added dp problems

algorithms/CPlusPlus/Dynamic-Programming/minimum-pathsum.cpp

@@ -0,0 +1,37 @@
+// (problem Link) - [https://leetcode.com/problems/minimum-path-sum/]
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int minSumPathUtil(int i, int j,vector<vector<int>> &matrix,vector<vector<int>> &dp)
+{
+  if(i==0 && j == 0)
+    return matrix[0][0];
+  if(i<0 || j<0)
+    return 1e9;
+  if(dp[i][j]!=-1) return dp[i][j];
+    
+  int up = matrix[i][j]+minSumPathUtil(i-1,j,matrix,dp);
+  int left = matrix[i][j]+minSumPathUtil(i,j-1,matrix,dp);
+  
+  return dp[i][j] = min(up,left);
+  
+}
+
+int minSumPath(int n, int m, vector<vector<int> > &matrix){
+    vector<vector<int> > dp(n,vector<int>(m,-1));
+    return minSumPathUtil(n-1,m-1,matrix,dp);
+    
+}
+
+int main() {
+
+  vector<vector<int> > matrix{{5,9,6},
+                            {11,5,2}};
+                            
+  int n = matrix.size();
+  int m = matrix[0].size();
+  
+  cout<<minSumPath(n,m,matrix);
+}

algorithms/CPlusPlus/Dynamic-Programming/unique-paths.cpp

@@ -0,0 +1,46 @@
+// (problem link) - [https://leetcode.com/problems/unique-paths/]
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int countWaysUtil(int m, int n, vector<vector<int> > &dp) {
+  for(int i=0; i<m ;i++){
+      for(int j=0; j<n; j++){
+          
+          //base condition
+          if(i==0 && j==0){
+              dp[i][j]=1;
+              continue;
+          }
+          
+          int up=0;
+          int left = 0;
+          
+          if(i>0) 
+            up = dp[i-1][j];
+          if(j>0)
+            left = dp[i][j-1];
+            
+          dp[i][j] = up+left;
+      }
+  }
+  
+  return dp[m-1][n-1];
+
+  
+}
+
+int countWays(int m, int n){
+    vector<vector<int> > dp(m,vector<int>(n,-1));
+    return countWaysUtil(m,n,dp);
+    
+}
+
+int main() {
+
+  int m=3;
+  int n=2;
+  
+  cout<<countWays(m,n);
+}