Create Brackets in Matrix Chain Multiplication

Brackets in Matrix Chain Multiplication

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+class Solution{
+public:
+    pair<int,string> dp[27][27];
+    string matrixChainOrder(int p[], int n){
+        return f(1,n-1,p).second;
+    }
+
+    pair<int,string> f(int i,int j,int p[]){
+        if(i==j){
+            string curr = "";
+            curr += 'A' + i-1; 
+            return {0,curr};
+        }
+
+        if(dp[i][j].second != "") return dp[i][j];
+
+        int val = INT_MAX;
+        string s = "";
+
+        for(int k=i;k<j;k++){
+            pair<int,string> a =  f(i,k,p);
+            pair<int,string> b =  f(k+1,j,p);
+            int q = p[i-1]*p[j]*p[k] + a.first + b.first;
+            if(q<val){
+                val = q;
+                s = "(" + a.second + b.second + ")";
+            }
+        }
+        return dp[i][j] = {val,s};
+    }
+};