当我解决动态编程问题时,我发现了一个奇怪的问题。
// Problem 01
// A child is running up a staircase with n steps and can hop either 1 step, 2 steps, or 3 steps at a time. Implement a method to count how many possible ways the child can run up the stairs.
#include <cstdio>
#include <iostream>
#include <sstream>
#include <vector>
using namespace std;
// 1st method
// top-down dynamic programming
long steps(int n, vector<long>& d) {
if (d[n] > 0L)
return d[n];
//
if (n == 1)
return 1L;
else if (n == 2) // 1,1 2
return 2L;
else if (n == 3) // 1,1,1 1,2 2,1 3
return 4L;
//
long s = steps(n-1, d) + steps(n-2, d) + steps(n-3, d);
d[n] = s;
return s;
}
long solve(int n) {
vector<long> d;
for (int i = 0; i < n; ++i) {
d.push_back(-1L);
}
long r = steps(n, d);
return r;
}
// 2nd method
// bottom-up dynamic programming
// and remove the redundant array
long steps2(int n) {
if (n == 1)
return 1L;
else if (n == 2) // 1,1 2
return 2L;
else if (n == 3) // 1,1,1 1,2 2,1 3
return 4L;
//
long s = 0L;
long s1 = 4L;
long s2 = 2L;
long s3 = 1L;
for (int i = 4; i < n; ++i) {
s = s1 + s2 + s3;
s3 = s2;
s2 = s1;
s1 = s;
}
s = s1 + s2 + s3;
return s;
}
long solve2(int n) {
return steps2(n);
}
////////////////////// Test ////////////////////////
class Test {
public:
Test() {
basicTests();
}
private:
int num_fail = 0;
void basicTests() {
printf("C++ version: %ld\n", __cplusplus);
// customize your own tests here
printf("%d, %ld\n", 20, solve(20));
printf("%d, %ld\n", 20, solve2(20));
}
};
////////////////////// Main ////////////////////////
int main() {
Test t = Test(); // change the method you want to test here.
return 0;
}
当我运行代码时,两种方法都会给出相同的结果,看起来是正确的。
C++ version: 201103
20, 121415
20, 121415
但是当我使用调试模式, 有时 时,第一个结果似乎是错误的,就像这样。
C++ version: 201103
20, 4210418572061733749
20, 121415
有什么问题?
答案 0 :(得分:1)
在repository/component/identity
中,您使用solve
值填充向量d
,索引0 ... n-1。在步骤中,您会立即检查n
值为d[n]
的{{1}}。
你正在使用未定义的值 - 得到垃圾结果