【BZOJ1742】[Usaco2005 nov]Grazing on the Run 边跑边吃草【区间DP】

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【题目链接】

算是比较经典的区间DP，比较重要的思路是，把未来的花费放到现在计算。

一开始写了个空间O(n^2)的记忆化搜索，结果被卡内存了，最后换成循环了...

/* Forgive me Not */#include <cstdio>#include <cstring>#include <algorithm>using namespace std;const int maxn = 3001, inf = 0x3f3f3f3f;int n, s, pos[maxn], dp[maxn][2][2];inline int iread() {int f = 1, x = 0; char ch = getchar();for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';return f * x;}int main() {n = iread(); s = iread();for(int i = 1; i <= n; i++) pos[i] = iread();pos[++n] = s;sort(pos + 1, pos + 1 + n);s = lower_bound(pos + 1, pos + 1 + n, s) - pos;for(int i = 1; i <= n; i++) dp[i][1][0] = dp[i][1][1] = inf;dp[s][1][0] = dp[s][1][1] = 0;for(int i = 2; i <= n; i++) for(int l = 1; l <= n - i + 1; l++) {int r = l + i - 1;dp[l][i & 1][1] = min(dp[l + 1][~i & 1][1] + (n - i + 1) * (pos[l + 1] - pos[l]), dp[l + 1][~i & 1][0] + (n - i + 1) * (pos[r] - pos[l]));dp[l][i & 1][0] = min(dp[l][~i & 1][0] + (n - i + 1) * (pos[r] - pos[r - 1]), dp[l][~i & 1][1] + (n - i + 1) * (pos[r] - pos[l]));}printf("%d\n", min(dp[1][n & 1][0], dp[1][n & 1][1]));return 0;}

记忆化搜索：

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;const int maxn = 3001, inf = 0x3f3f3f3f;int n, s, pos[maxn], dp[maxn][maxn][2];inline int iread() {int f = 1, x = 0; char ch = getchar();for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';return f * x;}inline int iabs(int x) {return x < 0 ? -x : x;}inline int dfs(int l, int r, bool left) {if(l == r) return l == s ? 0 : inf;if(~dp[l][r][left]) return dp[l][r][left];int res = 0;if(left) res = min(dfs(l + 1, r, 1) + (n - r + l) * iabs(pos[l + 1] - pos[l]), dfs(l + 1, r, 0) + (n - r + l) * iabs(pos[r] - pos[l]));else res = min(dfs(l, r - 1, 0) + (n - r + l) * iabs(pos[r] - pos[r - 1]), dfs(l, r - 1, 1) + (n - r + l) * iabs(pos[r] - pos[l]));return dp[l][r][left] = res;}int main() {n = iread(); s = iread();for(int i = 1; i <= n; i++) pos[i] = iread();pos[++n] = s;sort(pos + 1, pos + 1 + n);s = lower_bound(pos + 1, pos + 1 + n, s) - pos;memset(dp, -1, sizeof(dp));printf("%d\n", min(dfs(1, n, 0), dfs(1, n, 1)));return 0;}

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