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86 lines
1.6 KiB
86 lines
1.6 KiB
package class22;
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public class Code03_SplitNumber {
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// n为正数
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public static int ways(int n) {
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if (n < 0) {
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return 0;
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}
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if (n == 1) {
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return 1;
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}
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return process(1, n);
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}
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// 上一个拆出来的数是pre
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// 还剩rest需要去拆
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// 返回拆解的方法数
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public static int process(int pre, int rest) {
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if (rest == 0) {
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return 1;
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}
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if (pre > rest) {
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return 0;
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}
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int ways = 0;
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for (int first = pre; first <= rest; first++) {
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ways += process(first, rest - first);
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}
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return ways;
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}
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public static int dp1(int n) {
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if (n < 0) {
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return 0;
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}
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if (n == 1) {
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return 1;
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}
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int[][] dp = new int[n + 1][n + 1];
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for (int pre = 1; pre <= n; pre++) {
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dp[pre][0] = 1;
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dp[pre][pre] = 1;
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}
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for (int pre = n - 1; pre >= 1; pre--) {
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for (int rest = pre + 1; rest <= n; rest++) {
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int ways = 0;
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for (int first = pre; first <= rest; first++) {
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ways += dp[first][rest - first];
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}
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dp[pre][rest] = ways;
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}
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}
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return dp[1][n];
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}
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public static int dp2(int n) {
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if (n < 0) {
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return 0;
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}
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if (n == 1) {
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return 1;
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}
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int[][] dp = new int[n + 1][n + 1];
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for (int pre = 1; pre <= n; pre++) {
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dp[pre][0] = 1;
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dp[pre][pre] = 1;
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}
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for (int pre = n - 1; pre >= 1; pre--) {
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for (int rest = pre + 1; rest <= n; rest++) {
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dp[pre][rest] = dp[pre + 1][rest];
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dp[pre][rest] += dp[pre][rest - pre];
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}
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}
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return dp[1][n];
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}
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public static void main(String[] args) {
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int test = 39;
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System.out.println(ways(test));
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System.out.println(dp1(test));
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System.out.println(dp2(test));
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}
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}
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