UVA 348 Optimal Array Multiplication Sequence 最优矩阵链乘 dp经典

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这么久了还在dp入门这折腾orz。

题意：最优矩阵链乘，给出n个矩阵的大小，求出计算顺序，让计算量最小。

记忆化搜索，状态转移公式为 dp(begin, end) = { dp(begin, k) + dp(k + 1, end) + x[begin] * y[k] * y[end] | begin <= k <= end }

代码：

/**  Author:      illuz <iilluzen[at]gmail.com>*  Blog:        http://blog.csdn.net/hcbbt*  File:        348.cpp*  Create Date: 2013-09-26 20:01:23*  Descripton:  dp, martrix */#include <cstdio>#include <cstring>const int MAXN = 15;const int INF = 0x7fffffff;int x[MAXN], y[MAXN];int d[MAXN][MAXN], r[MAXN][MAXN];int dp(int a, int b) {if (d[a][b] != -1) return d[a][b];r[a][b] = a;if (a == b) return d[a][b] = 0;d[a][b] = INF;int t;for (int i = a; i < b; i++) {t = dp(a, i) + dp(i + 1, b) + x[a] * y[i] * y[b];if (t < d[a][b]) {d[a][b] = t;r[a][b] = i;}}return d[a][b];}void print(int a, int b) {if (a > b) return;if (a == b) printf("A%d", a + 1);else {printf("(");print(a, r[a][b]);printf(" x ");print(r[a][b] + 1, b);printf(")");}}int main() {int n, cas = 0;while (scanf("%d", &n) && n) {memset(d, -1, sizeof(d));for (int i = 0; i < n; i++)scanf("%d%d", &x[i], &y[i]);// dpdp(0, n - 1);printf("Case %d: ", ++cas);print(0, n - 1);puts("");}return 0;}