i) {
+            for (int j=1;j<cols;++j) {
+                DP[i][j] = min(DP[i-1][j],DP[i][j-1]) + grid[i][j];
+            }
+        }
+        
+        // return 
+        return DP[rows-1][cols-1];
+    }
+
+    */