【TopCoder】SRM 680 DIV 2

1. BearPair之bigDistance
1.1 题目概述
在 <= 50的字符串中找位置i，j 满足
(1) s[i] != s[j];
(2) abs(i-j)尽可能大。
若不存在返回-1， 否则返回最大值。

1.2 基本思路
没什么好说的，串长这么短 O(n^2)直接A了。

1.3 代码

class BearPair {
public:    
    int pos[26];
    
    int bigDistance(string s) {
        int len = s.length();
        int mx = -1;
        
        rep(i, 0, len) {
            rep(j, 0, len) {
                if (s[j]==s[i])
                    continue;
                
                mx = max(mx, abs(j-i));
            }
        }
        
        return mx;
    }
};

2. BearChairs之findPositions
2.1 题目描述
一家餐馆，椅子排成一行从1开始，足够长，有N个元素的数组atLeast表示第i个顾客希望他的椅子编号大于等于atLeast[i]。
同时，需要保证任意两个顾客的椅子间相隔至少为d，并且顾客最终得到的椅子编号越小越好。这里，顾客的请求是有序的。
求最终的椅子编号。

2.2 基本思路
基本想法是贪心，第k个顾客最好的可能性是得到atLeast[k]编号的椅子。
如果此时该顾客与前k-1个顾客的间隔都大于等于d，那么答案就是atLeast[k]。
假设不满足，如果我们可以使前k-1个顾客的椅子编号按升序排列，那么当answer[j]-d<answer[k] && answer[k]<answer[j]+d
时，下一个最优的候选项即为answer[j]+d，而该候选项一定满足answer[1..j]。仅需判断其是否满足answer[j+1..k-1]即可。
因此，使用set维护已经确定的最优位置，即可解。

2.3 代码

class BearChairs {
public:
    static const int maxn = 1005;
    
    vi findPositions(vi vc, int d) {
        int sz = SZ(vc), tmp;
        vi ret;
        sti st;
        sti::iterator iter;
        
        rep(i, 0, sz) {
            int pos = vc[i];
            for (iter=st.begin(); iter!=st.end(); ++iter) {
                tmp = *iter;
                if (tmp-d<pos && pos<tmp+d) {
                    pos = tmp + d;
                }
            }
            
            ret.pb(pos);
            st.insert(pos);
        }
        
        return ret;
    }
    
};

2.4 数据发生器

import sys
import string
from random import randint

    
def GenData(fileName):
    with open(fileName, "w") as fout:
        t = 1
        bound = 10**6
        # fout.write("%d
" % (t))
        for tt in xrange(t):
            n = randint(1, 1000)
            atLeast = []
            for i in xrange(n):
                x = randint(1, bound)
                atLeast.append(x)
            fout.write(" ".join(map(str, atLeast)) + "
")
            d = randint(1, 10**6)
            fout.write("%d
" % (d))
                
        
def MovData(srcFileName, desFileName):
    with open(srcFileName, "r") as fin:
        lines = fin.readlines()
    with open(desFileName, "w") as fout:
        fout.write("".join(lines))

        
def CompData():
    print "comp"
    srcFileName = "F:Qt_prjhdojdata.out"
    desFileName = "F:workspacecpp_hdojdata.out"
    srcLines = []
    desLines = []
    with open(srcFileName, "r") as fin:
        srcLines = fin.readlines()
    with open(desFileName, "r") as fin:
        desLines = fin.readlines()
    n = min(len(srcLines), len(desLines))-1
    for i in xrange(n):
        ans2 = int(desLines[i])
        ans1 = int(srcLines[i])
        if ans1 > ans2:
            print "%d: wrong" % i

            
if __name__ == "__main__":
    srcFileName = "F:Qt_prjhdojdata.in"
    desFileName = "F:workspacecpp_hdojdata.in"
    GenData(srcFileName)
    MovData(srcFileName, desFileName)
    
    

3. BearFair2之isFair
3.1 题目描述
有一个包含n(n%3 == 0)个元素的集合，其中的元素都在[1,b]区间，其中mod3等于0、1、2的元素个数均为n/3。
现有两个长度均为q数组upTo, quantity表示集合中的元素在区间[1, upTo[i]]的数目为quantity[i]。
判定是否存在这样一个集合满足upTo和quantity。
其中upTo的元素在[1,b]区间内，quantity的元素在[1,n]区间内，b在区间[1,1000]内。

3.2 基本思路
这是一个判定问题，首先以upTo作为first, quantity作为second重新构建pair数组，排序后，可以做初步的剪枝。
但仍需进一步判定是否存在这样的集合。基本思路是网络流，难点是如何构建图。
对pair树组的每个结点编号1001...1001+q-1
对1..b编号为1...b
对%3==0作结点mod0
对%3==1作结点mod1
对%3==2作结点mod2
可以这样建图：
1）st对pair结点建边，容量为对应的quantity[i]-quantity[i-1]；
2）pair结点对它包含的区间中的每个结点建边，容量为1；
3）编号1..b对其对应的modx建边，容量为1；
4）modx对ed建边，容量为n/3。
需要注意pair数组可能没有覆盖[1，b]，对余下的区间仍需要建边，与上述类似。
然后，判定最大流是否为n即可。
使用Dinic解该网络流。

3.3 代码

class BearFair2 {

    typedef struct {
        int v, f, nxt;
    } edge_t;

public:    
    static const int INF = 0x3f3f3f3f;
    static const int maxv = 1100;
    static const int maxe = 1e5+5;
    static const int st = maxv - 1;
    static const int ed = maxv - 2;
    static const int mod0 = maxv - 3;
    static const int mod1 = maxv - 4;
    static const int mod2 = maxv - 5;
    
    int head_[maxv];
    int head[maxv], l;
    int Q[maxv];
    int dis[maxv];
    edge_t E[maxe];
    int n, b;
    
    void init() {
        memset(head, -1, sizeof(head));
        l = 0;
    }
    
    void addEdge(int u, int v, int c) {
        E[l].v = v;
        E[l].f = c;
        E[l].nxt = head[u];
        head[u] = l++;
        
        E[l].v = u;
        E[l].f = 0;
        E[l].nxt = head[v];
        head[v] = l++;
    }
    
    bool bfs() {
        int l = 0, r = 0;
        int u, v, k;
        
        memset(dis, 0, sizeof(dis));
        Q[r++] = st;
        dis[st] = 1;
        
        while (l < r) {
            u = Q[l++];
            for (k=head[u]; k!=-1; k=E[k].nxt) {
                v = E[k].v;
                if (E[k].f && !dis[v]) {
                    dis[v] = dis[u] + 1;
                    if (v == ed)
                        return false;
                    Q[r++] = v;
                }
            }
        }
        
        return true;
    }
    
    int dfs(int u, int val) {
        if (val==0 || u==ed)
            return val;
        
        int ret = 0, tmp;
        int v;
        
        for (int& k=head_[u]; k!=-1; k=E[k].nxt) {
            v = E[k].v;
            if (E[k].f && dis[v]==dis[u]+1 && (tmp=dfs(v, min(val, E[k].f)))>0) {
                ret += tmp;
                val -= tmp;
                E[k].f -= tmp;
                E[k^1].f += tmp;
                if (val == 0)
                    break;
            }
        }
        
        return ret;
    }
    
    int Dinic() {
        int ret = 0, tmp;
        
        while (1) {
            if (bfs())
                break;
            
            memcpy(head_, head, sizeof(head));
            while (1) {
                tmp = dfs(st, INF);
                if (tmp == 0)
                    break;
                ret += tmp;
            }
        }
        
        return ret;
    }
    
    string isFair(int n, int b, vector <int> upTo, vector <int> quan) {
        this->n = n;
        this->b = b;
        init();
        
        vpii vp;
        int sz = SZ(upTo);
        
        rep(i, 0, sz) {
            vp.pb(mp(upTo[i], quan[i]));
        }
        
        sort(all(vp));
        rep(i, 0, sz) {
            if (vp[i].sec > vp[i].sec)
                return "unfair";
            
            if (i && vp[i].sec<vp[i-1].sec)
                return "unfair";
            
            if (i && vp[i].fir==vp[i-1].fir && vp[i].sec!=vp[i-1].sec)
                return "unfair";
        }
        
        int fr = 1, pm = 0;
        
        rep(i, 0, sz) {
            addEdge(st, 1001+i, vp[i].sec-pm);
            while (fr <= vp[i].fir) {
                addEdge(1001+i, fr, 1);
                ++fr;
            }
            pm = vp[i].sec;
        }
        
        if (fr <= b) {
            addEdge(st, 1001+sz, n-pm);
            while (fr <= b) {
                addEdge(1001+sz, fr, 1);
                ++fr;
            }
        }
        
        for (int i=1; i<=b; i+=3)
            addEdge(i, mod1, 1);
        for (int i=2; i<=b; i+=3)
            addEdge(i, mod2, 1);
        for (int i=3; i<=b; i+=3)
            addEdge(i, mod0, 1);
        
        addEdge(mod0, ed, n/3);
        addEdge(mod1, ed, n/3);
        addEdge(mod2, ed, n/3);
        
        int flow = 0;
        
        flow = Dinic();
        if (flow == n)
            return "fair";
        else
            return "unfair";
    }
};

3.4 数据发生器

import sys
import string
from random import randint

    
def GenData(fileName):
    with open(fileName, "w") as fout:
        t = 1
        bound = 10**6
        # fout.write("%d
" % (t))
        for tt in xrange(t):
            n = randint(1, 16) * 3
            b = randint(1, n)
            fout.write("%d %d
" % (n, b))
            q = randint(1, 50)
            upTo = []
            for i in xrange(q):
                x = randint(1, b)
                upTo.append(x)
            fout.write(" ".join(map(str, upTo)) + "
")
            quantity = []
            for i in xrange(q):
                x = randint(0, n)
                quantity.append(x)
            fout.write(" ".join(map(str, quantity)) + "
")
                
        
def MovData(srcFileName, desFileName):
    with open(srcFileName, "r") as fin:
        lines = fin.readlines()
    with open(desFileName, "w") as fout:
        fout.write("".join(lines))

        
def CompData():
    print "comp"
    srcFileName = "F:Qt_prjhdojdata.out"
    desFileName = "F:workspacecpp_hdojdata.out"
    srcLines = []
    desLines = []
    with open(srcFileName, "r") as fin:
        srcLines = fin.readlines()
    with open(desFileName, "r") as fin:
        desLines = fin.readlines()
    n = min(len(srcLines), len(desLines))-1
    for i in xrange(n):
        ans2 = int(desLines[i])
        ans1 = int(srcLines[i])
        if ans1 > ans2:
            print "%d: wrong" % i

            
if __name__ == "__main__":
    srcFileName = "F:Qt_prjhdojdata.in"
    desFileName = "F:workspacecpp_hdojdata.in"
    GenData(srcFileName)
    MovData(srcFileName, desFileName)