From 8abedd35ca8adc82da209002780e55923eb89838 Mon Sep 17 00:00:00 2001
From: himanshu010 <himanshuaswal@yahoo.com>
Date: Tue, 15 Dec 2020 15:19:40 +0530
Subject: [PATCH] add: optimal bst

---
 .../Optimal Binary Search Tree gfg.cpp        | 113 ++++++++++++++++++
 1 file changed, 113 insertions(+)
 create mode 100644 C++/Dynamic Programming/Optimal Binary Search Tree gfg.cpp

diff --git a/C++/Dynamic Programming/Optimal Binary Search Tree gfg.cpp b/C++/Dynamic Programming/Optimal Binary Search Tree gfg.cpp
new file mode 100644
index 00000000..80508b74
--- /dev/null
+++ b/C++/Dynamic Programming/Optimal Binary Search Tree gfg.cpp	
@@ -0,0 +1,113 @@
+/*
+*-----------------------------------------------------------*
+|                                                           |
+|                                                           |
+|               AUTHOR: Himanshu Aswal                      |
+|     ( website: himanshu010.github.io/Portfolio_website )  |
+|                                                           |
+|                                                           |
+*-----------------------------------------------------------*
+*/
+#include<bits/stdc++.h>
+#define moduli 998244353
+#define int long long int
+#define ld long double
+#define F first
+#define S second
+#define P pair<int,int>
+#define pb push_back
+#define vi vector<int>
+#define vvi vector<vector<int>>
+#define vb vector<bool>
+#define um unordered_map
+using namespace std;
+
+void findMinConfig(vi keys, vi value, int n) {
+    vector<vector<P>>dp(n, vector<P>(n));
+    for (int i = 0; i < n; ++i)
+    {
+        dp[i][i] = {value[i], i};
+    }
+    int cur = 1;
+    while (cur <= n) {
+        int start = 0;
+        int end = start + cur;
+
+        while (end < n) {
+            int total = 0;
+            int mn = INT_MAX;
+            int root = start;
+            for (int i = start; i <= end; ++i)
+            {
+                total += value[i];
+                if (i == start) {
+                    mn = min(mn, dp[i + 1][end].F);
+                    if (mn == dp[i + 1][end].F) {
+                        root = i;
+                    }
+
+                }
+                else if (i == end) {
+                    mn = min(mn, dp[start][i - 1].F);
+                    if (mn == dp[start][end - 1].F) {
+                        root = i;
+                    }
+                }
+                else {
+                    mn = min(mn, dp[start][i - 1].F + dp[i + 1][end].F);
+                    if (mn == dp[start][i - 1].F + dp[i + 1][end].F) {
+                        root = i;
+                    }
+                }
+            }
+            dp[start][end].F = total + mn;
+            dp[start][end].S = root;
+            start = start + 1;
+            end = end + 1;
+        }
+        cur++;
+
+    }
+
+    for (auto x : dp) {
+        for (auto y : x) {
+            cout << y.F << ',' << y.S << ' ';
+        }
+        cout << endl;
+    }
+
+    cout << dp[0][n - 1].F << endl;
+}
+
+void solve(int tc) {
+    int i, j, k, n, m, ans = 0, cnt = 0, sum = 0;
+    cin >> n;
+    vector<int> keys(n), value(n);
+    for (int i = 0; i < n; ++i)
+    {
+        cin >> keys[i];
+    }
+    for (int i = 0; i < n; ++i)
+    {
+        cin >> value[i];
+    }
+
+    findMinConfig(keys, value, n);
+
+}
+int32_t main()
+{
+#ifndef ONLINE_JUDGE
+    freopen("input.txt", "r", stdin);
+    freopen("output.txt", "w", stdout);
+#endif
+    ios_base:: sync_with_stdio(false);
+    cin.tie(NULL);
+    cout.tie(NULL);
+    int tc = 1;
+    // int t;cin>>t;while(t--)
+    {
+        solve(tc);
+        tc++;
+    }
+}
\ No newline at end of file