代码实现

#include <stdio.h>
#include <stdlib.h>
#define NUM 10	//拆解的数字
#define DEBUG 0

int main(){
	int table[NUM][NUM/2+1] = {0}; //动态规画表格
	int count = 0; 
	int result = 0; 
	int i, j, k;
	printf("数字拆解\n");
	printf("3 = 2+1 = 1+1+1 有二种拆法\n");
	printf("4 = 3 + 1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1");
	printf("有四种拆法\n");
	printf("5 = 4 + 1 = 3 + 2 = 3 + 1 + 1");
	printf(" = 2 + 2 + 1 = 2 + 1 + 1 + 1 = 1 + 1 +1 +1 +1");
	printf("有六种拆法\n");
	printf("类推，求 %d 有几种拆法？", NUM);

	// 初始化
	for(i = 0; i < NUM; i++){
		table[i][0] = 1;
		table[i][1] = 1;
	}

	// 动态规划
	for(i = 2; i <= NUM; i++){ 
		for(j = 2; j <= i; j++){
			if(i + j > NUM) continue;
			count = 0;
			for(k = 1 ; k <= j; k++){
				count += table[i-k][(i-k >= k) ? k : i-k];
			}
			table[i][j] = count;
		}
	}
	
	// 计算并显示结果
	for(k = 1 ; k <= NUM; k++){
		result += table[NUM-k][(NUM-k >= k) ? k : NUM-k]; 
	}
	printf("\n\n数字 %d 一共有: %d 种拆法。\n",NUM,result);
	if(DEBUG) {
		printf("\nERROR!\n"); 
		for(i = 0; i < NUM; i++){
			for(j = 0; j < NUM/2+1; j++) printf("%2d", table[i][j]);
			printf("\n");
		}
	}
	return 0;
}

运行结果