From 2ffbe3fff99942b4338b5dd90c09d6b34e75db05 Mon Sep 17 00:00:00 2001
From: chayan das <110921638+Chayandas07@users.noreply.github.com>
Date: Sat, 28 Dec 2024 19:41:32 +0530
Subject: [PATCH] Create 689. Maximum Sum of 3 Non-Overlapping Subarrays

---
 ...Maximum Sum of 3 Non-Overlapping Subarrays | 62 +++++++++++++++++++
 1 file changed, 62 insertions(+)
 create mode 100644 689. Maximum Sum of 3 Non-Overlapping Subarrays

diff --git a/689. Maximum Sum of 3 Non-Overlapping Subarrays b/689. Maximum Sum of 3 Non-Overlapping Subarrays
new file mode 100644
index 0000000..107ab2c
--- /dev/null
+++ b/689. Maximum Sum of 3 Non-Overlapping Subarrays	
@@ -0,0 +1,62 @@
+class Solution {
+public:
+    void subarraySum(vector<int>& nums, vector<int>& subarr, int k) {
+        int n = nums.size();
+        int l = 0;
+        int r = 0;
+        int sum = 0;
+
+        while (r < n) {
+            while (r - l + 1 < k) {
+                sum += nums[r];
+                r++;
+            }
+            sum += nums[r];
+            subarr.push_back(sum);
+            sum -= nums[l];
+            l++;
+            r++;
+        }
+    };
+
+    int helper(int ind, vector<int>& subarr, int k, int count,
+               vector<vector<int>>& dp) {
+        int n = subarr.size();
+        if (count == 0)
+            return 0;
+        if (ind >= n)
+            return INT_MIN;
+        if (dp[ind][count] != -1)
+            return dp[ind][count];
+        int take = subarr[ind] + helper(ind + k, subarr, k, count - 1, dp);
+        int nottake = helper(ind + 1, subarr, k, count, dp);
+        return dp[ind][count] = max(take, nottake);
+    }
+    void solve(int ind, int count, vector<int>& ans, vector<int>& subarr, int k,
+               vector<vector<int>>& dp) {
+        int n = subarr.size();
+        if (count == 0)
+            return;
+        if (ind >= n)
+            return;
+
+        int take = subarr[ind] + helper(ind + k, subarr, k, count - 1, dp);
+        int nottake = helper(ind + 1, subarr, k, count, dp);
+
+        if (take >= nottake) {
+            ans.push_back(ind);
+            solve(ind + k, count - 1, ans, subarr, k, dp);
+        } else
+            solve(ind + 1, count, ans, subarr, k, dp);
+    }
+
+    vector<int> maxSumOfThreeSubarrays(vector<int>& nums, int k) {
+        int n = nums.size();
+        vector<int> subarr;
+        subarraySum(nums, subarr, k);
+        vector<vector<int>> dp(n + 1, vector<int>(4, -1));
+        vector<int> ans;
+        solve(0, 3, ans, subarr, k, dp);
+        return ans;
+    }
+};