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  1. #include <bits/stdc++.h>
  2. using namespace std;
  3. #define int              long long int
  4. #define double           long double
  5. #define print(a)         for(auto x : a) cout << x << " "; cout << endl
  6.  
  7.  
  8. const int M = 1000000007;
  9. const int N = 3e5+9;
  10. const int INF = 2e9+1;
  11. const int LINF = 2000000000000000001;
  12.  
  13. inline int power(int a, int b, int mod=M) {
  14.     int x = 1;
  15.     a %= mod;
  16.     while (b) {
  17.         if (b & 1) x = (x * a) % mod; 
  18.         a = (a * a) % mod;
  19.         b >>= 1;
  20.     }
  21.     return x;
  22. }
  23.  
  24.  
  25. //_ ***************************** START Below *******************************
  26.  
  27.  
  28.  
  29.  
  30. vector<int> a;
  31.  
  32. int consistency1(int n, int m, int k){
  33.  
  34. 	vector<vector<int>> dp(n+1, vector<int>(k+1, -INF));
  35. 	dp[0][0] = 0;
  36.  
  37. 	for(int i=m; i<=n; i++){
  38.  
  39. 		for(int x=1; x<=k; x++){
  40.  
  41. 			int sum = 0;
  42. 			int j = i;
  43. 			while(j>=i-m+1){
  44. 				sum += a[j-1];
  45. 				j--;
  46. 			}
  47.  
  48. 			while(j>=0){
  49. 				dp[i][x] = max(dp[i][x] , dp[j][x-1] + sum );
  50. 				j--;
  51. 			}
  52. 		}
  53. 	}
  54.  
  55. 	int maxi = -INF;
  56. 	for(int i=1; i<=n; i++){
  57. 		maxi = max(maxi, dp[i][k]);
  58. 	}
  59.  
  60. 	return maxi;
  61. }
  62.  
  63.  
  64.  
  65.  
  66. int consistency2(int n, int m, int k){
  67.  
  68. 	vector<vector<int>> dp(n+1, vector<int>(k+1, -INF));
  69. 	vector<vector<int>> pMaxi(n+1, vector<int>(k+1, 0));
  70. 	dp[0][0] = 0;
  71.  
  72. 	for(int x=1; x<=k; x++){
  73.  
  74. 		int sum = 0;
  75. 		for(int i=1, j=1; i<=n; i++){
  76. 			sum += a[i-1];
  77.  
  78. 			if(i-j == m){
  79. 				sum -= a[j-1];
  80. 				j++;
  81. 			}		
  82.  
  83. 			if(i-j+1 == m){
  84. 				dp[i][x] = pMaxi[j-1][x-1] + sum;
  85. 				pMaxi[i][x] = max(pMaxi[i-1][x], dp[i][x]);
  86. 			}
  87. 		}
  88. 	}
  89.  
  90.  
  91. 	return pMaxi[n][k];
  92. }
  93.  
  94.  
  95.  
  96.  
  97. //* Space optimized 
  98.  
  99. int consistency3(int n, int m, int k){
  100.  
  101. 	vector<int> prevPMaxi(n+1, 0);
  102. 	vector<int> curPMaxi(n+1, 0);
  103.  
  104. 	for(int x=1; x<=k; x++){
  105.  
  106. 		int sum = 0;
  107. 		for(int i=1, j=1; i<=n; i++){
  108. 			sum += a[i-1];
  109.  
  110. 			if(i-j == m){
  111. 				sum -= a[j-1];
  112. 				j++;
  113. 			}		
  114.  
  115. 			if(i-j+1 == m){
  116. 				int dp = prevPMaxi[j-1] + sum;
  117. 				curPMaxi[i] = max(curPMaxi[i-1], dp);
  118. 			}
  119. 		}
  120.  
  121. 		prevPMaxi = curPMaxi;
  122. 	}
  123.  
  124.  
  125. 	return prevPMaxi[n];
  126. }
  127.  
  128.  
  129.  
  130.  
  131. //? Approach 2 : 
  132. int consistency4(int n, int m, int k){
  133.  
  134.     vector<int> prevDp(n, 0);
  135.     vector<int> curDp(n, 0);      
  136.  
  137.     for(int x = 1; x <= k; x++){
  138.  
  139.         int sum = 0;
  140.         for(int i = 0, j = 0; i < n; i++){
  141.             sum += a[i];
  142.  
  143.             if(i - j == m){
  144.                 sum -= a[j];
  145.                 j++;
  146.             }
  147.  
  148.             if(i-1 >= 0)	curDp[i] = curDp[i-1];          
  149.  
  150.             if(i - j + 1 == m){
  151.                 if(j > 0)
  152.                     curDp[i] = max(curDp[i], prevDp[j-1] + sum);
  153.                 else
  154.                     curDp[i] = max(curDp[i], sum);
  155.             }
  156.         }
  157.  
  158.         prevDp = curDp;
  159.     }
  160.  
  161.     return prevDp[n-1];
  162. }
  163.  
  164.  
  165.  
  166.  
  167.  
  168.  
  169.  
  170.  
  171.  
  172.  
  173.  
  174. int practice(int n, int m, int k){
  175.  
  176.  
  177.     return 0;
  178. }
  179.  
  180.  
  181.  
  182.  
  183.  
  184. void solve() {
  185.  
  186.     int n, m, k;
  187.     cin>> n >> m >> k;
  188.  
  189.     a.resize(n);
  190.     for(int i=0; i<n; i++) cin >> a[i];
  191.  
  192.     // cout << consistency1(n, m, k) << " " << consistency2(n, m, k) << " " << consistency3(n, m, k) << endl;
  193.     cout << consistency4(n, m, k) << endl;
  194.  
  195.  
  196. }
  197.  
  198.  
  199.  
  200.  
  201.  
  202. int32_t main() {
  203.     ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  204.  
  205.     int t = 1;
  206.     // cin >> t;
  207.     while (t--) {
  208.         solve();
  209.     }
  210.  
  211.     return 0;
  212. }
Success #stdin #stdout 0s 5320KB
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https://ideone.com/uWZsje
language:
C++14 (gcc 8.3)
created:
3 hours ago
visibility:
public

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