3月13号周练——2015 Multi-University Training Contest 9

2015 Multi-University Training Contest 9

A. Expression（理解原理 区间DP）

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<iostream>
#include<vector>
#include<queue>
#include<cmath>
#define maxn 105
#define mod 1000000007
using namespace std;
long long dp[maxn][maxn];
long long A[maxn],C[maxn][maxn];
char operations[maxn];
int a[maxn],n;
/*初始化从0到maxn的阶乘模mod*/
void init()
{
    int i,j;
    A[0] = 1;
    for(i = 1;i < maxn; i++)
    {
        A[i] = (A[i-1]*i)%mod;
    }
    C[0][0] = 1;
    for(i=1; i<=100; i++)
    {
        C[i][0] = 1;
        for(j=1; j<=i; j++)
            C[i][j] = (C[i-1][j-1] + C[i-1][j])%mod;
    }
}
void solve()
{
    int len,l,r,k;
    for(l = 1;l <= n;l ++)
        dp[l][l] = a[l];
    for(len = 2;len <= n;len ++)
    {
        for(l = 1;l + len - 1 <= n; l ++)
        {
            long long t;
            r = l + len -1;
            for(k = l;k < r;k ++)
            {
                if(operations[k] == '+'){
                    t = (dp[l][k]*A[r-k-1] + dp[k+1][r]*A[k-l])%mod;
                }
                else if(operations[k] == '-'){
                    t = (dp[l][k]*A[r-k-1] - dp[k+1][r]*A[k-l])%mod;
                }
                else{
                    t = (dp[l][k]* dp[k+1][r])%mod;
                }
                dp[l][r] = (dp[l][r] + t* C[r-l-1][k-l])%mod;
            }
        }
    }
}
int main()
{
    init();
    while(cin >> n)
    {
        memset(dp, 0, sizeof(dp));
        int i,j;
        for(i = 1;i <= n;i ++){
            cin >> a[i];
        }
        for(i = 1;i < n;i ++){
            cin >> operations[i];
        }
        solve();
        cout << (dp[1][n]+mod)%mod << endl;              //此段代码借鉴的，为什么？
    }
    return 0;
}

小结：此题看过题解后，思路是对的，但是对取模的机制和组合数的求法不是很熟练，需要加强。

Travelling Salesman Problem

#include <iostream>
#include<cstdio>
#define maxn 105
#define black 1
#define white 0
using namespace std;
int n,m;
long long sum,min;
int map[maxn][maxn],color[maxn][maxn];    //color[][] = 0/1，1代表白色，0代表黑色
void init()
{
    int i ,j;
    bool tmp = true;
    for(i = 1;i <= n;i ++)
    {
            for(j = 1;j <= m;j ++)
            {
                    if(tmp)
                        color[i][j] = black;
                    else
                        color[i][j] = white;
                    tmp = !tmp;
            }
    }
}
int main()
{
    while(scanf("%d %d",&n,&m)!=EOF)
    {
            init();
            sum = 0;
            int i,j;
            for(i = 1;i <= n;i ++)
            {
                for(j = 1;j <= m;j ++)
                {
                    scanf("%d",&map[i][j]);
                    sum += map[i][j];
                }
            }
                /*行数n为奇数*/
                if(n%2!=0)
                {
                    printf("%lld\n",sum);
                    for(i = 1;i <= n;i ++)
                    {
                        if(i%2 != 0)
                        {
                            for(j = 1;i < m;i ++)
                                printf("R");
                        }
                        else
                        {
                                printf("D");
                                for(j= 1;j < m;j ++)
                                        printf("L");
                        }
                    }
                }
                /*行数为偶数，但列数为奇数*/
                else if(m%2 !=  0)
                {
                        printf("%lld\n",sum);
                        for(i = 1;i <= m;i ++)
                        {
                                if(i%2 != 0)
                                {
                                        for(j = 1;i < n;i ++)
                                        printf("D");
                                }
                                else
                                {
                                        printf("L");
                                        for(j= 1;j < n;j ++)
                                                printf("U");
                                }
                        }
                }
                /*行列都为偶数*/
                else
                {
                        
                }
        }
        return 0;
}