递归和迭代法来演示数学归纳法

wangxx · wangxx · commit 2969746737c9 · 2016-06-04T01:10:15.000+08:00
diff --git a/AK-wang/A0001/prove.c b/AK-wang/A0001/prove.c
@@ -0,0 +1,43 @@
+#include<stdio.h>
+//递归和归纳都是将复杂问题简单化的方法，只是方向不同，递归是"从一般到个别"，归纳是"从个别到一般"
+
+//用递归的思想来证明数学归纳法
+void prove1(int n)
+{
+	if(n == 0){
+		printf("step 0,the P(%d) true.\n", n);
+	}else{
+		prove1(n-1);
+		printf("step %d,if P(%d) true ,then P(%d) true also.\n", n, n - 1, n);
+    	printf("so,we can say \"P(%d) true.\"\n", n);
+
+	}
+}
+
+//用循环来表示数学归纳法
+void prove2(int n)
+{
+    int k;
+
+    printf("now we'll prove P(%d) true.\n", n);
+    k = 0;
+    printf("step 0 can prove P(%d) true.\n", k);
+    while(k < n)
+    {
+        printf("step %d can say \" if P(%d) true,then P(%d) true also\".\n", k + 1, k, k + 1);
+        k = k + 1;
+    }
+    printf("All prove over.\n");
+}
+
+int main()
+{
+    int n;
+    printf("input your number:n=");
+    scanf("%d",&n);
+    printf("\n");
+    prove1(n);
+    printf("\n");
+    prove2(n);
+    return 0;
+}
