最长递增子序列（LIS）

#pragma comment(linker,"/STACK:102400000,102400000")
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>
using namespace std;
#define clc(a, b) memset(a, b, sizeof(a))
const int inf = 0x3f;
const int INF = 0x3f3f3f3f;
const int maxn = 1000;
int n, a[maxn], dp[maxn];

int LIS()
{
int i, j, k = 0;
for(i = 0; i < n; i++)
{
dp[i] = 1;
for(j = 0; j < i; j++)
{
if(a[i] > a[j] && dp[i] < dp[j] + 1)
{
dp[i] = dp[j] + 1;
}
}
k = dp[i] > k ? dp[i] : k;
}
return k;
}
int main()
{
while(~scanf("%d", &n))
{
clc(dp, 0);
for(int i = 0; i < n; i++)
scanf("%d", &a[i]);
printf("LIS = ");
printf("%d\n", LIS());
}
}

#pragma comment(linker,"/STACK:102400000,102400000")
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>
using namespace std;
#define clc(a, b) memset(a, b, sizeof(a))
const int inf = 0x3f;
const int INF = 0x3f3f3f3f;
const int maxn = 1000;
const int mod = 1000000007;
int n, m, a[maxn], dp[maxn][maxn], sum[maxn];
//sum 记录长度为i的子序列个数 dp[i][j] 记录从i开始长度为j的个数
int LIS()
{
int i, j, k;
for(i = 1; i <= n; i++)
{
dp[i][1] = 1;
sum[1] = (dp[i][1] + sum[1]) % mod;
for(k = 2; k <= i; k++)
{
for(j = 1; j < i; j++)
{
if(a[i] > a[j])
{
dp[i][k] = (dp[i][k] + dp[j][k-1]) % mod;
}
}
sum[k] = (sum[k] + dp[i][k]) % mod;
//printf("i = %d, sum[%d] = %d\n", i, k, sum[k]);
}
}
return 0;
}
int main()
{
int q;
while(~scanf("%d %d", &n, &q))//n 数组长度, q个询问
{
clc(dp, 0);
clc(sum, 0);
for(int i = 1; i <= n; i++)
scanf("%d", &a[i]);
LIS();
while(q--)
{
scanf("%d", &m);
printf("%d\n", sum[m]);
}
}
return 0;
}

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>

using namespace std;

const int inf = 0x3f;
const int INF = 0x3f3f3f3f;
const int maxn = 1e5+5;

int lis[maxn], a[maxn], n;

int BinSearch(int len, int x)
{
int left = 0, right = len - 1;
while(left <= right)
{
int mid = (left + right) / 2;
if(lis[mid] <= x)
{
left = mid + 1;
}
else
{
right = mid - 1;
}
}
return left;
}
int LIS()
{
lis[0] = a[0];
int len = 1;
for(int i = 1; i < n; i++)
{
if(a[i] > lis[len-1])
{
lis[len++] = a[i];
}
else
{
int pos = BinSearch(len, a[i]);
lis[pos] = a[i];
}
}
return len;
}
int main()
{
while(~scanf("%d", &n))
{
for(int i = 0; i < n; i++)
{
scanf("%d", &a[i]);
}

int ans = LIS();
printf("%d\n", ans);
}
}