UVa 10131 - Is Bigger Smarter?

题目链接：UVa 10131 - Is Bigger Smarter?

LIS变形。讲解看这里。

先按重量递增排一下序。

然后用记忆化搜索或者递推都可以做。

记忆化搜索需要注意dp数组初值与非初值的区别。

还要注意排序后可能存在两个重量相同的排在一起，而题目要求的是重量严格递增。

两种方法用的时间差不多。

#include <iostream>
#include <stdio.h>
#include <algorithm>

using namespace std;

const int MAX_N = 1000 + 50;
struct Ele
{
    int w,s;
    int i;
};

Ele ele[MAX_N];
int dp[MAX_N];
int lis;

int cmp(const void *a, const void *b)
{
    Ele *_a = (Ele*)a;
    Ele *_b = (Ele*)b;
    return (_a -> w) - (_b -> w);
}
void outputLIS(int index)
{
    if(lis == 0)
        return;
    bool flag = false;
    if(dp[index] == lis)
    {
        flag = true;
        lis--;
    }
    outputLIS(index - 1);
    if(flag)
        cout << ele[index].i << endl;
}
int main()
{
    char str[1024];
    int num = 0;
    lis = 0;
    while(gets(str))
    {
        if(!str[0])
            break;
        sscanf(str,"%d%d",&ele[num].w,&ele[num].s);
        ele[num].i = num + 1;
        num++;
    }
    qsort(ele,num,sizeof(ele[0]),cmp);
    for(int i = 0;i < num;i++)
    {
        dp[i] = 1;
        for(int j = 0;j < i;j++)
        {
            if(ele[i].s < ele[j].s && ele[i].w != ele[j].w && dp[i] < dp[j] + 1)
            {
                dp[i] = dp[j] + 1;
                lis = max(lis,dp[i]);
            }
        }
    }
    cout << lis << endl;
    outputLIS(num - 1);
    return 0;
}

#include <iostream>
#include <stdio.h>
#include <algorithm>
#include <cstring>

using namespace std;

const int MAX_N = 1000 + 50;
struct Ele
{
    int w,s;
    int i;
};

Ele ele[MAX_N];
int dp[MAX_N];
int lis,num;

int cmp(const void *a, const void *b)
{
    Ele *_a = (Ele*)a;
    Ele *_b = (Ele*)b;
    return (_a -> w) - (_b -> w);
}
int DP(int i)
{
    if(dp[i] != 0)
        return dp[i];
    dp[i] = 1;
    for(int j = i + 1;j < num;j++)
    {
        if(ele[i].s > ele[j].s && ele[i].w != ele[j].w)
            dp[i] = max(dp[i],DP(j) + 1);
    }
    return dp[i];
}
void outputLIS(int index)
{
    if(lis == 0)
        return;
    if(dp[index] == lis)
    {
        cout << ele[index].i << endl;
        lis--;
    }
    outputLIS(index + 1);
}
int main()
{
    memset(dp,0,sizeof(dp));
    char str[1024];
    num = 0;
    lis = 0;
    while(gets(str))
    {
        if(!str[0])
            break;
        sscanf(str,"%d%d",&ele[num].w,&ele[num].s);
        ele[num].i = num + 1;
        num++;
    }
    qsort(ele,num,sizeof(ele[0]),cmp);
    for(int i = 0;i < num;i++)
        lis = max(lis,DP(i));
    cout << lis << endl;
    outputLIS(0);
    return 0;
}