64. Minimum Path Sum - DP with no Extra space

64. Minimum Path Sum - DP with no Extra space

Author: SteffiKeranJ

Dynamic-Programming/minPathSum.cpp

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+class Solution {
+public:
+    int minPathSum(vector<vector<int>>& grid) {
+        int m = grid.size(); // number of rows
+        int n =  grid[0].size(); // number of columns
+        
+        for(int i = 0; i < m; ++i){
+            for(int j = 0; j < n; ++j) {
+                if(i == 0&& j==0) continue;
+                if(i==0) { // for first row cells
+                    grid[i][j] += grid[i][j-1]; // add from the cell left to it
+                    continue; // go back to the loop
+                }
+                if(j ==0) { //for the first column cells
+                    grid[i][j] += grid[i-1][j]; // add from the cells above it
+                    continue;
+                }
+                // for any other cell
+                // sum by adding from the cell above it
+                int topSum = grid[i][j] + grid[i-1][j];
+                // sum by adding from the cell left to it
+                int leftSum = grid[i][j] + grid[i][j-1];
+                // choose the minimum sum path
+                grid[i][j] = min(topSum, leftSum);
+            }
+        }
+        
+        return grid[m-1][n-1];
+    }
+};