Codeforces Round #190 (Div. 1): E. Ciel and Gondolas（决策单调性DP+wqs二分）

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E. Ciel and Gondolas

 

题意：

bzoj5311：https://www.lydsy.com/JudgeOnline/problem.php?id=5311

同一道题目，但是bzoj可能需要读入挂

思路：

决策单调性Ⅰ：四边形不等式

wqs二分

没什么可讲的了

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<map>
#include<string>
#include<math.h>
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
#define LL long long
#define mod 1000000007
int n, k, sum[4005][4005];
typedef struct Res
{
	int id;
	int l, r;
}Res;
Res q[4005], now;
int dp[4005], cnt[4005];
int Cal(int x, int y)
{
	return (sum[y][y]-sum[x-1][y]-sum[y][x-1]+sum[x-1][x-1])/2;
}
int Check(int i, int j, int k)
{
	int a, b;
	a = dp[i]+Cal(i+1, k);
	b = dp[j]+Cal(j+1, k);
	if(a<b || a==b && cnt[i]<cnt[j])
		return 1;
	return 0;
}
int Sech(int i, int j, int c)
{
	int l, r, m;
	l = q[c].l, r = n;
	while(l<r)
	{
		m = (l+r)/2;
		if(Check(i, j, m))
			r = m;
		else
			l = m+1;
	}
	return r;
}
int Jud(int val)
{
	int L, R, i, x;
	L = 1, R = 0;
	now.id = 0, now.l = 1, now.r = n;
	q[++R] = now;
	for(i=1;i<=n;i++)
	{
		if(q[L].l>q[L].r)
			L++;
		q[L].l++;
		dp[i] = dp[q[L].id]+Cal(q[L].id+1, i)+val;
		cnt[i] = cnt[q[L].id]+1;
		if(R>=L && Check(q[R].id, i, n))
			continue;
		while(R>=L && Check(i, q[R].id, q[R].l))
			R--;
		if(R>=L)
		{
			x = Sech(i, q[R].id, R);
			q[R].r = x-1;
			now.id = i, now.l = x, now.r = n;
		}
		else
			now.id = i, now.l = i+1, now.r = n;
		q[++R] = now;
	}
	return cnt[n];
}
int main(void)
{
	int i, j, x, l, r, m;
	scanf("%d%d", &n, &k);
	for(i=1;i<=n;i++)
	{
		for(j=1;j<=n;j++)
		{
			scanf("%d", &x);
			sum[i][j] = sum[i][j-1]+sum[i-1][j]-sum[i-1][j-1]+x;
		}
	}
	l = 0, r = sum[n][n];
	while(l<r)
	{
		m = (l+r)/2;
		if(Jud(m)<=k)
			r = m;
		else
			l = m+1;
	}
	Jud(r);
	printf("%d\n", dp[n]-k*r);
	return 0;
}
/*
9 2
0 0 0 0 1 1 1 1 1
0 0 0 0 1 1 1 1 1
0 0 0 0 1 1 1 1 1
0 0 0 0 1 1 1 1 1
1 1 1 1 0 0 1 1 1
1 1 1 1 0 0 1 1 1
1 1 1 1 1 1 0 0 0
1 1 1 1 1 1 0 0 0
1 1 1 1 1 1 0 0 0
*/