I found a weird problem when I was solving a dynamic programming problem.
Code
// 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;
}
Results
When I run the code, both methods give the same results, seem correct.
C++ version: 201103
20, 121415
20, 121415
But when I using debug mode, sometimes the first result seems wrong, like this.
C++ version: 201103
20, 4210418572061733749
20, 121415
What's the problem?
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