Maximum Sum Problem GeeksForGeeks

Dp Learnings (27 Part Series)

1 House Robber leetcode problem
2 Jump game leetcode problem
… 23 more parts…
3 Jump game II leetcode problem
4 Cherry Pickup II Leetcode Problem
5 Partition Equals Subset Sum Leetcode problem or Subset sum equals to target
6 Maximum Sum Problem GeeksForGeeks
7 Count Palindrome Sub-Strings of a String GeeksForGeeks
8 Length of Longest Common Subsequence (LCS) and Longest common subsequence string leetcode
9 0/1 Knapsack Problem GeeksForGeeks both bounded and Unbounded
10 Shortest distance from source to all other nodes in a Directed Acyclic Graph
11 Coin change Leetcode
12 Coin Change 2 Leetcode
13 Target Sum or Partition with given difference Leetcode
14 Rod cutting Problem (similar to unbounded knapsack)
15 Length of longest common substring
16 Longest Palindromic subsequence (Same as Lcs)
17 Minimum Insertion steps needed to make a string palindrome (Same as LCS)
18 Minimum number of Insertion and deletion needed to convert String A to String B or make both the strings equal (same as lcs)
19 Shortest Common Super-sequence Leetcode (Same as Lcs string)
20 Distinct Subsequence Leetcode
21 Partition with given difference
22 Two best non overlapping events
23 Longest increasing subsequence
24 Edit distance
25 Maximum product subarray
26 Target sum
27 Maximum Multiplication Score

Problem Statement

A number n can be broken into three parts n/2, n/3, and n/4 (consider only the integer part). Each number obtained in this process can be divided further recursively. Find the maximum sum that can be obtained by summing up the divided parts together.
Note: Given number must be divided at least once.

Example 1

Input:
n = 12
Output: 13
Explanation: Break n = 12 in three parts
{12/2, 12/3, 12/4} = {6, 4, 3}, now current
sum is = (6 + 4 + 3) = 13. Further breaking 6,
4 and 3 into parts will produce sum less than
or equal to 6, 4 and 3 respectively.

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Solution

//User function Template for Java 
//recursive solution tc : o(3^n) as we are calling recursive function 3 times /2,/3 and /4
//space time complexity is : o(3^n) auxillary space for the stack as their will be 
// 3^n stack space that will be required
/* class Solution { public int maxSum(int n) { return solve(n); } public int solve(int n){ if(n==1 || n==0) return n; int a = n/2; int b = n/3; int c = n/4; return Integer.max(n, solve(a)+solve(b)+solve(c) ); } } */
// optimized solution using dynamic programming memoization top down approach
// time complexity is O(n) as at max there will be n states and dp will traverse those states 
// space complexity will be O(n) for dp and o(n) for stack space;
class Solution
{
    public int maxSum(int n) 
    { 
        int dp[] = new int[1000001];
        Arrays.fill(dp,-1);
        return solve(n,dp);
    } 
    public int solve(int n,int dp[]){
        if(n==1 || n==0) return n;
        if(dp[n]!=-1) return dp[n];
        int a = n/2;
        int b = n/3;
        int c = n/4;

        return dp[n]= Integer.max(n,
        solve(a,dp)+solve(b,dp)+solve(c,dp)
        );
    }
}

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Dp Learnings (27 Part Series)

1 House Robber leetcode problem
2 Jump game leetcode problem
… 23 more parts…
3 Jump game II leetcode problem
4 Cherry Pickup II Leetcode Problem
5 Partition Equals Subset Sum Leetcode problem or Subset sum equals to target
6 Maximum Sum Problem GeeksForGeeks
7 Count Palindrome Sub-Strings of a String GeeksForGeeks
8 Length of Longest Common Subsequence (LCS) and Longest common subsequence string leetcode
9 0/1 Knapsack Problem GeeksForGeeks both bounded and Unbounded
10 Shortest distance from source to all other nodes in a Directed Acyclic Graph
11 Coin change Leetcode
12 Coin Change 2 Leetcode
13 Target Sum or Partition with given difference Leetcode
14 Rod cutting Problem (similar to unbounded knapsack)
15 Length of longest common substring
16 Longest Palindromic subsequence (Same as Lcs)
17 Minimum Insertion steps needed to make a string palindrome (Same as LCS)
18 Minimum number of Insertion and deletion needed to convert String A to String B or make both the strings equal (same as lcs)
19 Shortest Common Super-sequence Leetcode (Same as Lcs string)
20 Distinct Subsequence Leetcode
21 Partition with given difference
22 Two best non overlapping events
23 Longest increasing subsequence
24 Edit distance
25 Maximum product subarray
26 Target sum
27 Maximum Multiplication Score

原文链接：Maximum Sum Problem GeeksForGeeks