CD42 子数组异或和为 0 的最多划分⭐
/*⭐DP⭐*/
public class CD42_1
{
public static int solution(int[] arr)
{
HashMap<Integer, Integer> map = new HashMap<>();
int[] dp = new int[arr.length];
int temp = 0;
dp[0] = arr[0] == 0 ? 1 : 0;
temp ^= arr[0];
map.put(arr[0], 0);
map.put(0, -1);
for (int i = 1; i < arr.length; i++)
{
temp ^= arr[i];
if (map.containsKey(temp))
{
int idx = map.get(temp);
dp[i] = idx == -1 ? 1 : dp[idx] + 1;
}
dp[i] = Math.max(dp[i], dp[i - 1]);
map.put(temp, i);
}
return dp[arr.length - 1];
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n;
n = in.nextInt();
int[] arr = new int[n];
for (int i = 0; i < n; i++)
arr[i] = in.nextInt();
System.out.println(solution(arr));
}
}
CD43 最小编辑代价⭐
/* ⭐DP⭐
* 令dp[i][j]的值代表s1[0..i-1]编辑成s2[0..j-1]的最小代价
* 则dp[i][j]=min(dp[i-1][j-1], dp[i-1][j-1]+replace, dp[i-1][j]+delete, dp[i][j-1]+insert)
*/
public class CD43_1
{
public static int solution(String s1, String s2, int insert, int delete, int replace)
{
int[][] dp = new int[s1.length() + 1][s2.length() + 1];
dp[0][0] = 0;
for (int i = 1; i < s1.length() + 1; i++)
dp[i][0] = i * delete;
for (int i = 1; i < s2.length() + 1; i++)
dp[0][i] = i * insert;
for (int i = 1; i < s1.length() + 1; i++)
for (int j = 1; j < s2.length() + 1; j++)
{
dp[i][j] = Math.min(dp[i - 1][j] + delete, dp[i][j - 1] + insert);
if (s1.charAt(i - 1) == s2.charAt(j - 1))
dp[i][j] = Math.min(dp[i][j], dp[i - 1][j - 1]);
else
dp[i][j] = Math.min(dp[i][j], dp[i - 1][j - 1] + replace);
}
return dp[s1.length()][s2.length()];
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
String s1, s2;
int insert, delete, replace;
s1 = in.nextLine();
s2 = in.nextLine();
insert = in.nextInt();
delete = in.nextInt();
replace = in.nextInt();
System.out.println(solution(s1, s2, insert, delete, replace));
}
}
CD44 字符串的交错组成⭐
/* ⭐DP⭐
* dp[i][j]的值代表aim[0..i+j-1]能否被str1[0..i-1]和str2[0..j-1]交错组成
*/
public class CD44_1
{
public static String solution(String s1, String s2, String aim)
{
if (aim.length() < s1.length() + s2.length()) return "NO";
boolean[][] dp = new boolean[s1.length() + 1][s2.length() + 1];
for (int i = 1; i <= s1.length(); i++)
{
if (aim.charAt(i - 1) != s1.charAt(i - 1))
break;
dp[i][0] = true;
}
for (int i = 1; i <= s2.length(); i++)
{
if (aim.charAt(i - 1) != s2.charAt(i - 1))
break;
dp[0][i] = true;
}
for (int i = 1; i <= s1.length(); i++)
for (int j = 1; j <= s2.length(); j++)
if ((dp[i - 1][j] && s1.charAt(i - 1) == aim.charAt(i + j - 1)) || (dp[i][j - 1] && s2.charAt(j - 1) == aim.charAt(i + j - 1)))
dp[i][j] = true;
return dp[s1.length()][s2.length()] ? "YES" : "NO";
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
String s1, s2, s3;
s1 = in.nextLine();
s2 = in.nextLine();
s3 = in.nextLine();
System.out.println(solution(s1, s2, s3));
}
}
CD45 龙与地下城游戏问题
/* DP
* dp[i][j]表示为从[i,j]到[n-1,m-1]至少需要的血量
*/
public class CD45_1
{
public static int solution(int[][] arr)
{
int n = arr.length, m = arr[0].length;
int[][] dp = new int[n][m];
for (int[] t : dp)
Arrays.fill(t, Integer.MAX_VALUE);
dp[n - 1][m - 1] = arr[n - 1][m - 1] < 0 ? -arr[n - 1][m - 1] + 1 : 1;
for (int i = n - 2; i >= 0; i--)
dp[i][m - 1] = Math.max(dp[i + 1][m - 1] - arr[i][m - 1], 1);
for (int i = m - 2; i >= 0; i--)
dp[n - 1][i] = Math.max(dp[n - 1][i + 1] - arr[n - 1][i], 1);
for (int i = n - 2; i >= 0; i--)
for (int j = m - 2; j >= 0; j--)
dp[i][j] = Math.min(Math.max(dp[i + 1][j] - arr[i][j], 1), Math.max(dp[i][j + 1] - arr[i][j], 1));
return dp[0][0];
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n, m;
n = in.nextInt();
m = in.nextInt();
int[][] arr = new int[n][m];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
arr[i][j] = in.nextInt();
System.out.println(solution(arr));
}
}
CD46 数字字符串转换为字母组合的种数
/* DP */
public class CD46_1
{
public static int solution(String str)
{
int MOD = (int) (1E9 + 7);
int[] dp = new int[str.length()];
if (str.charAt(0) == '0') return 0;
dp[0] = 1;
dp[1] = (check(str.charAt(0), str.charAt(1)) ? 1 : 0) + (str.charAt(1) != '0' ? 1 : 0);
for (int i = 2; i < str.length(); i++)
{
if (str.charAt(i) == '0')
{
if (str.charAt(i - 1) == '1' || str.charAt(i - 1) == '2')
dp[i] = dp[i - 2];
else
return 0;
}
else
dp[i] = (dp[i - 1] + (check(str.charAt(i - 1), str.charAt(i)) ? dp[i - 2] : 0)) % MOD;
}
return dp[str.length() - 1];
}
public static boolean check(char ch1, char ch2)
{
if (ch1 == '0') return false;
else if (ch1 == '1') return true;
else if (ch1 == '2') return (ch2 >= '0' && ch2 <= '6');
else return false;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
String s;
s = in.nextLine();
System.out.println(solution(s));
}
}
/* DP */
public class CD46_2
{
// 暴力递归
public static int solution1(String str)
{
return cal(str, 0);
}
public static int cal(String s, int idx)
{
int res = 0;
if (idx == s.length()) return 1;
if (idx < s.length() && s.charAt(idx) != '0')
res = cal(s, idx + 1) % (int) (1E9 + 7);
if (idx < s.length() - 1 && check(s.charAt(idx), s.charAt(idx + 1)))
res = (res + cal(s, idx + 2)) % (int) (1E9 + 7);
return res;
}
public static boolean check(char ch1, char ch2)
{
if (ch1 == '0') return false;
else if (ch1 == '1') return true;
else if (ch1 == '2') return (ch2 >= '0' && ch2 <= '6');
else return false;
}
// 优化
public static int solution2(String str)
{
int strLen = str.length();
int[] dp = new int[strLen];
dp[strLen - 1] = str.charAt(strLen - 1) == '0' ? 0 : 1;
if (str.charAt(strLen - 2) == '0')
dp[strLen - 2] = 0;
else
dp[strLen - 2] = (check(str.charAt(strLen - 2), str.charAt(strLen - 1)) ? 1 : 0) + (str.charAt(strLen - 1) != '0' ? 1 : 0);
for (int i = strLen - 3; i >= 0; i--)
{
if (str.charAt(i) != '0')
dp[i] = dp[i + 1];
if (check(str.charAt(i), str.charAt(i + 1)))
dp[i] = (dp[i] + dp[i + 2]) % (int) (1E9 + 7);
}
return dp[0];
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
String s;
s = in.nextLine();
System.out.println(solution2(s));
}
}
CD47 表达式得到期望结果的组成种数❗
/* ❗DP❗ */
public class CD47_1
{
public static int solution(String str, boolean desired)
{
return cal(str, desired, 0, str.length() - 1);
}
public static int cal(String str, boolean desired, int l, int r)
{
if (l == r)
{
if (str.charAt(l) == '1')
return desired ? 1 : 0;
else
return desired ? 0 : 1;
}
int res = 0;
if (desired)
{
for (int i = l + 1; i < r; i += 2)
{
switch (str.charAt(i))
{
case '&':
res = res + cal(str, true, l, i - 1) * cal(str, true, i + 1, r);
break;
case '^':
res = res + cal(str, true, l, i - 1) * cal(str, false, i + 1, r);
res = res + cal(str, false, l, i - 1) * cal(str, true, i + 1, r);
break;
case '|':
res = res + cal(str, true, l, i - 1) * cal(str, true, i + 1, r);
res = res + cal(str, false, l, i - 1) * cal(str, true, i + 1, r);
res = res + cal(str, true, l, i - 1) * cal(str, false, i + 1, r);
break;
}
}
}
else
{
for (int i = l + 1; i < r; i += 2)
{
switch (str.charAt(i))
{
case '&':
res = res + cal(str, true, l, i - 1) * cal(str, true, i + 1, r);
res = res + cal(str, false, l, i - 1) * cal(str, true, i + 1, r);
res = res + cal(str, true, l, i - 1) * cal(str, false, i + 1, r);
break;
case '^':
res = res + cal(str, true, l, i - 1) * cal(str, true, i + 1, r);
res = res + cal(str, false, l, i - 1) * cal(str, false, i + 1, r);
break;
case '|':
res = res + cal(str, false, l, i - 1) * cal(str, false, i + 1, r);
break;
}
}
}
return res;
}
public static boolean isValid(char[] exp)
{
if ((exp.length & 1) == 0)
{
return false;
}
for (int i = 0; i < exp.length; i = i + 2)
{
if ((exp[i] != '1') && (exp[i] != '0'))
{
return false;
}
}
for (int i = 1; i < exp.length; i = i + 2)
{
if ((exp[i] != '&') && (exp[i] != '|') && (exp[i] != '^'))
{
return false;
}
}
return true;
}
public static long solution2(String express, boolean desired)
{
int MOD = (int) (1E9 + 7);
char[] exp = express.toCharArray();
if (!isValid(exp)) return 0;
long[][] t = new long[exp.length][exp.length];
long[][] f = new long[exp.length][exp.length];
t[0][0] = exp[0] == '0' ? 0 : 1;
f[0][0] = exp[0] == '1' ? 0 : 1;
for (int i = 2; i < exp.length; i += 2)
{
t[i][i] = exp[i] == '0' ? 0 : 1;
f[i][i] = exp[i] == '1' ? 0 : 1;
for (int j = i - 2; j >= 0; j -= 2)
{
for (int k = j; k < i; k += 2)
{
if (exp[k + 1] == '&')
{
t[j][i] = (t[j][i] + (t[j][k] * t[k + 2][i]) % MOD) % MOD;
f[j][i] = (f[j][i] + (((f[j][k] + t[j][k]) % MOD) * f[k + 2][i]) % MOD + (f[j][k] * t[k + 2][i]) % MOD) % MOD;
}
else if (exp[k + 1] == '|')
{
t[j][i] = (t[j][i] + ((((f[j][k] + t[j][k]) % MOD) * t[k + 2][i]) % MOD + (t[j][k] * f[k + 2][i]) % MOD) % MOD) % MOD;
f[j][i] = (f[j][i] + (f[j][k] * f[k + 2][i]) % MOD) % MOD;
}
else
{
t[j][i] = (t[j][i] + ((f[j][k] * t[k + 2][i]) % MOD + (t[j][k] * f[k + 2][i]) % MOD) % MOD) % MOD;
f[j][i] = (f[j][i] + ((f[j][k] * f[k + 2][i]) % MOD + (t[j][k] * t[k + 2][i]) % MOD) % MOD) % MOD;
}
}
}
}
return desired ? t[0][t.length - 1] : f[0][f.length - 1];
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
String str, desired;
str = in.nextLine();
desired = in.nextLine();
System.out.println(solution2(str, !"false".equals(desired)));
}
}
CD91 排成一条线的纸牌博弈问题❗
/*❗❗*/
public class CD91_1
{
public static int solution1(int[] arr)
{
if (arr == null || arr.length == 0) return 0;
return Math.max(f(arr, 0, arr.length - 1), s(arr, 0, arr.length - 1));
}
public static int f(int[] arr, int i, int j)
{
if (i == j) return arr[i];
return Math.max(arr[i] + s(arr, i + 1, j), arr[j] + s(arr, i, j - 1));
}
public static int s(int[] arr, int i, int j)
{
if (i == j) return 0;
return Math.min(f(arr, i + 1, j), f(arr, i, j - 1));
}
public static int solution2(int[] arr)
{
if (arr == null || arr.length == 0) return 0;
int[][] f = new int[arr.length][arr.length];
int[][] s = new int[arr.length][arr.length];
for (int j = 0; j < arr.length; j++)
{
f[j][j] = arr[j];
for (int i = j - 1; i >= 0; i--)
{
f[i][j] = Math.max(arr[i] + s[i + 1][j], arr[j] + s[i][j - 1]);
s[i][j] = Math.min(f[i + 1][j], f[i][j - 1]);
}
}
return Math.max(f[0][arr.length - 1], s[0][arr.length - 1]);
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n;
n = in.nextInt();
int[] arr = new int[n];
for (int i = 0; i < n; i++)
arr[i] = in.nextInt();
System.out.println(solution2(arr));
}
}
CD92 跳跃游戏
public class CD92_1
{
public static int solution(int[] arr)
{
int cur = 0, next = 0, ans = 0;
for (int i = 0; i < arr.length; i++)
{
if (cur < i)
{
ans++;
cur = next;
}
next = Math.max(next, i + arr[i]);
}
return ans;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n;
n = in.nextInt();
int[] arr = new int[n];
for (int i = 0; i < n; i++)
arr[i] = in.nextInt();
System.out.println(solution(arr));
}
}
CD93 数组中的最长连续序列⭐
public class CD93_1
{
public static int solution(int[] arr)
{
int ans = 0;
HashMap<Integer, Integer> map = new HashMap<>();
for (int i = 0; i < arr.length; i++)
{
if (!map.containsKey(arr[i]))
{
map.put(arr[i], 1);
if (map.containsKey(arr[i] + 1))
ans = Math.max(ans, merge(arr[i], arr[i] + 1, map));
if (map.containsKey(arr[i] - 1))
ans = Math.max(ans, merge(arr[i] - 1, arr[i], map));
}
}
return ans;
}
public static int merge(int less, int more, HashMap<Integer, Integer> map)
{
int left = less - map.get(less) + 1;
int right = more + map.get(more) - 1;
int len = right - left + 1;
map.put(left, len);
map.put(right, len);
return len;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n;
n = in.nextInt();
int[] arr = new int[n];
for (int i = 0; i < n; i++)
arr[i] = in.nextInt();
System.out.println(solution(arr));
}
}
CD94 N 皇后问题
public class CD94_1
{
// 递归
public static int solution(int n)
{
int[] vis = new int[n];
return cal(0, vis, n);
}
public static int cal(int row, int[] vis, int n)
{
if (row == n) return 1;
int res = 0;
for (int col = 0; col < n; col++)
{
if (!isValid(vis, row, col)) continue;
vis[row] = col;
res += cal(row + 1, vis, n);
}
return res;
}
public static boolean isValid(int[] vis, int row, int col)
{
for (int r = 0; r < row; r++)
if (col == vis[r] || row + col == r + vis[r] || col - row == vis[r] - r)
return false;
return true;
}
// 二进制优化
public static int solution2(int n)
{
if (n < 1 || n > 32) return 0;
int upperLim = n == 32 ? -1 : (1 << n) - 1;
return process2(upperLim, 0, 0, 0);
}
public static int process2(int upperLim, int colLim, int leftDiaLim, int rightDiaLim)
{
if (colLim == upperLim) return 1;
int pos = 0;
int mostRightOne = 0;
pos = upperLim & (~(colLim | leftDiaLim | rightDiaLim));
int res = 0;
while (pos != 0)
{
mostRightOne = pos & (~pos + 1);
pos = pos - mostRightOne;
res += process2(upperLim, colLim | mostRightOne, (leftDiaLim | mostRightOne) << 1, (rightDiaLim | mostRightOne) >>> 1);
}
return res;
}
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
int n;
n = in.nextInt();
System.out.println(solution2(n));
}
}
