uva1609 Foul Play

思维 创造条件使一轮比赛之后仍满足1号打败至少一半，并剩下至少一个t'

紫书上的思路很清晰
阶段1,3保证黑色至少消灭1半

#include<cstdio>
#include<vector>
using namespace std;

const int maxn = 1024 + 5;
char table[maxn][maxn];

int main() {
  int n;
  while(scanf("%d", &n) == 1) {
    for(int i = 1; i <= n; i++) scanf("%s", table[i]+1);

    vector<int> win, lose; // teams that team 1 win/lose against.
    for(int i = 2; i <= n; i++)
      if(table[1][i] == '1') win.push_back(i);
      else lose.push_back(i);

    int nt = n;

    while(nt > 1) {
      vector<int> win2, lose2, final; // phase 3/4

      // Phase 1
      for(int i = 0; i < lose.size(); i++) {
        int tlose = lose[i];
        bool matched = false;
        for(int j = 0; j < win.size(); j++) {
          int& twin = win[j];
          if(twin > 0 && table[twin][tlose] == '1') {  //尽量通过配对消灭黑
            printf("%d %d
", twin, tlose);
            win2.push_back(twin); // go to the next round
            twin = 0; // not available   本轮已经配对
            matched = true;
            break;
          }
        }
        if(!matched) final.push_back(tlose); // to phase 3/4
      }

      // Phase 2
      bool first = true;
      for(int i = 0; i < win.size(); i++) {
        int twin = win[i];
        if(twin > 0) {
          if(first) { printf("1 %d
", twin);first = false; }
          else final.push_back(twin);
        }
      }

      // Phase 3/4
      for(int i = 0; i < final.size(); i += 2) {    //3,4阶段可以一起处理
        printf("%d %d
", final[i], final[i+1]);
        int keep = final[i];
        if(table[final[i+1]][keep] == '1') keep = final[i+1];
        if(table[1][keep] == '1') win2.push_back(keep);
        else lose2.push_back(keep);
      }
      win = win2;
      lose = lose2;
      nt >>= 1;
    }
  }
  return 0;
}