欢迎您访问程序员文章站本站旨在为大家提供分享程序员计算机编程知识!
您现在的位置是: 首页  >  IT编程

Ural 1029 Ministry 题解

程序员文章站 2023-11-30 15:39:52
Ural 1029 Ministry 题解 [TOC] 题意 给定一个$n\times m(1\le n \le10,1\le m \le500)$的矩阵,矩阵中的每个值都是一个小于等于$10^9$的正整数。 现在从第$1$行的任意位置开始,在第$n$行的任意位置结束。每次有$3$种移动选择(不能移 ......

ural 1029 ministry 题解

题意

给定一个\(n\times m(1\le n \le10,1\le m \le500)\)的矩阵,矩阵中的每个值都是一个小于等于\(10^9\)的正整数。

现在从第\(1\)行的任意位置开始,在第\(n\)行的任意位置结束。每次有\(3\)种移动选择(不能移动到矩阵外)。

设当前位置为\((i,j)\)

  • 移动到\((i+1,j)\)

  • 移动到\((i,j-1)\)

  • 移动到\((i,j+1)\)

每条路径的价值是路径走过所有的位置上的值的和(小于等于\(10^9\))。

问在所有路径中,路径价值最小的,输出这条路径所有位置的列号。

题解

考虑记忆化搜索(dp也可以)。

对于每个点,记忆化搜索可以移动到它的\(3\)种位置,取最小值即可,顺便记录一下路径。

也可以无脑最短路。

tips:

  1. wa\(1\)的同学不要着急,test\(1\)并不是样例,仔细找找有没有错误。

  2. \((i,j)\)的答案为\(dp(i,j)\),矩阵中的值为\(a(i,j)\),状态转移方程如果是\(dp(i,j)=\min\{dp(i-1,j),dp(i,j-1),dp(i,j+1) \}+a(i,j)\)可能会wa\(1\),改为\(dp(i,j)=\min\{dp(i-1,j)+a(i,j),dp(i,j-1)+a(i,j),dp(i,j+1)+a(i,j) \}\)即可ac。目前并不知道原因(我太弱了),如果有知道的可以在评论区留言,谢谢!

程序

ac

// #pragma gcc optimize(2)
// #pragma g++ optimize(2)
// #pragma comment(linker,"/stack:102400000,102400000")

// #include <bits/stdc++.h>
#include <map>
#include <set>
#include <list>
#include <array>
#include <cfenv>
#include <cmath>
#include <ctime>
#include <deque>
#include <mutex>
#include <queue>
#include <ratio>
#include <regex>
#include <stack>
#include <tuple>
#include <atomic>
#include <bitset>
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <chrono>
#include <cstdio>
#include <cwchar>
#include <future>
#include <limits>
#include <locale>
#include <memory>
#include <random>
#include <string>
#include <thread>
#include <vector>
#include <cassert>
#include <climits>
#include <clocale>
#include <complex>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <ctgmath>
#include <cwctype>
#include <fstream>
#include <iomanip>
#include <numeric>
#include <sstream>
#include <ccomplex>
#include <cstdbool>
#include <iostream>
#include <typeinfo>
#include <valarray>
#include <algorithm>
#include <cinttypes>
#include <cstdalign>
#include <stdexcept>
#include <typeindex>
#include <functional>
#include <forward_list>
#include <system_error>
#include <unordered_map>
#include <unordered_set>
#include <scoped_allocator>
#include <condition_variable>
// #include <conio.h>
// #include <windows.h>
using namespace std;

typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
typedef float fl;
typedef double ld;
typedef long double ld;
typedef pair<int,int> pii;
#if (win32) || (win64) || (__win32) || (__win64) || (_win32) || (_win64) || (windows)
#define lld "%i64d"
#define llu "%i64u"
#else
#define lld "%lld"
#define llu "%llu"
#endif
#define ui(n) ((unsigned int)(n))
#define ll(n) ((long long)(n))
#define ull(n) ((unsigned long long)(n))
#define fl(n) ((float)(n))
#define ld(n) ((double)(n))
#define ld(n) ((long double)(n))
#define char(n) ((char)(n))
#define bool(n) ((bool)(n))
#define fixpoint(n) fixed<<setprecision(n)

const int inf=1061109567;
const int ninf=-1044266559;
const ll linf=4557430888798830399;
const ld eps=1e-15;
#define mod (1000000007)
#define pi (3.1415926535897932384626433832795028841971)

/*
#define mb_len_max 5
#define shrt_min (-32768)
#define shrt_max 32767
#define ushrt_max 0xffffu
#define int_min (-2147483647 - 1)
#define int_max 2147483647
#define uint_max 0xffffffffu
#define long_min (-2147483647l - 1)
#define long_max 2147483647l
#define ulong_max 0xfffffffful
#define llong_max 9223372036854775807ll
#define llong_min (-9223372036854775807ll - 1)
#define ullong_max 0xffffffffffffffffull
*/

#define mp make_pair
#define mt make_tuple
#define all(a) (a).begin(),(a).end()
#define pall(a) (a).rbegin(),(a).rend()
#define log2(x) log(x)/log(2)
#define log(x,y) log(x)/log(y)
#define sz(a) ((int)(a).size())
#define rep(i,n) for(int i=0;i<((int)(n));i++)
#define rep1(i,n) for(int i=1;i<=((int)(n));i++)
#define repa(i,a,n) for(int i=((int)(a));i<((int)(n));i++)
#define repa1(i,a,n) for(int i=((int)(a));i<=((int)(n));i++)
#define repd(i,n) for(int i=((int)(n))-1;i>=0;i--)
#define repd1(i,n) for(int i=((int)(n));i>=1;i--)
#define repda(i,n,a) for(int i=((int)(n));i>((int)(a));i--)
#define repda1(i,n,a) for(int i=((int)(n));i>=((int)(a));i--)
#define for(i,a,n,step) for(int i=((int)(a));i<((int)(n));i+=((int)(step)))
#define repv(itr,v) for(__typeof((v).begin()) itr=(v).begin();itr!=(v).end();itr++)
#define repv(i,v) for(auto i:v)
#define repe(i,v) for(auto &i:v)
#define ms(x,y) memset(x,y,sizeof(x))
#define mc(x) ms(x,0)
#define minf(x) ms(x,63)
#define mcp(x,y) memcpy(x,y,sizeof(y))
#define sqr(x) ((x)*(x))
#define un(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define filein(x) freopen(x,"r",stdin)
#define fileout(x) freopen(x,"w",stdout)
#define fileio(x)\
    freopen(x".in","r",stdin);\
    freopen(x".out","w",stdout)
#define filein2(filename,name) ifstream name(filename,ios::in)
#define fileout2(filename,name) ofstream name(filename,ios::out)
#define file(filename,name) fstream name(filename,ios::in|ios::out)
#define pause system("pause")
#define cls system("cls")
#define fs first
#define sc second
#define pc(x) putchar(x)
#define gc(x) x=getchar()
#define endl pc('\n')
#define sf scanf
#define pf printf

inline int read()
{
    int x=0,w=0;char ch=0;while(!isdigit(ch)){w|=ch=='-';ch=getchar();}while(isdigit(ch))x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
    return w?-x:x;
}
inline void write(int x){if(x<0)putchar('-'),x=-x;if(x>9)write(x/10);putchar(x%10+'0');}

inline ll powmod(ll a,ll b){ll res=1;a%=mod;assert(b>=0);for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res%mod;}
inline ll gcdll(ll a,ll b){return b?gcdll(b,a%b):a;}
const int dx[]={0,1,0,-1,1,-1,-1,1};
const int dy[]={1,0,-1,0,-1,-1,1,1};
/************************************************************begin************************************************************/
const int maxn=110,maxm=510;

int n,m,a[maxn][maxm],dp[maxn][maxm];
pair<int,int> pre[maxn][maxm];

inline int sol(int x,int y)
{
    if(y<1||y>m) return dp[x][y]=inf;
    if(dp[x][y]!=-1) return dp[x][y]; else dp[x][y]=0;

    int res=sol(x-1,y)+a[x][y];
    dp[x][y]=res;
    pre[x][y]={x-1,y};

    res=sol(x,y-1)+a[x][y];
    if(res<dp[x][y])
    {
        dp[x][y]=res;
        pre[x][y]={x,y-1};
    }

    res=sol(x,y+1)+a[x][y];
    if(res<dp[x][y])
    {
        dp[x][y]=res;
        pre[x][y]={x,y+1};
    }

    return dp[x][y];
}

inline void print(int x,int y)
{
    if(x>1) print(pre[x][y].fs,pre[x][y].sc);
    cout<<y<<' ';
}

int main()
{
    cin>>n>>m;
    rep1(i,n) rep1(j,m) cin>>a[i][j];

    ms(dp,-1);
    rep1(j,m) dp[1][j]=a[1][j];

    int ans=1;
    rep1(j,m) if(sol(n,j)<sol(n,ans)) ans=j;
    
    print(n,ans);

    return 0;
}
/*************************************************************end**************************************************************/

wa\(1\)程序

// #pragma gcc optimize(2)
// #pragma g++ optimize(2)
// #pragma comment(linker,"/stack:102400000,102400000")

// #include <bits/stdc++.h>
#include <map>
#include <set>
#include <list>
#include <array>
#include <cfenv>
#include <cmath>
#include <ctime>
#include <deque>
#include <mutex>
#include <queue>
#include <ratio>
#include <regex>
#include <stack>
#include <tuple>
#include <atomic>
#include <bitset>
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <chrono>
#include <cstdio>
#include <cwchar>
#include <future>
#include <limits>
#include <locale>
#include <memory>
#include <random>
#include <string>
#include <thread>
#include <vector>
#include <cassert>
#include <climits>
#include <clocale>
#include <complex>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <ctgmath>
#include <cwctype>
#include <fstream>
#include <iomanip>
#include <numeric>
#include <sstream>
#include <ccomplex>
#include <cstdbool>
#include <iostream>
#include <typeinfo>
#include <valarray>
#include <algorithm>
#include <cinttypes>
#include <cstdalign>
#include <stdexcept>
#include <typeindex>
#include <functional>
#include <forward_list>
#include <system_error>
#include <unordered_map>
#include <unordered_set>
#include <scoped_allocator>
#include <condition_variable>
// #include <conio.h>
// #include <windows.h>
using namespace std;

typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
typedef float fl;
typedef double ld;
typedef long double ld;
typedef pair<int,int> pii;
#if (win32) || (win64) || (__win32) || (__win64) || (_win32) || (_win64) || (windows)
#define lld "%i64d"
#define llu "%i64u"
#else
#define lld "%lld"
#define llu "%llu"
#endif
#define ui(n) ((unsigned int)(n))
#define ll(n) ((long long)(n))
#define ull(n) ((unsigned long long)(n))
#define fl(n) ((float)(n))
#define ld(n) ((double)(n))
#define ld(n) ((long double)(n))
#define char(n) ((char)(n))
#define bool(n) ((bool)(n))
#define fixpoint(n) fixed<<setprecision(n)

const int inf=1061109567;
const int ninf=-1044266559;
const ll linf=4557430888798830399;
const ld eps=1e-15;
#define mod (1000000007)
#define pi (3.1415926535897932384626433832795028841971)

/*
#define mb_len_max 5
#define shrt_min (-32768)
#define shrt_max 32767
#define ushrt_max 0xffffu
#define int_min (-2147483647 - 1)
#define int_max 2147483647
#define uint_max 0xffffffffu
#define long_min (-2147483647l - 1)
#define long_max 2147483647l
#define ulong_max 0xfffffffful
#define llong_max 9223372036854775807ll
#define llong_min (-9223372036854775807ll - 1)
#define ullong_max 0xffffffffffffffffull
*/

#define mp make_pair
#define mt make_tuple
#define all(a) (a).begin(),(a).end()
#define pall(a) (a).rbegin(),(a).rend()
#define log2(x) log(x)/log(2)
#define log(x,y) log(x)/log(y)
#define sz(a) ((int)(a).size())
#define rep(i,n) for(int i=0;i<((int)(n));i++)
#define rep1(i,n) for(int i=1;i<=((int)(n));i++)
#define repa(i,a,n) for(int i=((int)(a));i<((int)(n));i++)
#define repa1(i,a,n) for(int i=((int)(a));i<=((int)(n));i++)
#define repd(i,n) for(int i=((int)(n))-1;i>=0;i--)
#define repd1(i,n) for(int i=((int)(n));i>=1;i--)
#define repda(i,n,a) for(int i=((int)(n));i>((int)(a));i--)
#define repda1(i,n,a) for(int i=((int)(n));i>=((int)(a));i--)
#define for(i,a,n,step) for(int i=((int)(a));i<((int)(n));i+=((int)(step)))
#define repv(itr,v) for(__typeof((v).begin()) itr=(v).begin();itr!=(v).end();itr++)
#define repv(i,v) for(auto i:v)
#define repe(i,v) for(auto &i:v)
#define ms(x,y) memset(x,y,sizeof(x))
#define mc(x) ms(x,0)
#define minf(x) ms(x,63)
#define mcp(x,y) memcpy(x,y,sizeof(y))
#define sqr(x) ((x)*(x))
#define un(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define filein(x) freopen(x,"r",stdin)
#define fileout(x) freopen(x,"w",stdout)
#define fileio(x)\
    freopen(x".in","r",stdin);\
    freopen(x".out","w",stdout)
#define filein2(filename,name) ifstream name(filename,ios::in)
#define fileout2(filename,name) ofstream name(filename,ios::out)
#define file(filename,name) fstream name(filename,ios::in|ios::out)
#define pause system("pause")
#define cls system("cls")
#define fs first
#define sc second
#define pc(x) putchar(x)
#define gc(x) x=getchar()
#define endl pc('\n')
#define sf scanf
#define pf printf

inline int read()
{
    int x=0,w=0;char ch=0;while(!isdigit(ch)){w|=ch=='-';ch=getchar();}while(isdigit(ch))x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
    return w?-x:x;
}
inline void write(int x){if(x<0)putchar('-'),x=-x;if(x>9)write(x/10);putchar(x%10+'0');}

inline ll powmod(ll a,ll b){ll res=1;a%=mod;assert(b>=0);for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res%mod;}
inline ll gcdll(ll a,ll b){return b?gcdll(b,a%b):a;}
const int dx[]={0,1,0,-1,1,-1,-1,1};
const int dy[]={1,0,-1,0,-1,-1,1,1};
/************************************************************begin************************************************************/
const int maxn=110,maxm=510;

int n,m,a[maxn][maxm],dp[maxn][maxm];
pair<int,int> pre[maxn][maxm];

inline int sol(int x,int y)
{
    if(y<1||y>m) return dp[x][y]=inf;
    if(dp[x][y]!=-1) return dp[x][y]; else dp[x][y]=0;

    int res=sol(x-1,y);
    dp[x][y]=res;
    pre[x][y]={x-1,y};

    res=sol(x,y-1);
    if(res<dp[x][y])
    {
        dp[x][y]=res;
        pre[x][y]={x,y-1};
    }

    res=sol(x,y+1);
    if(res<dp[x][y])
    {
        dp[x][y]=res;
        pre[x][y]={x,y+1};
    }

    dp[x][y]+=a[x][y];
    return dp[x][y];
}

inline void print(int x,int y)
{
    if(x>1) print(pre[x][y].fs,pre[x][y].sc);
    cout<<y<<' ';
}

int main()
{
    cin>>n>>m;
    rep1(i,n) rep1(j,m) cin>>a[i][j];

    ms(dp,-1);
    rep1(j,m) dp[1][j]=a[1][j];

    int ans=1;
    rep1(j,m) if(sol(n,j)<sol(n,ans)) ans=j;
    
    print(n,ans);

    return 0;
}
/*************************************************************end**************************************************************/