Thursday, May 12, 2016

Lintcode: K Sum I


Related: Lintcode K Sum II
http://www.cnblogs.com/yuzhangcmu/p/4279676.html
http://www.jiuzhang.com/solutions/k-sum/
https://github.com/yuzhangcmu/LeetCode/blob/master/lintcode/dp/KSum.java
Given n distinct positive integers, integer k (k <= n) and a number target. Find k numbers where sum is target.
Calculate how many solutions there are?
    public int  kSum1(int A[], int k, int target) {
 9         if (target < 0) {
10             return 0;
11         }
12         
13         int len = A.length;
15         int[][][] D = new int[len + 1][k + 1][target + 1];
16         
17         for (int i = 0; i <= len; i++) {
18             for (int j = 0; j <= k; j++) {
19                 for (int t = 0; t <= target; t++) {
20                     if (j == 0 && t == 0) {
21                         // select 0 number from i to the target: 0
22                         D[i][j][t] = 1;
23                     } else if (!(i == 0 || j == 0 || t == 0)) {
24                         D[i][j][t] = D[i - 1][j][t];
25                         if (t - A[i - 1] >= 0) {
26                             D[i][j][t] += D[i - 1][j - 1][t - A[i - 1]];
27                         }
28                     }
29                 }
30             }
31         }
32         
33         return D[len][k][target];
34     }
我们可以把最外层的Matrix可以省去。
这里最优美的地方,在于我们把target作为外层循环,并且从右往左计算。这里的原因是:
D[i][j][t] += D[i - 1][j - 1][t - A[i - 1]];
这个表达式说明D[i][j][t]是把上一级i的结果累加过来。这里我们省去了i这一级,也就是说在D[j][t]这个表里就地累加。而且t - A[i - 1]小于t。
在以下图表示就是说D[j][t]是来自于上一行的在t左边的这些值中挑一些加起来。
所以我们就必须从右往左逐列计算来避免重复的累加。
1. 如果你从左往右按列计算,每一列会被重复地加总,就会有重复计算。我们可以想象一下,len = 0为上表,len = 1为下表。
现在我们只有一个表,就是下面这个(因为第一个维度被取消了),现在如果你从左往右计算,被sum的区域会被填掉,覆盖
len = 0 那张表留下的值,下一个值的计算就不会准确了。
2. 或者如果你逐行计算,也是不可以的。因为你也是把生成D[j][t](在图里写的是D[i][j])的被sum的区域覆盖,也会造成结果不准确。
3. 所以,只要我们逐列计算,并且顺序是从右往左,即使我们只有一个二维表,我们的被sum区域也可以保持洁净,从空间角度来想,
就相当于从len=0那张表中取值。
总结:这种思维方式可能在面试里很难遇到,不过,可以开拓我们思维,这里同样是动规时如果取得上一级的值的问题,并且它考虑了省
去一级,就地利用二维空间的值,那么就要考虑我们上一级的旧表不要被覆盖。可以在大脑中构思一个三维空间,一个三维表由多个二维
表构成,如果把它们用一个表来做,再思考一下即可。
 1 // 2 dimension
 2     public int  kSum(int A[], int k, int target) {
 4         if (target < 0) {
 5             return 0;
 6         }
 7         
 8         int len = A.length;
 9         
10         // D[i][j]: k = i, target j, the solution.
11         int[][] D = new int[k + 1][target + 1];
12         
13         // only one solution for the empty set.
14         D[0][0] = 1;
15         for (int i = 1; i <= len; i++) {
16             for (int t = target; t > 0; t--) {
17                 for (int j = 1; j <= k; j++) {
18                     if (t - A[i - 1] >= 0) {
19                         D[j][t] += D[j - 1][t - A[i - 1]];
20                     }
21                 }
22             }
23         }
24         
25         return D[k][target];
26     }

https://github.com/yuzhangcmu/LeetCode/blob/master/lintcode/dp/KSum.java
public int  kSum(int A[], int k, int target) {
    // write your code here
    if (target < 0) {
        return 0;
    }
 
    int len = A.length;
 
    // D[i][j]: k = i, target j, the solution.
    int[][] D = new int[k + 1][target + 1];
 
    // only one solution for the empty set.
    D[0][0] = 1;
    for (int i = 1; i <= len; i++) {
     
            for (int j = 1; j <= k; j++) {
                for (int t = target; t > 0; t--) {
                if (t - A[i - 1] >= 0) {
                    D[j][t] += D[j - 1][t - A[i - 1]];
                }
            }
        }
    }
 
    return D[k][target];
}

X. DFS
http://blog.csdn.net/wankunde/article/details/44058097
思路一: 迭代,开始时依次选择一个点,然后根据新的target值和新的数组,选择k-1个数,思路直接简单。但是存在重复计算。该算法复杂度为 Nk ,指数递增,所以在lintcode中就计算超时了。
public int kSum(int A[], int k, int target) { if (A.length < k || k == 0) return 0; if(k == 1){ for(int i=0;i<A.length;i++) if(A[i] == target) return 1; return 0; } else { int[] B = new int[A.length - 1]; if (A.length > 1) System.arraycopy(A, 1, B, 0, A.length - 1); return kSum(B, k - 1, target - A[0]) + kSum(B, k, target); } }
http://blog.welkinlan.com/2015/08/20/k-sum-i-ii-lintcode-java/
We can use backtracking to solve this problem, which is O(n^k). However, this is TLE    public int kSum(int A[], int k, int target) {
        // write your code here
        ArrayList<Integer> result = new  ArrayList<Integer>();
        if (A == null || A.length == 0) {
            return 0;
        }
        result.add(0);
        helper(A, k, target, result, 0, new ArrayList<Integer>());
        return result.get(0);
    }
    
    private void helper(int A[], int k, int target, ArrayList<Integer> result, int curIndex, ArrayList<Integer> curList) {
        if (curList.size() == k) {
            if (target == 0) {
                result.set(0, result.get(0) + 1);
            }
            return;
        }
        for (int i = curIndex; i < A.length; i++) {
            curList.add(A[i]);
            helper(A, k, target - A[i], result, i + 1, curList);
            curList.remove(curList.size() - 1);
        }
    }
http://codeanytime.blogspot.com/2014/12/lintcode-k-sum.html
    void helper(vector<int> A,int k, int start,int target, int & ans) {
        if (k < 0 || target < 0) return;
        if (k == 0 && target == 0) {
            ans++;
            return;
        }
        for(int i = start; i <= A.size()-k; i++)
            helper(A, k-1, i+1, target - A[i], ans);
    }
    int solutionKSum(vector<int> A,int k,int target) {
        int ans = 0;
        helper(A, k, 0, target, ans);
        return ans;
    }
另外,还有一些题目的变形,比如如果要求所有组合,满足
sum < k,
sum = k,
sum > k,
或者是 closest to k

No comments:

Post a Comment

Labels

GeeksforGeeks (1107) LeetCode (985) Algorithm (795) Review (759) to-do (631) LeetCode - Review (506) Classic Algorithm (324) Dynamic Programming (292) Classic Interview (288) Google Interview (242) Tree (145) POJ (139) Difficult Algorithm (132) LeetCode - Phone (127) EPI (125) Different Solutions (120) Bit Algorithms (118) Lintcode (113) Cracking Coding Interview (110) Smart Algorithm (109) Math (107) HackerRank (89) Binary Search (81) Binary Tree (80) Graph Algorithm (74) Greedy Algorithm (72) DFS (66) LeetCode - Extended (62) Interview Corner (61) Stack (60) List (58) Advanced Data Structure (56) Codility (54) BFS (53) ComProGuide (52) Algorithm Interview (50) Geometry Algorithm (48) Binary Search Tree (46) USACO (46) Trie (45) Mathematical Algorithm (42) ACM-ICPC (41) Interval (41) Data Structure (40) Knapsack (40) Space Optimization (40) Jobdu (39) Recursive Algorithm (39) LeetCode Hard (38) Matrix (38) String Algorithm (38) Backtracking (36) Codeforces (36) Introduction to Algorithms (36) Must Known (36) Beauty of Programming (35) Sort (35) Union-Find (34) Array (33) prismoskills (33) Segment Tree (32) Sliding Window (32) Data Structure Design (31) HDU (31) Google Code Jam (30) Permutation (30) Puzzles (30) Array O(N) (29) Company-Airbnb (29) Company-Zenefits (28) Microsoft 100 - July (28) Palindrome (28) to-do-must (28) Priority Queue (27) Random (27) Graph (26) Company - LinkedIn (25) GeeksQuiz (25) Logic Thinking (25) Pre-Sort (25) hihocoder (25) Queue (24) Company-Facebook (23) High Frequency (23) TopCoder (23) Algorithm Game (22) Hash (22) Post-Order Traverse (22) Binary Indexed Trees (21) Bisection Method (21) DFS + Review (21) Lintcode - Review (21) Brain Teaser (20) CareerCup (20) Company - Twitter (20) Merge Sort (20) Follow Up (19) O(N) (19) Time Complexity (19) Two Pointers (19) UVA (19) Ordered Stack (18) Probabilities (18) Company-Uber (17) Game Theory (17) Topological Sort (17) Codercareer (16) Heap (16) Shortest Path (16) String Search (16) Tree Traversal (16) itint5 (16) Difficult (15) Iterator (15) BST (14) Number (14) Number Theory (14) Amazon Interview (13) Basic Algorithm (13) Codechef (13) Euclidean GCD (13) KMP (13) Long Increasing Sequence(LIS) (13) Majority (13) mitbbs (13) Combination (12) Computational Geometry (12) LeetCode - Classic (12) Modify Tree (12) Reconstruct Tree (12) Reservoir Sampling (12) Reverse Thinking (12) 尺取法 (12) AOJ (11) DFS+Backtracking (11) Fast Power Algorithm (11) Graph DFS (11) LCA (11) LeetCode - DFS (11) Miscs (11) Princeton (11) Proof (11) Tree DP (11) X Sum (11) 挑战程序设计竞赛 (11) Bisection (10) Bucket Sort (10) Coin Change (10) Company - Microsoft (10) DFS+Cache (10) Facebook Hacker Cup (10) HackerRank Easy (10) O(1) Space (10) Rolling Hash (10) SPOJ (10) Theory (10) Tutorialhorizon (10) DP-Multiple Relation (9) DP-Space Optimization (9) Divide and Conquer (9) Kadane - Extended (9) Mathblog (9) Max-Min Flow (9) Prefix Sum (9) Quick Sort (9) Simulation (9) Stack Overflow (9) Stock (9) System Design (9) TreeMap (9) Use XOR (9) Book Notes (8) Bottom-Up (8) Company-Amazon (8) DFS+BFS (8) LeetCode - DP (8) Left and Right Array (8) Linked List (8) Longest Common Subsequence(LCS) (8) Prime (8) Suffix Tree (8) Tech-Queries (8) Traversal Once (8) 穷竭搜索 (8) Algorithm Problem List (7) Expression (7) Facebook Interview (7) Fibonacci Numbers (7) Game Nim (7) Graph BFS (7) HackerRank Difficult (7) Hackerearth (7) Interval Tree (7) Inversion (7) Kadane’s Algorithm (7) Level Order Traversal (7) Math-Divisible (7) Probability DP (7) Quick Select (7) Radix Sort (7) n00tc0d3r (7) 蓝桥杯 (7) Catalan Number (6) Classic Data Structure Impl (6) DFS+DP (6) DP - Tree (6) DP-Print Solution (6) Dijkstra (6) Dutch Flag (6) How To (6) Interviewstreet (6) Knapsack - MultiplePack (6) Manacher (6) Minimum Spanning Tree (6) Morris Traversal (6) Multiple Data Structures (6) One Pass (6) Programming Pearls (6) Pruning (6) Rabin-Karp (6) Randomized Algorithms (6) Sampling (6) Schedule (6) Stream (6) Suffix Array (6) Threaded (6) TreeSet (6) Xpost (6) reddit (6) AI (5) Algorithm - Brain Teaser (5) Art Of Programming-July (5) Big Data (5) Brute Force (5) Code Kata (5) Codility-lessons (5) Coding (5) Company - WMware (5) Convex Hull (5) Crazyforcode (5) Cycle (5) DP-Include vs Exclude (5) Fast Slow Pointers (5) Graph Cycle (5) Hash Strategy (5) Immutability (5) Java (5) Matrix Chain Multiplication (5) Maze (5) Microsoft Interview (5) Pre-Sum (5) Quadtrees (5) Quick Partition (5) Quora (5) SPFA(Shortest Path Faster Algorithm) (5) Subarray Sum (5) Sudoku (5) Sweep Line (5) Word Search (5) jiuzhang (5) 单调栈 (5) 树形DP (5) 1point3acres (4) Abbreviation (4) Anagram (4) Anagrams (4) Approximate Algorithm (4) Backtracking-Include vs Exclude (4) Brute Force - Enumeration (4) Chess Game (4) Consistent Hash (4) Distributed (4) Eulerian Cycle (4) Find Rule (4) Flood fill (4) Graph-Classic (4) HackerRank AI (4) Histogram (4) Kadane Max Sum (4) Knapsack - Mixed (4) Knapsack - Unbounded (4) LeetCode - Recursive (4) LeetCode - TODO (4) MST (4) MinMax (4) N Queens (4) Nerd Paradise (4) Parallel Algorithm (4) Practical Algorithm (4) Probability (4) Programcreek (4) Spell Checker (4) Stock Maximize (4) Subset Sum (4) Subsets (4) Symbol Table (4) Triangle (4) Water Jug (4) algnotes (4) fgdsb (4) to-do-2 (4) 最大化最小值 (4) A Star (3) Algorithm - How To (3) Algorithm Design (3) B Tree (3) Big Data Algorithm (3) Caterpillar Method (3) Coins (3) Company - Groupon (3) Company - Indeed (3) Cumulative Sum (3) DP-Fill by Length (3) DP-Two Variables (3) Dedup (3) Dequeue (3) Dropbox (3) Easy (3) Finite Automata (3) Github (3) GoLang (3) Graph - Bipartite (3) Include vs Exclude (3) Joseph (3) Jump Game (3) K (3) Knapsack-多重背包 (3) LeetCode - Bit (3) Linked List Merge Sort (3) LogN (3) Master Theorem (3) Min Cost Flow (3) Minesweeper (3) Missing Numbers (3) NP Hard (3) O(N) Hard (3) Online Algorithm (3) Pascal's Triangle (3) Pattern Match (3) Project Euler (3) Rectangle (3) Scala (3) SegmentFault (3) Shuffle (3) Sieve of Eratosthenes (3) Stack - Smart (3) State Machine (3) Subtree (3) Transform Tree (3) Trie + DFS (3) Two Pointers Window (3) Warshall Floyd (3) With Random Pointer (3) Word Ladder (3) bookkeeping (3) codebytes (3) Activity Selection Problem (2) Advanced Algorithm (2) AnAlgorithmADay (2) Application of Algorithm (2) Array Merge (2) BOJ (2) BT - Path Sum (2) Balanced Binary Search Tree (2) Bellman Ford (2) Binary Search - Smart (2) Binomial Coefficient (2) Bit Counting (2) Bit Mask (2) Bit-Difficult (2) Bloom Filter (2) Book Coding Interview (2) Branch and Bound Method (2) Clock (2) Codesays (2) Company - Baidu (2) Company-Snapchat (2) Complete Binary Tree (2) DFS+BFS, Flood Fill (2) DP - DFS (2) DP-3D Table (2) DP-Classical (2) DP-Output Solution (2) DP-Slide Window Gap (2) DP-i-k-j (2) DP-树形 (2) Distributed Algorithms (2) Divide and Conqure (2) Doubly Linked List (2) Edit Distance (2) Factor (2) Forward && Backward Scan (2) GoHired (2) Graham Scan (2) Graph BFS+DFS (2) Graph Coloring (2) Graph-Cut Vertices (2) Hamiltonian Cycle (2) Huffman Tree (2) In-order Traverse (2) Include or Exclude Last Element (2) Information Retrieval (2) Interview - Linkedin (2) Invariant (2) Islands (2) Linked Interview (2) Linked List Sort (2) Longest SubArray (2) Lucene-Solr (2) Math-Remainder Queue (2) Matrix Power (2) Median (2) Minimum Vertex Cover (2) Negative All Values (2) Number Each Digit (2) Numerical Method (2) Object Design (2) Order Statistic Tree (2) Parent-Only Tree (2) Parentheses (2) Parser (2) Peak (2) Programming (2) Range Minimum Query (2) Regular Expression (2) Return Multiple Values (2) Reuse Forward Backward (2) Robot (2) Rosettacode (2) Scan from right (2) Search (2) SimHash (2) Simple Algorithm (2) Skyline (2) Spatial Index (2) Strongly Connected Components (2) Summary (2) TV (2) Tile (2) Traversal From End (2) Tree Sum (2) Tree Traversal Return Multiple Values (2) Word Break (2) Word Graph (2) Word Trie (2) Yahoo Interview (2) Young Tableau (2) 剑指Offer (2) 数位DP (2) 1-X (1) 51Nod (1) Akka (1) Algorithm - New (1) Algorithm Series (1) Algorithms Part I (1) Analysis of Algorithm (1) Array-Element Index Negative (1) Array-Rearrange (1) Augmented BST (1) Auxiliary Array (1) Auxiliary Array: Inc&Dec (1) BACK (1) BK-Tree (1) BZOJ (1) Basic (1) Bayes (1) Beauty of Math (1) Big Integer (1) Big Number (1) Binary (1) Binary Sarch Tree (1) Binary String (1) Binary Tree Variant (1) Bipartite (1) Bit-Missing Number (1) BitMap (1) BitMap index (1) BitSet (1) Bug Free Code (1) BuildIt (1) C/C++ (1) CC Interview (1) Cache (1) Calculate Height at Same Recusrion (1) Cartesian tree (1) Check Tree Property (1) Chinese (1) Circular Buffer (1) Cloest (1) Clone (1) Code Quality (1) Codesolutiony (1) Company - Alibaba (1) Company - Palantir (1) Company - WalmartLabs (1) Company-Apple (1) Company-Epic (1) Company-Salesforce (1) Company-Yelp (1) Compression Algorithm (1) Concurrency (1) Cont Improvement (1) Convert BST to DLL (1) Convert DLL to BST (1) Custom Sort (1) Cyclic Replacement (1) DFS-Matrix (1) DP - Probability (1) DP Fill Diagonal First (1) DP-Difficult (1) DP-End with 0 or 1 (1) DP-Fill Diagonal First (1) DP-Graph (1) DP-Left and Right Array (1) DP-MaxMin (1) DP-Memoization (1) DP-Node All Possibilities (1) DP-Optimization (1) DP-Preserve Previous Value (1) DP-Print All Solution (1) Database (1) Detect Negative Cycle (1) Diagonal (1) Directed Graph (1) Do Two Things at Same Recusrion (1) Domino (1) Dr Dobb's (1) Duplicate (1) Equal probability (1) External Sort (1) FST (1) Failure Function (1) Fraction (1) Front End Pointers (1) Funny (1) Fuzzy String Search (1) Game (1) Generating Function (1) Generation (1) Genetic algorithm (1) GeoHash (1) Geometry - Orientation (1) Google APAC (1) Graph But No Graph (1) Graph Transpose (1) Graph Traversal (1) Graph-Coloring (1) Graph-Longest Path (1) Gray Code (1) HOJ (1) Hanoi (1) Hard Algorithm (1) How Hash (1) How to Test (1) Improve It (1) In Place (1) Inorder-Reverse Inorder Traverse Simultaneously (1) Interpolation search (1) Interview (1) Interview - Facebook (1) Isomorphic (1) JDK8 (1) K Dimensional Tree (1) Knapsack - Fractional (1) Knapsack - ZeroOnePack (1) Knight (1) Knuth Shuffle (1) Kosaraju’s algorithm (1) Kruskal (1) Kth Element (1) Least Common Ancestor (1) LeetCode - Binary Tree (1) LeetCode - Coding (1) LeetCode - Detail (1) LeetCode - Related (1) Linked List Reverse (1) Linkedin (1) Linkedin Interview (1) Local MinMax (1) Logic Pattern (1) Longest Common Subsequence (1) Longest Common Substring (1) Longest Prefix Suffix(LPS) (1) Machine Learning (1) Maintain State (1) Manhattan Distance (1) Map && Reverse Map (1) Math - Induction (1) Math-Multiply (1) Math-Sum Of Digits (1) Matrix - O(N+M) (1) Matrix BFS (1) Matrix Graph (1) Matrix Search (1) Matrix+DP (1) Matrix-Rotate (1) Max Min So Far (1) Memory-Efficient (1) MinHash (1) MinMax Heap (1) Monotone Queue (1) Monto Carlo (1) Multi-End BFS (1) Multi-Reverse (1) Multiple DFS (1) Multiple Tasks (1) Next Element (1) Next Successor (1) Offline Algorithm (1) PAT (1) Parenthesis (1) Partition (1) Path Finding (1) Patience Sort (1) Persistent (1) Pigeon Hole Principle (1) Power Set (1) Pratical Algorithm (1) PreProcess (1) Probabilistic Data Structure (1) Python (1) Queue & Stack (1) RSA (1) Ranking (1) Rddles (1) ReHash (1) Realtime (1) Recurrence Relation (1) Recursive DFS (1) Recursive to Iterative (1) Red-Black Tree (1) Region (1) Resources (1) Reverse Inorder Traversal (1) Robin (1) Selection (1) Self Balancing BST (1) Similarity (1) Sort && Binary Search (1) Square (1) Streaming Algorithm (1) String Algorithm. Symbol Table (1) String DP (1) String Distance (1) SubMatrix (1) Subsequence (1) System of Difference Constraints(差分约束系统) (1) TSP (1) Ternary Search Tree (1) Test (1) Test Cases (1) Thread (1) TimSort (1) Top-Down (1) Tournament (1) Tournament Tree (1) Transform Tree in Place (1) Tree Diameter (1) Tree Rotate (1) Tree Without Tree Predefined (1) Trie and Heap (1) Trie vs Hash (1) Trie vs HashMap (1) Triplet (1) Two Data Structures (1) Two Stacks (1) USACO - Classical (1) USACO - Problems (1) UyHiP (1) Valid Tree (1) Vector (1) Virtual Matrix (1) Wiggle Sort (1) Wikipedia (1) ZOJ (1) ZigZag (1) baozitraining (1) codevs (1) cos126 (1) javabeat (1) jum (1) namic Programming (1) sqrt(N) (1) 两次dijkstra (1) 九度 (1) 二进制枚举 (1) 夹逼法 (1) 归一化 (1) 折半枚举 (1) 枚举 (1) 状态压缩DP (1) 男人八题 (1) 英雄会 (1) 逆向思维 (1)

Popular Posts