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POJ 2533 —— Longest Ordered Subsequence 最长上升子序列裸题

2016-02-20 23:49 447 查看
原题:http://poj.org/problem?id=2533

题意:求最长递增子序列

注意:n = 0 n = 1 答案都是1

O(n²)

#include<cstdio>
const int maxn = 1100;
int n;
int dp[maxn];
int a[maxn];
int main()
{
while(~scanf("%d", &n))
{
int ans = 0;
for(int i = 1;i<=n;i++)
{
scanf("%d", &a[i]);
dp[i] = 1;
}
if(n == 0 || n == 1)
{
printf("1\n");
continue;
}
for(int i = 2;i<=n;i++)
{
dp[i] = 1;
for(int j = 1;j<i;j++)
{
if(a[i] > a[j] && dp[i] < dp[j] + 1)
dp[i] = dp[j] + 1;
if(ans < dp[i])
ans = dp[i];
}
}
printf("%d\n", ans);
}
return 0;
}


O(nlogn)

<span style="font-size:10px;">#include<cstdio>
const int maxn = 1100;
int stack[maxn];
int n;
int main()
{
while(~scanf("%d", &n))
{
int top = 0;
stack[0] = -1;
for(int i = 1;i<=n;i++)
{
int temp;
scanf("%d", &temp);
if(temp > stack[top])
stack[++top] = temp;
else
{
int l = 1, r = top;
int mid;
while(l <= r)
{
mid = (l + r) / 2;
if(temp > stack[mid])
l = mid + 1;
else
r = mid - 1;
}
stack[l] = temp;
}
}
printf("%d\n", top);
}
return 0;
}</span>


用lower_bound()

#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn = 1100;
int a[maxn], stack[maxn];
int n;

int main()
{
while(~scanf("%d", &n))
{
for(int i = 0;i<n;i++)
scanf("%d", &a[i]);
int top = 0;
stack[0] = -1;
for(int i = 0;i<n;i++)
{
if(a[i] > stack[top])
{
stack[++top] = a[i];
continue;
}
int pos = lower_bound(stack, stack+top, a[i]) - stack;
stack[pos] = a[i];
}
printf("%d\n", top);
}
return 0;
}
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