39 lines
1.0 KiB
C++
39 lines
1.0 KiB
C++
#include <iostream>
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#include <vector>
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using namespace std;
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int main(){
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int len, n;
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cin >> len >> n;
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vector<int> a(n + 2);
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vector<vector<int>> dp(n + 2, vector<int>(n + 2, 0));
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//设置dp[i][j]为切割木棍[i, j]段 0|---1|-----2|----3|--4| 最少所需的费用 a[0] = 0 a[1] = x,,, a[n + 1] = len
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a[0] = 0; a[n + 1] = len;
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for(int i = 1; i <= n; i++){
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cin >> a[i];
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}
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//a[i]是分点
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/*这个不对
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for(int i = 0; i <= n + 1; i++){
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for(int j = i; j <= n + 1 ;j++){
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dp[i][j] = 114514;
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for(int k = i + 1; k < j; k++){
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dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + a[j] - a[i]);
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}
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if(dp[i][j] == 114514) dp[i][j] = 0;
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}
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} */
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// 区间 DP，按长度递增
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for(int l = 2; l <= n + 1; l++){ // 区间长度至少2
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for(int i = 0; i + l <= n + 1; i++){
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int j = i + l;
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dp[i][j] = INT_MAX;
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for(int k = i + 1; k < j; k++){
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dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + a[j] - a[i]);
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}
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if(dp[i][j] == INT_MAX) dp[i][j] = 0;
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}
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}
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cout << dp[0][n + 1] << endl;
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return 0;
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}
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