UVALive 5983 二分答案+dp

Posted 2020-08-04 stupid_one

想了很久都想不出怎么dp，然后发现有些例子，如果你开始不确定起始值的话，是不能dp的，每种状态都有可能，所以只能二分一个答案，确定开始的val值，来dp了。

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;

#include <iostream>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <string>
const int maxn=500+20;
LL dp[maxn][maxn];
int n,m;
int a[maxn][maxn];
bool check (LL val)
{
    dp[1][1]=val;
    for (int i=1;i<=n;++i)
    {
        for (int j=1;j<=m;++j)
        {
            if (i==1 && j==1)continue;
            if (dp[i-1][j]<=0) dp[i-1][j]=-inf; //如果小于0，证明已经不能走了
            if (dp[i][j-1]<=0) dp[i][j-1]=-inf;
            if (dp[i-1][j]<=0 && dp[i][j-1]<=0) dp[i][j]=-inf;
            else dp[i][j]=max(dp[i-1][j],dp[i][j-1])+a[i][j];
        }
    }
    return dp[n][m]>0;
}
void work ()
{
    scanf("%d%d",&n,&m);
    for (int i=1;i<=n;++i)
        for (int j=1;j<=m;++j)
            scanf("%d",&a[i][j]);
    LL begin=1,end=1LL*500*500*1000+20;
    while (begin<=end)
    {
        LL mid = (begin+end)>>1;
        //printf ("%d\\n",mid);
        if (check(mid))
            end=mid-1;
        else begin=mid+1;
    }
    printf ("%lld\\n",begin);
    //check(998);
    //check(3);
     //printf ("%d\\n",check(1002));
//    printf ("%lld\\n",dp[2][4]);
    return ;
}

int main()
{
#ifdef local
    freopen("data.txt","r",stdin);
#endif
    for (int i=1;i<=500;++i)
    {
        dp[0][i]=-inf;
        dp[i][0]=-inf;
    }
    dp[0][0]=-inf;
    dp[0][1]=0;
    dp[1][0]=0;
    int t;
    scanf("%d",&t);
    while (t--) work();
    return 0;
}

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