You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
86 lines
1.6 KiB
86 lines
1.6 KiB
package 第01期.mca_test;
|
|
|
|
public class Code03_SplitNumber {
|
|
|
|
// n为正数
|
|
public static int ways(int n) {
|
|
if (n < 0) {
|
|
return 0;
|
|
}
|
|
if (n == 1) {
|
|
return 1;
|
|
}
|
|
return process(1, n);
|
|
}
|
|
|
|
// 上一个拆出来的数是pre
|
|
// 还剩rest需要去拆
|
|
// 返回拆解的方法数
|
|
public static int process(int pre, int rest) {
|
|
if (rest == 0) {
|
|
return 1;
|
|
}
|
|
if (pre > rest) {
|
|
return 0;
|
|
}
|
|
int ways = 0;
|
|
for (int first = pre; first <= rest; first++) {
|
|
ways += process(first, rest - first);
|
|
}
|
|
return ways;
|
|
}
|
|
|
|
public static int dp1(int n) {
|
|
if (n < 0) {
|
|
return 0;
|
|
}
|
|
if (n == 1) {
|
|
return 1;
|
|
}
|
|
int[][] dp = new int[n + 1][n + 1];
|
|
for (int pre = 1; pre <= n; pre++) {
|
|
dp[pre][0] = 1;
|
|
dp[pre][pre] = 1;
|
|
}
|
|
for (int pre = n - 1; pre >= 1; pre--) {
|
|
for (int rest = pre + 1; rest <= n; rest++) {
|
|
int ways = 0;
|
|
for (int first = pre; first <= rest; first++) {
|
|
ways += dp[first][rest - first];
|
|
}
|
|
dp[pre][rest] = ways;
|
|
}
|
|
}
|
|
return dp[1][n];
|
|
}
|
|
|
|
public static int dp2(int n) {
|
|
if (n < 0) {
|
|
return 0;
|
|
}
|
|
if (n == 1) {
|
|
return 1;
|
|
}
|
|
int[][] dp = new int[n + 1][n + 1];
|
|
for (int pre = 1; pre <= n; pre++) {
|
|
dp[pre][0] = 1;
|
|
dp[pre][pre] = 1;
|
|
}
|
|
for (int pre = n - 1; pre >= 1; pre--) {
|
|
for (int rest = pre + 1; rest <= n; rest++) {
|
|
dp[pre][rest] = dp[pre + 1][rest];
|
|
dp[pre][rest] += dp[pre][rest - pre];
|
|
}
|
|
}
|
|
return dp[1][n];
|
|
}
|
|
|
|
public static void main(String[] args) {
|
|
int test = 39;
|
|
System.out.println(ways(test));
|
|
System.out.println(dp1(test));
|
|
System.out.println(dp2(test));
|
|
}
|
|
|
|
}
|