2015
05-23

# Dynamic Programming?

Dynamic Programming, short for DP, is the favorite of iSea. It is a method for solving complex problems by breaking them down into simpler sub-problems. It is applicable to problems exhibiting the properties of overlapping sub-problems which are only slightly smaller and optimal substructure.
Ok, here is the problem. Given an array with N integers, find a continuous subsequence whose sum’s absolute value is the smallest. Very typical DP problem, right?

The first line contains a single integer T, indicating the number of test cases.
Each test case includes an integer N. Then a line with N integers Ai follows.

Technical Specification
1. 1 <= T <= 100
2. 1 <= N <= 1 000
3. -100 000 <= Ai <= 100 000

The first line contains a single integer T, indicating the number of test cases.
Each test case includes an integer N. Then a line with N integers Ai follows.

Technical Specification
1. 1 <= T <= 100
2. 1 <= N <= 1 000
3. -100 000 <= Ai <= 100 000

2
2
1 -1
4
1 2 1 -2

Case 1: 0
Case 2: 1

dp[i]=min(dp[i],abs(sum(A[j],A[i])))

#include"stdio.h"
#include"string.h"
#define N 1101

int abs(int a)
{
if(a>0)return a;
return -a;
}

int main()
{
int T;
int n;
int A[N];
int dp[N];
int i,j,t;
int ans,cnt;

scanf("%d",&T);
cnt=1;
while(T--)
{
scanf("%d",&n);
scanf("%d",&A[0]);
ans=dp[0]=abs(A[0]);
for(i=1;i<n;i++)
{
scanf("%d",&A[i]);
dp[i]=abs(A[i]);
t=A[i];
//因为要求是连续的，所以得从i-1开始
for(j=i-1;j>=0;j--)
{
t+=A[j];
if(abs(t)<dp[i])
dp[i]=abs(t);
}
if(dp[i]<ans)ans=dp[i];
}
printf("Case %d: %d\n",cnt++,ans);
}
return 0;
}