Coins in a Line

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题目来源： http://leetcode.com/2011/02/coins-in-line.html

二维DP。代码如下：

#include <iostream>#include <vector>#include <cassert>using namespace std;const int MAX_N = 100; void printMoves(int P[][MAX_N], int A[], int N) {  int sum1 = 0, sum2 = 0;  int m = 0, n = N-1;  bool myTurn = true;  while (m <= n) {    int P1 = P[m+1][n]; // If take A[m], opponent can get...    int P2 = P[m][n-1]; // If take A[n]    cout << (myTurn ? "I" : "You") << " take coin no. ";    if (P1 <= P2) {      cout << m+1 << " (" << A[m] << ")";      m++;    } else {      cout << n+1 << " (" << A[n] << ")";      n--;    }    cout << (myTurn ? ", " : ".\n");    myTurn = !myTurn;  }  cout << "\nThe total amount of money (maximum) I get is " << P[0][N-1] << ".\n";}int maxMoney(int A[], int N) {  int P[MAX_N][MAX_N] = {0};  int a, b, c;  for (int i = 0; i < N; i++) {    for (int m = 0, n = i; n < N; m++, n++) {      assert(m < N); assert(n < N);      a = ((m+2 <= N-1)             ? P[m+2][n] : 0);      b = ((m+1 <= N-1 && n-1 >= 0) ? P[m+1][n-1] : 0);      c = ((n-2 >= 0)               ? P[m][n-2] : 0);      P[m][n] = max(A[m] + min(a,b),                    A[n] + min(b,c));    }  }  printMoves(P, A, N);  return P[0][N-1];}int maxMoney2(int A[], int n){int P[MAX_N][MAX_N] = {0};for(int i=0; i<n; i++)P[i][i] = A[i];for(int len=2; len<=n; len++){for(int i=0; i+len<=n; i++){int j = i+len-1;if(len == 2){P[i][j] = max(A[i], A[j]);}else{int a1 = A[i] + min(P[i+2][j], P[i+1][j-1]);int a2 = A[j] + min(P[i+1][j-1], P[i][j-2]);P[i][j] = max(a1, a2);}}}printMoves(P, A, n);return P[0][n-1];}int main(){int A[] = { 3, 2, 2, 3, 1, 2 };int res1 = maxMoney(A, 6);int res2 = maxMoney2(A, 6);cout << res1 << " " << res2 << endl;return 0;}

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