新生多校第6场 LLM找对象（DP+离散化）

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题解：

dp[i][j][0]:前i天已经j天不穿拖鞋且第i天穿了拖鞋的最大值

dp[i][j][1]:前i天已经j天不穿拖鞋且第i天没穿拖鞋的最大值

状态转移：

dp[i][j][0]=max(dp[i-1][j][0],dp[i-1][j][1]);

dp[i][j][1]=max(dp[i][j][1],dp[i-1][j-1][0]+d[i]);(d[i]表示第i天有多少个妹子)

#include<set>#include<map>       #include<stack>              #include<queue>              #include<vector>      #include<string>    #include<math.h>     #include<stdio.h>              #include<iostream>              #include<string.h>              #include<stdlib.h>      #include<algorithm>     #include<functional>      using namespace std;typedef long long ll;#define inf  1000000000         #define mod 1000000007               #define maxn  1705   #define PI acos(-1.0) #define lowbit(x) (x&-x)   #define eps 1e-9  int dp[maxn][maxn][2], a[maxn*100], b[maxn*100], c[maxn*100], d[maxn*100];int main(void){int n, k, i, j, cnt, p;while (scanf("%d%d", &n, &k) != EOF){cnt = 0;p = 1;memset(a, 0, sizeof(a));memset(c, 0, sizeof(c));memset(d, 0, sizeof(d));memset(dp, 0, sizeof(dp));for (i = 1;i <= n;i++)scanf("%d", &a[i]), b[i] = a[i];k = min(k, n);sort(b + 1, b + n + 1);int num = unique(b + 1, b + n + 1) - b - 1;c[1] = b[1];cnt = 1;for (i = 2;i <= num;i++){if (b[i] - b[i - 1] > 1)c[++cnt] = b[i] - 1;c[++cnt] = b[i];}for (i = 1;i <= n;i++)a[i] = lower_bound(c + 1, c + cnt + 1, a[i]) - c;sort(a + 1, a + n + 1);for (i = 1;i <= max(n, cnt);i++)d[a[i]]++;for (i = 1;i <= max(cnt, n);i++){for (j = 1;j <= k;j++){if (j > i)break;dp[i][j][0] = max(dp[i - 1][j][0], dp[i - 1][j][1]);dp[i][j][1] = max(dp[i][j][1], dp[i - 1][j - 1][0] + d[i]);}}int ans=0, tmp;for (i = 0;i <= k;i++){tmp = max(dp[max(n, cnt)][i][1], dp[max(n, cnt)][i][0]);ans = max(ans, tmp);}printf("%d\n", ans);}return 0;}

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