最长递增子序列问题(费用流)
http://acm.nefu.edu.cn/JudgeOnline/problemShow.php?problem_id=487
费用流,每次沿着最长边增广
//http://www.cnblogs.com/IMGavin/ #include <iostream> #include <stdio.h> #include <cstdlib> #include <cstring> #include <queue> #include <vector> #include <map> #include <stack> #include <set> #include <bitset> #include <algorithm> using namespace std; typedef long long LL; #define gets(A) fgets(A, 1e8, stdin) const int INF = 0x3F3F3F3F, N = 20008, MOD = 1003, M = 2000000; int len; int dp[N];//dp[i]表示当前状态若最长子序列长度为i+1时,序列最后位置数字(尽可能小) int LIS(int *a,int n){//n为a的长度,a为待处理序列,返回a最长子序列长度 int i,j,len,pos; dp[0]=a[0]; len=0; for(i=1;i<n;i++){ pos=lower_bound(dp,dp+len+1,a[i])-dp; dp[pos]=a[i]; if(pos>len){ len++; } } len++; return len; } struct Node{ int u, v, cap, cost; int next; }edge[M];//有向图,u到v的容量,费用 int tot; int head[N], pre[N], path[N], dis[N]; bool inq[N]; void init(){ tot = 0; memset(head, -1, sizeof(head)); } void add(int u, int v, int cap, int cost){ edge[tot].u = u; edge[tot].v = v; edge[tot].cap = cap; edge[tot].cost = cost; edge[tot].next = head[u]; head[u] = tot++; edge[tot].u = v; edge[tot].v = u; edge[tot].cap = 0; edge[tot].cost = -cost; edge[tot].next = head[v]; head[v] = tot++; } bool SPFA(int st, int des){//计算最小费用 memset(inq, 0, sizeof(inq)); memset(dis, 0x3f, sizeof(dis)); queue <int> q; q.push(st); dis[st] = 0; inq[st] = true; while(!q.empty()){ int u = q.front(); q.pop(); inq[u] = false; for(int i = head[u]; ~i; i = edge[i].next){ int v = edge[i].v; if(edge[i].cap > 0 && dis[v] > dis[u] + edge[i].cost){ dis[v] = dis[u] + edge[i].cost; pre[v] = u; path[v] = i; if(!inq[v]){ inq[v] = true; q.push(v); } } } } return dis[des] == 1 - len; } int EdmondsKarp(int st, int des){//最小费用最大流 int mincost = 0, flow = 0;//最小费用与流量 while(SPFA(st, des)){ int f = INF; for(int i = des; i != st; i = pre[i]){ if(f > edge[path[i]].cap){ f = edge[path[i]].cap; } } for(int i = des; i != st; i = pre[i]){ edge[path[i]].cap -= f; edge[path[i]^1].cap += f; } mincost += f * dis[des]; flow += f; } return flow; } int a[N]; int in[N], out[N]; int main(){ int n; while(~scanf("%d", &n)){ memset(in, 0, sizeof(in)); memset(out, 0, sizeof(out)); for(int i = 1; i <= n; i++){ scanf("%d", &a[i]); } len = LIS(a + 1, n); printf("%d\n", len); init(); for(int i = 1; i < n; i++){ for(int j = i + 1; j <= n; j++){ if(a[i] < a[j]){ add(i, j, 1, -1); out[i]++; in[j]++; } } } for(int i = 1; i <= n; i++){ if(!in[i]){ add(0, i, 1, 0); } if(!out[i]){ add(i, n + 1, 1, 0); } } int ans = EdmondsKarp(0, n + 1); printf("%d\n", ans); add(0, 1, INF, 0); add(n, n + 1, INF, 0); ans += EdmondsKarp(0, n + 1); printf("%d\n", ans); } return 0; }