uva 1169 Robotruck（简单区间dp）

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一个二位平面上有n个垃圾，现在用一个机器人去捡起来，且是按照输入顺序捡，放回位于原点处的垃圾桶中，两点之间的距离算曼哈顿距离，机器人的最大承重量为C，求捡完所有垃圾机器人走动的最小距离。

sumdis[i], sum weight[i]都表示前缀和。

dp[i]表示第i个捡完时的最小距离。

考虑某次见掉i与j之间的所有垃圾。

dp[i] = min{dp[i], dp[j-1] + sumdis[i] - sumdis[j] + dis[j] + dis[i]} && sumweight[i] - sumweight[j - 1] <= c;

dp[n]就是最后的结果。

/*****************************************Author      :Crazy_AC(JamesQi)Time        :2016File Name   :*****************************************/// #pragma comment(linker, "/STACK:1024000000,1024000000")#include <iostream>#include <algorithm>#include <iomanip>#include <sstream>#include <string>#include <stack>#include <queue>#include <deque>#include <vector>#include <map>#include <set>#include <cstdio>#include <cstring>#include <cmath>#include <cstdlib>#include <climits>using namespace std;#define MEM(x,y) memset(x, y,sizeof x)#define pk push_back#define lson rt << 1#define rson rt << 1 | 1#define bug cout << "BUG HERE\n"typedef long long LL;typedef unsigned long long ULL;typedef pair<int,int> ii;typedef pair<ii,int> iii;const double eps = 1e-10;const int inf = 1 << 30;const int INF = 0x3f3f3f3f;const int MOD = 1e9 + 7;int nCase = 0;const int maxn = 100010;int n, c;int sumdis[maxn], sumweight[maxn];int dp[maxn];struct Node {int x, y, w;}a[maxn];int getdis(int i,int j) {return abs(a[i].x - a[j].x) + abs(a[i].y - a[j].y);}int main(){// freopen("in.txt","r",stdin);// freopen("out.txt","w",stdout);int t;scanf("%d",&t);while(t--) {scanf("%d%d",&c,&n);if (nCase) puts("");nCase++;for (int i = 1;i <= n;++i) {scanf("%d%d%d",&a[i].x,&a[i].y,&a[i].w);sumdis[i] = sumdis[i - 1] + getdis(i, i - 1);sumweight[i] = sumweight[i - 1] + a[i].w;}for (int i = 1;i <= n;++i) {dp[i] = INF;for (int j = i;j >= 1;--j) {int w = sumweight[i] - sumweight[j - 1];if (w > c) break;int dis = getdis(0, j) + sumdis[i] - sumdis[j] + getdis(0, i);dp[i] = min(dp[i], dp[j - 1] + dis);}}printf("%d\n", dp[n]);}return 0;}

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