zoukankan      html  css  js  c++  java
  • LeetCode 1043. Partition Array for Maximum Sum

    原题链接在这里:https://leetcode.com/problems/partition-array-for-maximum-sum/

    题目:

    Given an integer array A, you partition the array into (contiguous) subarrays of length at most K.  After partitioning, each subarray has their values changed to become the maximum value of that subarray.

    Return the largest sum of the given array after partitioning.

    Example 1:

    Input: A = [1,15,7,9,2,5,10], K = 3
    Output: 84
    Explanation: A becomes [15,15,15,9,10,10,10]

    Note:

    1. 1 <= K <= A.length <= 500
    2. 0 <= A[i] <= 10^6

    题解:

    When encounter such kind of problem.

    Could think from a simpler example. Say only one element, then 2 elements and more. Virtualize them, find routines.

    Use array dp to memorize maxmimum sum up to i.

    If, A = [1], then A becomes A[1]. dp = [1].

    A = [1, 15], then A becomes A[15, 15]. dp = [1, 30].

    A = [1, 15, 7], then A becomes A[15, 15, 15]. dp = [1, 30, 45].

    A = [1, 15, 7, 9], then A becomes A[15, 15, 15, 9]. dp = [1, 30, 45, 54].

    ...

    The routine is like from i back k(<= K) steps, find the maxmimum element, curMax * k + dp[i-k](if available).

    Finally return dp[A.length-1].

    Time Complexity: O(n*K). n = A.length.

    Space: O(n).

    AC Java:

     1 class Solution {
     2     public int maxSumAfterPartitioning(int[] A, int K) {
     3         int len = A.length;
     4         int [] dp = new int[len];
     5         for(int i = 0; i<len; i++){
     6             dp[i] = Integer.MIN_VALUE;
     7             int curMax = A[i];
     8             
     9             for(int k = 1; k<=K & i-k+1>=0; k++){
    10                 curMax = Math.max(curMax, A[i-k+1]);
    11                 dp[i] = Math.max(dp[i], (i-k<0 ? 0 : dp[i-k]) + curMax*k);
    12             }
    13         }
    14         
    15         return dp[len-1];
    16     }
    17 }
  • 相关阅读:
    leetcode_138复制带随机指针的链表
    minSTL
    LLVM
    STL基础_迭代器
    mysql数据库表清空后id如何从1开始自增
    explain用法和结果分析
    MySQL多表查询与子查询
    数据结构与算法笔记
    MySQL数据库的SQL语言与视图
    mysql忘记密码解决方案
  • 原文地址:https://www.cnblogs.com/Dylan-Java-NYC/p/11300836.html
Copyright © 2011-2022 走看看