【蓝桥日记③】2016第七届省赛（软件类）JavaA组✿答案解析
文章目录
官网题库中搜索相应题目
1、煤球数目
考点：找规律，模拟求和
package sevenSession;
/*** 2016第七届 1、煤球数目 ***/
public class test1 {
public static void main(String[] args) {
int pre = 1, res = 1;
for (int i = 2; i <= 100; i++) {
pre += i;
res += pre;
}
System.out.println(res);
}
}
答案：
171700
2、生日蜡烛
考点：暴力枚举
package sevenSession;
/*** 2016第七届 2、生日蜡烛 ***/
public class test2 {
public static void main(String[] args) {
int candles = 236, begin = 0;
for (int j = 1; j <= 100; j++) {
int k = j, sum = 0;
while (sum < candles) {
sum += k;
k += 1;
}
if (sum == candles) {
begin = j;
break;
}
}
System.out.println(begin);
}
}
答案：
26
3、搭积木
考点：全排列
package sevenSession;
/*** 2016第七届 3、搭积木 ***/
public class test3 {
static int res;
public static void main(String[] args) {
int[] a = {
0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
res = 0;
backtrack(a, 0, a.length);
System.out.println(res);
}
static private void backtrack(int[] a, int begin, int end) {
if (begin == end) {
if (check(a)) res++;
return;
}
for (int i = begin; i < end; i++) {
int t = a[i]; a[i] = a[begin]; a[begin] = t;
backtrack(a, begin + 1, end);
t = a[i]; a[i] = a[begin]; a[begin] = t;
}
}
static private boolean check(int[] a) {
if (a[0] > a[1] || a[0] > a[2]) return false;
if (a[1] > a[3] || a[1] > a[4]) return false;
if (a[2] > a[4] || a[2] > a[5]) return false;
if (a[3] > a[6] || a[3] > a[7]) return false;
if (a[4] > a[7] || a[4] > a[8]) return false;
if (a[5] > a[8] || a[5] > a[9]) return false;
return true;
}
}
答案：
768
4、分小组
考点：排列组合
package sevenSession;
/*** 2016第七届 4、分小组 ***/
public class test4 {
public static String remain(int[] a) {
String s = "";
for (int i = 0; i < a.length; i++) {
if (a[i] == 0) s += (char) (i + 'A');
}
return s;
}
public static void f(String s, int[] a) {
for (int i = 0; i < a.length; i++) {
if (a[i] == 1) continue;
a[i] = 1;
for (int j = i + 1; j < a.length; j++) {
if (a[j] == 1) continue;
a[j] = 1;
for (int k = j + 1; k < a.length; k++) {
if (a[k] == 1) continue;
a[k] = 1;
if (k == 3)
System.out.println(s + " " + (char)(i + 'A') + (char)(j + 'A') + (char)(k + 'A') + " " + remain(a));
a[k] = 0;
}
a[j] = 0;
}
a[i] = 0;
}
}
public static void main(String[] args) {
int[] a = new int[9];
a[0] = 1;
for (int b = 1; b < a.length; b++) {
a[b] = 1;
for (int c = b + 1; c < a.length; c++) {
a[c] = 1;
String s = "A" + (char) (b + 'A') + (char) (c + 'A');
f(s, a);
a[c] = 0;
}
a[b] = 0;
}
}
}
答案：
System.out.println(s + " " + (char)(i + 'A') + (char)(j + 'A') + (char)(k + 'A') + " " + remain(a));
5、抽签
考点：排列组合+递归
package sevenSession;
/*** 2016第七届 5、抽签 ***/
public class test5 {
public static void f(int[] a, int k, int n, String s) {
if (k == a.length) {
if (n == 0) System.out.println(s);
return;
}
String s2 = s;
for (int i = 0; i <= a[k]; i++) {
f(a, k + 1, n - i, s2);
s2 += (char) (k + 'A');
}
}
public static void main(String[] args) {
int[] a = {
4, 2, 2, 1, 1, 3};
f(a, 0, 5, "");
}
}
答案：
f(a, k + 1, n - i, s2);
6、寒假作业
考点：排列组合
package sevenSession;
/*** 2016第七届 6、剪邮票 ***/
public class test6 {
static int res;
public static void main(String[] args) {
int[] a = new int[13];
for (int i = 1; i <= 13; i++) a[i - 1] = i;
res = 0;
backtrack(a, 0, 13);
System.out.println(res);
}
static private void backtrack(int[] a, int begin, int end) {
if (begin == end && check(a)) {
res++;
return;
}
for (int i = begin; i < end; i++) {
int t = a[begin]; a[begin] = a[i]; a[i] = t;
backtrack(a, begin + 1, end);
t = a[begin]; a[begin] = a[i]; a[i] = t;
}
}
static private boolean check(int[] a) {
return a[0] + a[1] == a[2] && a[3] - a[4] == a[5] &&
a[6] * a[7] == a[8] && (a[9] % a[10] == 0 && a[9] / a[10] == a[11]);
}
}
答案：
64
7、剪邮票
考点：组合问题+DFS
package sevenSession;
import java.util.ArrayDeque;
import java.util.Queue;
/*** 2016第七届 7、剪邮票 ***/
public class test7 {
static int res = 0;
public static void main(String[] args) {
int[] a = new int[12];
backtrack(a, 0, 12, 5);
System.out.println(res);
}
static private void backtrack(int[] a, int begin, int end, int k) {
if (end - begin + 1 < k) return;
if (k == 0) {
if(check(a)) res++;
}
for (int i = begin; i < end; i++) {
a[i] = 1;
backtrack(a, i + 1, end, k - 1);
a[i] = 0;
}
}
static private boolean check(int[] a) {
Queue<int[]> queue = new ArrayDeque<>();
boolean[] mark = new boolean[12];
for (int i = 0; i < 12; i++) {
if (a[i] == 1) {
queue.offer(new int[]{
i / 4, i % 4});
mark[i] = true;
break;
}
}
if (queue.isEmpty()) return false;
int cnt = 1;
int[] dirs = {
-1, 0, 1, 0, -1};
while (!queue.isEmpty()) {
int[] cur = queue.poll();
for (int i = 0; i < 4; i++) {
int x = cur[0] + dirs[i], y = cur[1] + dirs[i + 1];
int xy = x * 4 + y;
if (x < 0 || y < 0 || x >= 3 || y >= 4) continue;
if (a[xy] == 0 || mark[xy]) continue;
queue.offer(new int[]{
x, y});
mark[xy] = true;
cnt++;
}
}
return cnt == 5;
}
}
答案：
116
8、取球博弈
考点：博弈+记忆化搜索
package sevenSession;
import java.util.Arrays;
import java.util.Scanner;
/*** 2016第七届 8、取球博弈 ***/
public class test8 {
static int[] ns = new int[3];
static char[][][] cache = new char[1000][2][2];
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
for (int i = 0; i < 3; i++) ns[i] = sc.nextInt();
Arrays.sort(ns);
char[] res = new char[5];
for (int i = 0; i < 5; i++) {
int num = sc.nextInt();
res[i] = f(num, 0, 0);
}
sc.close();
for (char c : res) System.out.print(c + " ");
}
private static char f(int num, int me, int you) {
if (num < ns[0]) {
if ((me & 1) == 1 && (you & 1) == 0) {
cache[num][me][you] = '+';
return '+';
} else if ((me & 1) == 0 && (you & 1) == 1) {
cache[num][me][you] = '-';
return '-';
} else {
cache[num][me][you] = '0';
return '0';
}
}
if (cache[num][me][you] != '\0') return cache[num][me][you];
boolean fair = false;
for (int n : ns) {
if (num >= n) {
char c = f(num - n, you, (me + n) % 2);
if (c == '-') {
cache[num][me][you] = '+';
return '+';
} else if (c == '0') {
fair = true;
}
}
}
if (fair) {
cache[num][me][you] = '0';
return '0';
}
cache[num][me][you] = '-';
return '-';
}
}
9、交换瓶子
package sevenSession;
import java.util.Scanner;
/*** 2016第七届 9、交换瓶子 ***/
public class test9 {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int[] ns = new int[n + 1];
for (int i = 0; i < n; i++) {
ns[i + 1] = sc.nextInt();
}
sc.close();
int res = 0, i = 1, j = 0;
while (i <= n) {
if (i != ns[i]) {
for (j = i + 1; j <= n; j++) {
if (ns[j] == i) break;
}
int t = ns[i];
ns[i] = ns[j];
ns[j] = t;
res++;
continue;
}
i++;
}
System.out.println(res);
}
}
10、压缩变换
方法一：暴力法（4/8）
package sevenSession;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;
/*** 2016第七届 10、压缩变换 ***/
public class test10 {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int[] nums = new int[n];
for (int i = 0; i < n; i++) nums[i] = sc.nextInt();
sc.close();
int[] res = new int[n];
HashMap<Integer, Integer> map = new HashMap<>();
for (int i = 0; i < n; i++) {
if (!map.containsKey(nums[i])) {
res[i] = -nums[i];
} else {
res[i] = getKinds(nums, map.get(nums[i]), i);
}
map.put(nums[i], i);
}
for (int x : res) System.out.print(x + " ");
}
private static int getKinds(int[] nums, int begin, int end) {
HashSet<Integer> set = new HashSet<Integer>();
for (int i = begin + 1; i < end; i++) set.add(nums[i]);
return set.size();
}
}
方法二：线段树，区间查询（AC）
线段树知识可以参考我的往期总结：高级数据结构（Ⅲ）线段树（Segment Tree）
package sevenSession;
import java.util.HashMap;
import java.util.Scanner;
/*** 2016第七届 10、压缩变换 线段树区间查询 ***/
public class test10_2 {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int[] nums = new int[n];
for (int i = 0; i < n; i++) nums[i] = sc.nextInt();
sc.close();
SegmentTree segTree = new SegmentTree();
int[] res = new int[n];
HashMap<Integer, Integer> map = new HashMap<>();
for (int i = 0; i < n; i++) {
if (!map.containsKey(nums[i])) {
res[i] = -nums[i];
segTree.update(i, 1);
} else {
res[i] = segTree.query(map.get(nums[i]) + 1, i - 1);
segTree.update(map.get(nums[i]), 0);
segTree.update(i, 1);
}
map.put(nums[i], i);
}
for (int x : res) System.out.print(x + " ");
}
}
class SegmentTree {
private static final int N = 100001;
private TreeNode root;
class TreeNode {
TreeNode left, right;
int cnt;
}
public SegmentTree() {
root = new TreeNode();
}
public void update(int index, int val) {
root = update(root, 0, N, index, val);
}
private TreeNode update(TreeNode node, int low, int high, int index, int val) {
createNode(node);
if (low == high && low == index) {
node.cnt = val;
return node;
}
int mid = low + (high - low) / 2;
if (index >= low && index <= mid) {
node.left = update(node.left, low, mid, index, val);
} else {
node.right = update(node.right, mid + 1, high, index, val);
}
node.cnt = node.left.cnt + node.right.cnt;
return node;
}
public int query(int L, int R) {
return query(root, 0, N, L, R);
}
private int query(TreeNode node, int low, int high, int L ,int R) {
if (low > R || high < L) return 0;
if (low >= L && high <= R) return node.cnt;
int mid = low + (high - low) / 2;
int sumLeft = query(node.left, low, mid, L, R);
int sumRight = query(node.right, mid + 1, high, L, R);
return sumLeft + sumRight;
}
private void createNode(TreeNode node) {
if (node.left == null) node.left = new TreeNode();
if (node.right == null) node.right = new TreeNode();
}
}
3~7是排列组合题，只要会一个，举一反三。取球博弈，想想还是第一次真正做博弈的题目呢，之前只刷过简单的题，现在用记忆化搜索和递归来进行模拟，很有趣。最后一道题压缩变换又用到了线段树区间求和，算是对前面的学习巩固了下。还是那句话，加油加油ヾ(◍°∇°◍)ﾉﾞ！
