UVa 1627 - Team them up

contents

  1. 1. Problem
  2. 2. Sample Input
  3. 3. Sample Output
  4. 4. Solution

Problem

現在有 2 個 team,每個 team 至少一個成員,同一個 team 成員之間必然會互相認識,不同 team 的成員之間則不一定。

給定他們互相認識的關係圖,請問他們可以分屬的 team 的情況,並且輸出 team 人數差距最少的那一組。

Sample Input

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2
5
3 4 5 0
1 3 5 0
2 1 4 5 0
2 3 5 0
1 2 3 4 0
5
2 3 5 0
1 4 5 3 0
1 2 5 0
1 2 3 0
4 3 2 1 0

Sample Output

1
2
3
4
No solution
3 1 3 5
2 2 4

Solution

對於不認識的兩個人,保證他們在不同的 team。

取補圖,建造相互不認識的兩個人的關係圖,對於每一個 component 做二分圖判定,找到每個二分圖的兩個集合大小。

對於每一個二分圖結果,使用背包問題的解法,將兩個 team 的總數劃分均勻。

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#include <stdio.h>
#include <string.h>
#include <vector>
#include <algorithm>
#include <assert.h>
using namespace std;
#define MAXN 128
int g[MAXN][MAXN], visited[MAXN];
int color[MAXN], n;
int dfs(int u, int c, vector<int> &s0, vector<int> &s1) {
visited[u] = 1, color[u] = c;
if (c == 0) s0.push_back(u);
else s1.push_back(u);
for (int i = 1; i <= n; i++) {
if ((!(g[u][i] == 1 && g[i][u] == 1)) && i != u) {
if (visited[i] == 0) {
if (!dfs(i, !color[u], s0, s1))
return 0;
} else {
if (color[u] == color[i])
return 0;
}
}
}
return 1;
}
int main() {
int testcase, x;
scanf("%d", &testcase);
while (testcase--) {
scanf("%d", &n);
while (getchar() != '\n');
memset(g, 0, sizeof(g));
memset(visited, 0, sizeof(visited));
memset(color, 0, sizeof(color));
for (int i = 1; i <= n; i++) {
while (scanf("%d", &x) == 1 && x)
g[i][x] = 1;
}
int ok = 1, m = 0;
vector<int> s0[MAXN], s1[MAXN];
for (int i = 1; i <= n; i++) {
if (visited[i] == 0) {
m++;
ok &= dfs(i, 0, s0[m], s1[m]);
}
}
if (!ok) {
puts("No solution");
} else {
int dp[MAXN][MAXN] = {}, from[MAXN][MAXN] = {};
dp[0][0] = 1;
for (int i = 1; i <= m; i++) {
for (int j = 0; j <= n; j++) {
if (dp[i - 1][j]) {
dp[i][j + s0[i].size()] = 1;
dp[i][j + s1[i].size()] = 1;
from[i][j + s0[i].size()] = 0;
from[i][j + s1[i].size()] = 1;
}
}
}
int ch = -1;
for (int i = n/2; i >= 1; i--) {
if (dp[m][i]) ch = i, i = -1;
}
assert(ch > 0);
vector<int> team1, team2;
for (int i = m; i >= 1; i--) {
if (from[i][ch] == 0) {
ch -= s0[i].size();
team1.insert(team1.end(), s0[i].begin(), s0[i].end());
team2.insert(team2.end(), s1[i].begin(), s1[i].end());
} else {
ch -= s1[i].size();
team1.insert(team1.end(), s1[i].begin(), s1[i].end());
team2.insert(team2.end(), s0[i].begin(), s0[i].end());
}
}
printf("%d", team1.size());
for (int i = 0; i < team1.size(); i++)
printf(" %d", team1[i]);
puts("");
printf("%d", team2.size());
for (int i = 0; i < team2.size(); i++)
printf(" %d", team2[i]);
puts("");
}
if (testcase) puts("");
}
return 0;
}
/*
2
5
3 4 5 0
1 3 5 0
2 1 4 5 0
2 3 5 0
1 2 3 4 0
5
2 3 5 0
1 4 5 3 0
1 2 5 0
1 2 3 0
4 3 2 1 0
*/