From 7d7a050d2390a43101730a65dd8fad93e69b99c4 Mon Sep 17 00:00:00 2001
From: keineahnung2345 <mimifasosofamire1123@gmail.com>
Date: Wed, 21 Oct 2020 10:45:44 +0800
Subject: [PATCH] 1D DP

---
 1626. Best Team With No Conflicts.cpp | 43 +++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/1626. Best Team With No Conflicts.cpp b/1626. Best Team With No Conflicts.cpp
index 05df689..47e97d9 100644
--- a/1626. Best Team With No Conflicts.cpp	
+++ b/1626. Best Team With No Conflicts.cpp	
@@ -194,3 +194,46 @@ class Solution {
         return backtrack(scores, ages, players, 0, -1, 0);
     }
 };
+
+//1D DP
+//each cell means the optimal can be got using the previous i players
+//https://leetcode.com/problems/best-team-with-no-conflicts/discuss/899475/Fairly-easy-DP
+//Runtime: 232 ms, faster than 51.78% of C++ online submissions for Best Team With No Conflicts.
+//Memory Usage: 19.2 MB, less than 5.33% of C++ online submissions for Best Team With No Conflicts.
+class Solution {
+public:
+    int bestTeamScore(vector<int>& scores, vector<int>& ages) {
+        int n = scores.size();
+        
+        vector<int> players(n);
+        iota(players.begin(), players.end(), 0);
+        
+        //sort 
+        sort(players.begin(), players.end(), 
+            [&](int& p1, int& p2){
+                return (ages[p1] == ages[p2]) ? (scores[p1] < scores[p2]) : (ages[p1] < ages[p2]);
+            });
+        
+        vector<int> dp(n);
+        //the actual index
+        int pi, pj;
+        
+        //visit the players, the younger the earlier to be visited
+        for(int i = 0; i < n; ++i){
+            //map to the actual index
+            pi = players[i];
+            dp[i] = scores[pi];
+            
+            //visit players younger than pi
+            for(int j = 0; j < i; ++j){
+                pj = players[j];
+                if(scores[pj] <= scores[pi]){
+                    //dp[i]: the optimal score can be got formed of players of younger than or equal to pi
+                    dp[i] = max(dp[i], dp[j]+scores[pi]);
+                }
+            }
+        }
+        
+        return *max_element(dp.begin(), dp.end());
+    }
+};