2013 通化邀请赛

A：求平均数，水题，注意输出的格式。

D：从后往前做并查集，并记录集合个数即可

E：数论，先把L / G 分解质因子，然后这些质因子要分给三个数，就是A（3，2）每个因子的个数再相乘

G：暴力dfs剪枝。

H：记忆化搜索，dp[20][20][20][20][2]的状态，前4维的状态记录牌取的情况，最后一维记录是谁取的。

A：

#include <stdio.h>
#include <string.h>
#include <math.h>

int t;
double sum;
int main() {
scanf("%d", &t);
while (t--) {
sum = 0;
double num;
for (int i = 0; i < 12; i++) {
scanf("%lf", &num);
sum += num;
}
sum /= 12;
printf("$%d", (int)sum);
sum = (sum - floor(sum));
int s = int(sum * 100 + 0.5);
if (s != 0) {
printf(".");
printf("%d", s / 10);
s %= 10;
if (s != 0)
printf("%d", s);
}
printf("\n");
}
return 0;
}

D：
#include <stdio.h>
#include <string.h>

const int N = 10005;
const int M = 100005;

int n, m, a[M], b[M], parent
, ans[M];

void init() {
for (int i = 0; i < n; i++)
parent[i] = i;
}

int find(int x) {
if (x == parent[x]) return x;
return parent[x] = find(parent[x]);
}

int main() {
while (~scanf("%d%d", &n, &m)) {
init();
for (int i = 0; i < m; i++)
scanf("%d%d", &a[i], &b[i]);
int sum = n;
for (int i = m - 1; i >= 0; i--) {
ans[i] = sum;
int pa = find(a[i]);
int pb = find(b[i]);
if (pa != pb) {
parent[pa] = pb;
sum--;
}
}
for (int i = 0; i < m; i++)
printf("%d\n", ans[i]);
}
return 0;
}

E：
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <iostream>
using namespace std;

int t;
long long n, m;

long long solve(long long n, long long m) {
if (m % n) return 0;
long long num = m / n;
long long Max = sqrt(num);
long long ans = 1;
for (int i = 2; i <= Max && i <= num; i++) {
if (num % i == 0) {
long long count = 0;
while (num % i == 0) {
count++;
num /= i;
}
ans *= (6 * count);
}
}
if (num > 1)
ans *= 6;
return ans;
}

int main() {
scanf("%d", &t);
while (t--) {
cin >> n >> m;
cout << solve(n, m) << endl;
}
return 0;
}

H：
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
const int INF = 0x3f3f3f3f;
const int N = 25;
int t, n, num1
, num2
, dp

[2];

int dfs(int s1, int e1, int s2, int e2, int who) {
int &ans = dp[s1][e1][s2][e2][who];
if (ans != -1) return ans;
if (s1 > e1 && s2 > e2) return ans = 0;
if (who == 1) {
ans = 0;
if (s1 <= e1) {
ans = max(ans, dfs(s1 + 1, e1, s2, e2, (!who)) + who * num1[s1]);
ans = max(ans, dfs(s1, e1 - 1, s2, e2, (!who)) + who * num1[e1]);
}
if (s2 <= e2) {
ans = max(ans, dfs(s1, e1, s2 + 1, e2, (!who)) + who * num2[s2]);
ans = max(ans, dfs(s1, e1, s2, e2 - 1, (!who)) + who * num2[e2]);
}
}
else {
ans = INF;
if (s1 <= e1) {
ans = min(ans, dfs(s1 + 1, e1, s2, e2, (!who)) + who * num1[s1]);
ans = min(ans, dfs(s1, e1 - 1, s2, e2, (!who)) + who * num1[e1]);
}
if (s2 <= e2) {
ans = min(ans, dfs(s1, e1, s2 + 1, e2, (!who)) + who * num2[s2]);
ans = min(ans, dfs(s1, e1, s2, e2 - 1, (!who)) + who * num2[e2]);
}
}
return ans;
}

int main() {
scanf("%d", &t);
while (t--) {
memset(dp, -1, sizeof(dp));
scanf("%d", &n);
for (int i = 1; i <= n; i++)
scanf("%d", &num1[i]);
for (int i = 1; i <= n; i++)
scanf("%d", &num2[i]);
printf("%d\n", dfs(1, n, 1, n, 1));
}
return 0;
}

G：
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;

const int N = 10;
int n, m, q, x, y, g

, s[32], sn, ans, tmp;

int bitcount(int x) {
if (x == 0) return 0;
return bitcount(x / 2) + (x&1);
}

void table() {
sn = 0;
for (int i = 0; i < 32;i ++) {
if (bitcount(i) <= 3)
s[sn++] = i;
}
}

bool judge(int d, int s) {
for (int i = 0; i < m; i++) {
if (g[d][i] == 1 && (s&(1<<i)))
return false;
}
return true;
}

bool checkup(int x, int y) {
int flag = 0;
for (int i = x - 1; i >= 0; i--) {
if (flag&& g[i][y] == 2) return false;
else if (flag && g[i][y] == 1) return true;
if (g[i][y]) flag = 1;
}
return true;
}

bool checklf(int x, int y) {
int flag = 0;
for (int i = y - 1; i >= 0; i--) {
if (flag && g[x][i] == 2) return false;
else if (flag && g[x][i] == 1) return true;
if (g[x][i]) flag = 1;
}
return true;
}

bool check(int d) {
for (int i = 0; i < m; i++) {
if (g[d][i] == 2) {
if (!checkup(d, i))
return false;
if (!checklf(d, i))
return false;
}
}
return true;
}

void dfs(int d, int num) {
if (n == 5) {
if (num + (n - d) * 3 <= ans) return;
}
else {
if (num + (n - d) * 2 <= ans) return;
}
if (d == n) {
ans = max(ans, num);
return;
}
for (int i = 0; i < sn; i++) {
if (s[i] > tmp) continue;
if (judge(d, s[i])) {
for (int j = 0; j < m; j++) {
if (s[i]&(1<<j))
g[d][j] = 2;
}
if (check(d)) {
dfs(d + 1, num + bitcount(s[i]));
}
for (int j = 0; j < m; j++) {
if (s[i]&(1<<j))
g[d][j] = 0;
}
}
}
}

int main() {
table();
while (~scanf("%d%d%d", &n, &m, &q)) {
ans = 0; tmp = (1<<m) - 1;
memset(g, 0, sizeof(g));
while (q--) {
scanf("%d%d", &x, &y);
g[x][y] = 1;
}
dfs(0, 0);
printf("%d\n", ans);
}
return 0;
}