UVa348 - Optimal Array Multiplication Sequence 區間DP

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

const int maxn = 10, INF = 0x7fffffff;
int N;
int r[maxn + 5], c[maxn + 5], a[maxn + 5][maxn + 5], pre[maxn + 5], post[maxn + 5];

int dp(int i, int j) {
#if 0  //遞歸
	if (a[i][j] != INF) return a[i][j];
	for (int k = i; k < j; k++) {
		a[i][j] = min(a[i][j], dp(i, k) + dp(k + 1, j) + r[i] * c[k] * c[j]);
	}
#endif
#if 1  //遞推
	for (int d = 1; d <= N; d++) {
		for (int i = 1; i + d <= N; i++) {
			int j = i + d;
			for (int k = i; k < j; k++) {
				a[i][j] = min(a[i][j], a[i][k] + a[k + 1][j] + r[i] * c[k] * c[j]);
			}
		}
	}
#endif
	return a[i][j];
}

void getb(int i, int j) {
	if (i == j) return;
	pre[i]++; post[j]++;
	int p;
	for (int k = i; k < j; k++) {
		if (a[i][k] + a[k + 1][j] + r[i] * c[k] * c[j] == a[i][j]) {
			p = k;
			break;
		}
	}
	getb(i, p);
	getb(p + 1, j);
}

int main()
{
	int kase = 0;
	while (~scanf("%d", &N) && N) {
		for (int i = 1; i <= N; i++) {
			for (int j = 1; j <= N; j++) {
				a[i][j] = INF;
			}
		}
		for (int i = 1; i <= N; i++) {
			scanf("%d%d", &r[i], &c[i]);
			a[i][i] = 0;
		}
		dp(1, N);
		memset(pre, 0, sizeof(pre));
		memset(post, 0, sizeof(post));
		getb(1, N);
		printf("Case %d: ", ++kase);
		for (int i = 1; i <= N; i++) {
			for (int j = 1; j <= pre[i]; j++) {
				printf("(");
			}
			printf("A%d", i);
			for (int j = 1; j <= post[i]; j++) {
				printf(")");
			}
			if (i != N) printf(" x ");
		}
		puts("");
	}
	return 0;
}