AtCoder Beginner Contest 185题解(模拟、背包、贪心、线性dp、树状数组)

这场好水啊。。。手速场,手速不够还是不行啊。


A - ABC Preparation

签到题,取四个值当中最小的即可。

#include <bits/stdc++.h>
using namespace std;
int main() {
	int ans = 0x3f3f3f3f;
	for (int i = 0; i < 4; i++) {
		int x;
		cin >> x;
		ans = min(ans, x);
	}
	printf("%d", ans);
	return 0;
}

B - Smartphone Addiction

直接模拟,对于每个充电和耗电的区间计算是否满足要求即可。

#include <bits/stdc++.h>
using namespace std;
int n, m, t, limit;
int a, b, lst;
int main() {
	cin >> n >> m >> t;
	limit = n;
	for (int i = 1; i <= m; i++) {
		cin >> a >> b;
		n -= a - lst;
		if (n <= 0) {
			puts("No");
			return 0;
		}
		n += b - a;
		n = min(n, limit);
		lst = b;
	}
	n -= t - lst;
	if (n <= 0) {
		puts("No");
		return 0;
	}
	puts("Yes");
	return 0;
}

C - Duodecim Ferra

直接背包dp,记 (f[i][j]) 代表用 (i) 个正整数凑出 (j) 的方案数,(f[i][j]+=f[i-1][j-k]),注意因为是正整数所以当 (j<i)(f[i][j]=0)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int L;
ll f[15][205];
int main() {
	scanf("%d", &L);
	f[0][0] = 1;
	for (int i = 1; i <= 12; i++) {
		for (int k = 1; k <= L; k++) {
			for (int j = L; j >= max(k, i); j--) {
				f[i][j] += f[i - 1][j - k];
			}
		}
	}
	printf("%lld", f[12][L]);
	return 0;
}

D - Stamp

题意比较迷惑,看了样例才懂。

直接取每一段白色的长度的最小值,(k) 一定不能大于这个,而 (k) 越大越好,所以 (k) 一定等于这个。然后再对每一个空隙计算,设某一段是 (L),则需 (lceilfrac{L}{k} ceil)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n, m, a[200005];
ll ans;
int gcd(int x, int y) {
	return y == 0 ? x : gcd(y, x % y);
}
int main() {
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= m; i++) scanf("%d", &a[i]);
	sort(a + 1, a + 1 + m);
	int lst = 0, g = 1e9 + 7;
	a[++m] = n + 1;
	for (int i = 1; i <= m; i++) {
		if (a[i] - lst - 1 != 0) g = min(g, a[i] - lst - 1);
		lst = a[i];
	}
	lst = 0;
	for (int i = 1; i <= m; i++) {
		if (a[i] - lst - 1 != 0) ans += (a[i] - lst - 1 + g - 1) / g;
		lst = a[i];
	}
	printf("%lld", ans);
	return 0;
}

E - Sequence Matching

思博dp题,记 (dp[i][j]) 为答案,有方程 (dp[i][j]=min(dp[i-1][j],dp[i][j-1])+1),这是第一种转移,意义是删掉 (i) 或者 (j)

(a[i]=b[j]) 则还可以从 (dp[i-1][j-1]) 转移,因为有 (a[i],b[j]) 这一对不会影响答案。若没有则还可以 (dp[i-1][j-1]) 意义也是不删但是 (y + 1)

注意初始化 (dp[i][0]=i,dp[0][j]=j,dp[0][0]=0)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n, m, a[1005], b[1005];
int dp[1005][1005];
int main() {
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
	for (int i = 1; i <= m; i++) scanf("%d", &b[i]);
	memset(dp, 0x3f, sizeof(dp));
	dp[0][0] = 0;
	for (int i = 1; i <= n; i++) dp[i][0] = i;
	for (int i = 1; i <= m; i++) dp[0][i] = i;
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= m; j++) {
			if (a[i] == b[j]) dp[i][j] = min(dp[i][j], dp[i - 1][j - 1]);
			dp[i][j] = min(dp[i][j], dp[i - 1][j] + 1);
			dp[i][j] = min(dp[i][j], dp[i][j - 1] + 1);
			dp[i][j] = min(dp[i][j], dp[i - 1][j - 1] + 1);
		}
	}
	printf("%d", dp[n][m]);
	return 0;
}

F - Range Xor Query

考虑第二种操作可以用前缀异或和做,(sum(l,r)=sum(1,r) ext{^}sum(1,l-1)),所以我们可以维护前缀和。对于第一种操作可以看成单调加(异或满足交换律),所以可以用树状数组维护,基本就是树状数组板子改几个运算符。

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n, m;
int a[300005];
int BIT[300005];
void add(int x, int v) {
	while (x <= n) {
		BIT[x] ^= v;
		x += (x & (-x));
	}
}
int ask(int x) {
	int ret = 0;
	while (x) {
		ret ^= BIT[x];
		x -= (x & (-x));
	}
	return ret;
}
int main() {
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
		add(i, a[i]);
	}
	for (int i = 1; i <= m; i++) {
		int t, x, y;
		scanf("%d%d%d", &t, &x, &y);
		if (t == 1) {
			add(x, y);
		} else {
			printf("%d
", ask(y) ^ ask(x - 1));
		}
	}
	return 0;
}
原文地址:https://www.cnblogs.com/zcr-blog/p/14130431.html