zoukankan      html  css  js  c++  java
  • POJ 1651 Multiplication Puzzle(区间DP)

    题目链接:http://poj.org/problem?id=1651

    Multiplication Puzzle
    Time Limit: 1000MS   Memory Limit: 65536K
    Total Submissions: 5000   Accepted: 2988

    Description

    The multiplication puzzle is played with a row of cards, each containing a single positive integer. During the move player takes one card out of the row and scores the number of points equal to the product of the number on the card taken and the numbers on the cards on the left and on the right of it. It is not allowed to take out the first and the last card in the row. After the final move, only two cards are left in the row. 

    The goal is to take cards in such order as to minimize the total number of scored points. 

    For example, if cards in the row contain numbers 10 1 50 20 5, player might take a card with 1, then 20 and 50, scoring 
    10*1*50 + 50*20*5 + 10*50*5 = 500+5000+2500 = 8000

    If he would take the cards in the opposite order, i.e. 50, then 20, then 1, the score would be 
    1*50*20 + 1*20*5 + 10*1*5 = 1000+100+50 = 1150.

    Input

    The first line of the input contains the number of cards N (3 <= N <= 100). The second line contains N integers in the range from 1 to 100, separated by spaces.

    Output

    Output must contain a single integer - the minimal score.

    Sample Input

    6
    10 1 50 50 20 5
    

    Sample Output

    3650

    Source

    Northeastern Europe 2001, Far-Eastern Subregion
     
     
     
     

    区间DP

    dp[0][n-1]表示答案。

    求解dp[i][j]的时候,就是枚举[i+1,j-1]中最后删除的元素。

    dp[i][j]=min(a[k]*a[i]*a[j]+dp[i][k]+dp[k][j])   i<k<j

    代码:

    //============================================================================
    // Name        : POJ.cpp
    // Author      : 
    // Version     :
    // Copyright   : Your copyright notice
    // Description : Hello World in C++, Ansi-style
    //============================================================================
    
    #include <iostream>
    #include <stdio.h>
    #include <algorithm>
    #include <string.h>
    using namespace std;
    const int MAXN=110;
    const int INF=0x3f3f3f3f;
    int a[MAXN];
    int dp[MAXN][MAXN];
    int solve(int i,int j)
    {
        if(dp[i][j]!=INF)return dp[i][j];
        if(j==i+1)return dp[i][j]=0;
        for(int k=i+1;k<j;k++)
            dp[i][j]=min(dp[i][j],a[k]*a[i]*a[j]+solve(i,k)+solve(k,j));
        return dp[i][j];
    }
    int main()
    {
        //freopen("in.txt","r",stdin);
        //freopen("out.txt","w",stdout);
        int n;
        while(scanf("%d",&n)==1)
        {
            for(int i=0;i<n;i++)
                scanf("%d",&a[i]);
            for(int i=0;i<n;i++)
                for(int j=0;j<n;j++)
                    dp[i][j]=INF;
            printf("%d\n",solve(0,n-1));
        }
        return 0;
    }
    人一我百!人十我万!永不放弃~~~怀着自信的心,去追逐梦想
  • 相关阅读:
    MyBatisPlus乐观锁
    MyBatisPlus查询
    IDEA创建Java类时自动配置注释(作者,创建时间,版本等)
    MyBatisPlus自动填充处理
    Cannot read property '$createElement' of undefined
    IDEA中gradle的配置和使用
    android7.0以上https抓包
    转发unbuntu jdk 安装
    Unity 连接WebSocket
    Tween 使用
  • 原文地址:https://www.cnblogs.com/kuangbin/p/3051484.html
Copyright © 2011-2022 走看看