The longest zig-zag subsequence

类似于最长不降子序列。
找到最长的大小相间的子序列。
dp[k] 表示一个结构体，以k号结尾的最长zig-zag子序列长度，和期待下一个数是大还是小。

struct node{int len, state; //state, 0表示下一个数必须大，1表示必须小，2表示都可以
}

状态转移方程
dp[k].len = max( num[k]能接到dp[i]后面 ? dp[i].len+1 : 1 ), 0<=i<=k-1
边界

dp[0].len = 1;
dp[0].state = 2;

处理顺序
从左往右

#include <cstdio>struct node{int len, state;
};int main(){int n, ans = 1;scanf("%d", &n);int num[n];for(int i=0; i<n; i++) scanf("%d", &num[i]);node dp[n];dp[0].len = 1;dp[0].state = 2;for(int i=1; i<n; i++){dp[i].len = -1;for(int j=0; j<i; j++){node temp;if(dp[j].state==0){if(num[i]>num[j]){temp.len = dp[j].len+1;temp.state = 1;}else{temp.len = 1;temp.state = 2;}}else if(dp[j].state==1){if(num[i]<num[j]){temp.len = dp[j].len+1;temp.state = 0;}else{temp.len = 1;temp.state = 2;}}else{if(num[i]>num[j]){temp.len = dp[j].len + 1;temp.state = 1;}else if(num[i]<num[j]){temp.len = dp[j].len + 1;temp.state = 0;}else{temp.len = 1;temp.state = 2;}}if(temp.len > dp[i].len) dp[i] = temp;}if(dp[i].len > ans) ans = dp[i].len;}printf("%d", ans);return 0;
}

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